UNIT 4 WORK, WELLBEING, AND SCARCITY INTRODUCTION • Time is scarce and people value both free time and what they can buy with their earnings from the time they spend at work. • We can model these situations. First, we can define all the feasible actions that are available to the decision-maker, such as working shorter or longer hours and buying fewer or more goods. Second, we can describe which actions the decision-maker prefers. • There are unavoidable trade-offs in the presence of scarcity—satisfying one objective, such as having more free time, means satisfying other objectives less, such as having more possessions. • This model helps to explain differences in the hours that people work in different countries, and the changes in our hours of work throughout history. • We introduce conspicuous consumption effects to explain both why people work longer hours in countries where the very rich receive a larger fraction of the income and why, as a nation gets richer, its citizens may not become happier. • Measures of wellbeing such as GDP per capita focus narrowly on goods and services; we look at other measures. The hockey stick charts in Unit 1 illustrated the dramatic increases in goods and services consumed in countries that have experienced the capitalist revolution. This prompts the question of whether people have used eco- nomic progress as a way, not only to consume more goods, but also to enjoy more free time. The answer is both, but in different proportions in different countries. During the year 1600, the average British worker was at work for 266 days, meaning roughly two days off a week. This statistic did not change much until the Industrial Revolution of the eighteenth century, when wages began to rise, and working time rose too—to 318 days in 1870. The number of days off work had been cut by half! 157
Transcript
UNIT 4
WORK, WELLBEING, ANDSCARCITY
INTRODUCTION
• Time is scarce and people value both free time and what they can buywith their earnings from the time they spend at work.
• We can model these situations. First, we can define all the feasibleactions that are available to the decision-maker, such as working shorteror longer hours and buying fewer or more goods. Second, we candescribe which actions the decision-maker prefers.
• There are unavoidable trade-offs in the presence of scarcity—satisfyingone objective, such as having more free time, means satisfying otherobjectives less, such as having more possessions.
• This model helps to explain differences in the hours that people work indifferent countries, and the changes in our hours of work throughouthistory.
• We introduce conspicuous consumption effects to explain both whypeople work longer hours in countries where the very rich receive alarger fraction of the income and why, as a nation gets richer, its citizensmay not become happier.
• Measures of wellbeing such as GDP per capita focus narrowly on goodsand services; we look at other measures.
The hockey stick charts in Unit 1 illustrated the dramatic increases in goodsand services consumed in countries that have experienced the capitalistrevolution. This prompts the question of whether people have used eco-nomic progress as a way, not only to consume more goods, but also to enjoymore free time. The answer is both, but in different proportions in differentcountries.
During the year 1600, the average British worker was at work for 266days, meaning roughly two days off a week. This statistic did not changemuch until the Industrial Revolution of the eighteenth century, when wagesbegan to rise, and working time rose too—to 318 days in 1870. The numberof days off work had been cut by half!
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In 1930, John Maynard Keynes, a British economist, predicted a futureof free time in abundance, even warning of an embarrassment of riches inleisure. He published an essay entitled ‘Economic Possibilities for ourGrandchildren’, in which he suggested that, in the 100 years that wouldfollow, technological improvements would make us, on average, about eighttimes better off.
What he called ‘the economic problem, the struggle for subsistence’would be solved, and we would not have to work more than, say, 15 hoursper week to satisfy our economic needs. The question he raised was, ‘Howwould we cope with all the additional leisure time?’.
Keynes’ prediction for the rate of technological progress in countries suchas the UK and the US has been approximately right, and working hours haveindeed fallen, although much less than he expected. It seems extremelyunlikely that average working hours will be 15 hours per week by 2030.
In the US in the nineteenth century, hours of work initially increased formany workers who shifted from farming to industrial jobs. In 1865, the USabolished slavery, and former slaves used their freedom to work much less.From the late nineteenth century until the middle of the twentieth century,working time gradually fell. Figure 4.1 shows how annual working hourshave fallen since 1900 in many countries.
EXERCISE 4.1 WORKING HOURS ACROSS COUNTRIES AND TIMEUse Figure 4.1 to answer these questions.
1. Looking at both Panel A and B, describe what happened to workinghours over the period 1900–2000.
2. Compare working hours in the countries in Panel A with those in PanelB, and describe any differences you see.
3. What possible explanations can you suggest for why the decline inworking hours was greater in some countries than in others?
4. Why do you think that the decline in working hours is faster in mostcountries in the first half of the century compared to the second half?
5. In recent years, is there any country in which working hours haveincreased? Why do you think this happened?
If you want to compare workinghours in 1870 to those in themodern world, Michael Hubermanand Chris Minns calculate them intheir paper, ‘The Times They AreNot Changin’: Days and Hours ofWork in Old and New Worlds,1870–2000’ (http://tinyco.re/2758271). Explorations in Eco-nomic History 44 (4): pp. 538–67.
John Maynard Keynes. 1963. ‘Eco-nomic Possibilities for ourGrandchildren’ (http://tinyco.re/8213530). In Essays in Persuasion.New York, NY: W. W. Norton & Co.
An article by Tim Harford(http://tinyco.re/5829245) in the‘Undercover Economist’ column ofthe Financial Times examines whyKeynes’ prediction was wrong.
Figure 4.1 Annual hours of work (1900–2000).
Michael Huberman and Chris Minns.2007. ‘The Times they are not Changin’:Days and Hours of Work in Old and NewWorlds, 1870–2000’ (http://tinyco.re/2758271). Explorations in EconomicHistory 44 (4): pp. 538–567.
Figure 4.2 Annual hours of work and income (1870–2000).
Maddison Project. 2013. 2013 Edition.(http://tinyco.re/2251229) MichaelHuberman and Chris Minns. 2007. ‘TheTimes they are not Changin’: Days andHours of Work in Old and New Worlds,1870–2000’ (http://tinyco.re/2758271).Explorations in Economic History 44 (4):pp. 538–567. GDP is measured at PPP in1990 international Geary–Khamisdollars.
Think how you would respond if your employer offered you a six-foldincrease in your wage and the ability to choose your hours of work. At oneextreme, you could vastly increase your free time, shrinking your workingweek to a single day and keeping your consumption unchanged; at theother extreme, you could keep working unchanged hours and enjoy a six-fold increase in earnings.
Hourly earnings increased more than six-fold over the twentiethcentury for Americans, and their average annual work time fell by a littlemore than one-third. People at the end of the twentieth century enjoyeda four-fold increase in annual earnings with which they could buy goodsand services, but a much smaller increase of slightly less than one-fifth intheir free time. (The percentage increase in free time would be higher ifyou did not count time spent asleep as free time, but it is still smallrelative to the increase in earnings.)
Figure 4.2 shows trends in income and working hours since 1870 in theNetherlands, the US and France.
As in Unit 1, income is measured as GDP per capita in US dollars. This isnot the same as average earnings, but gives us a useful indication of averageincome for the purposes of comparison across countries and through time.In the late nineteenth and early twentieth centuries, average incomeapproximately tripled, and hours of work fell substantially.
During the rest of the twentieth century, income per head rose four-fold.Hours of work continued to fall in the Netherlands and France (albeit moreslowly) but levelled off in the US, where there has been little change since1960. At the end of this unit, we return to these cross-country differences.
While many countries have experienced similar trends, there are still dif-ferences in outcomes. Figure 4.3 illustrates the wide disparities in freetime and income between countries in 2013. Here, we have calculatedfree time by subtracting average annual working hours from the numberof hours in a year. You can see that the higher-income countries seem tohave lower working hours and more free time, but there are also somestriking differences between them. For example, the Netherlands and theUS have similar levels of income, but Dutch workers have much morefree time. And the US and Turkey have similar amounts of free time, buta large difference in income.
An article gives more historicaldetail on the hours that peopleworked in the US: Robert Whaples.2001. ‘Hours of Work in U.S.History’ (http://tinyco.re/1660378)EH.net Encyclopedia.
Figure 4.3 Annual hours of free time per worker and income (2013).
OECD. Average annual hours actuallyworked per worker (http://tinyco.re/6892498). OECD. Level of GDP per capitaand productivity (http://tinyco.re/1840501). Accessed June 2016. Data forSouth Korea refers to 2012.
In many countries, there has been a huge increase in living standards since1870. But in some places, people have carried on working just as manyhours as before but consumed more, while in other countries, people nowhave much more free time. Why has this happened? We will provide someanswers to this question by studying a basic problem of economics—scarcity—and how we make choices when we cannot have everything thatwe want, such as goods and free time.
Study our model of decision making carefully! It will be used repeatedlythroughout the course, because it gives us an insight into a wide range ofeconomic problems.
QUESTION 4.1 CHOOSE THE CORRECT ANSWER(S)CHOOSE THE CORRECT ANSWER(S)Based on Figure 4.2, which of the following state-ments are true?
An increase in GDP per capita causes a reductionin the number of hours worked.The GDP per capita in the Netherlands is lowerthan that in the US because the Dutch work fewerhours.
Between 1870 and 2000, the French havemanaged to increase their GDP per capita morethan ten-fold, while more than halving the numberof hours worked.On the basis of the evidence in the graph, theFrench will one day be able to produce a GDP percapita of over $30,000 with less than 1,000 hoursof work.
QUESTION 4.2 CHOOSE THE CORRECT ANSWER(S)CHOOSE THE CORRECT ANSWER(S)Based on Figure 4.3, which of the following state-ments are true?
The plot gives strong evidence that workerschoose to enjoy more free time as their livingstandards rise.Workers in the US and Turkey enjoy a similaramount of free time despite the huge disparity ofincome.
If German workers worked as many hours as theNorwegians, they will be able to produce a similarlevel of output per capita.Japanese workers require more hours of work toproduce the same level of output per capita asKorean workers.
ceteris paribus Economists oftensimplify analysis by setting asidethings that are thought to be of lessimportance to the question ofinterest. The literal meaning of theexpression is ‘other things equal’. Inan economic model it means ananalysis ‘holds other things con-stant’.
incentive Economic reward orpunishment, which influences thebenefits and costs of alternativecourses of action.
relative price The price of onegood or service compared toanother (usually expressed as aratio).
4.1 BASIC CONCEPTS: PRICES, COSTS, ANDINCENTIVESIn this unit, we are going to build an economic model to help explain thetrends in free time as incomes rose historically, and the variation acrosscountries in these aspects of wellbeing. We highlight three key ideas of eco-nomic modelling:
• We see more by looking at less: A concept called ceteris paribus and othersimplifications help us focus on the variables of interest.
• Incentives matter: Incentives affect the benefits and costs of taking oneaction as opposed to another.
• We use relative prices: Using relative prices helps us comparealternatives.
Part of the process of learning to do economics involves learning a newlanguage. The terms listed above will recur frequently in the units thatfollow, and it is important to learn how to use them precisely and withconfidence.
Seeing more by looking at lessAs is common in scientific inquiry, economists often simplify an analysis bysetting aside things that are thought to be of less importance to the questionof interest, by using the phrase ‘holding other things constant’ or, moreoften, the Latin expression ceteris paribus, meaning ‘other things equal’. Forexample, later in the course we simplify an analysis of what people wouldchoose to buy by looking at the effect of changing a price—ignoring otherinfluences on our behaviour like brand loyalty, or what others would thinkof our choices. We ask, ‘What would happen if the price changed, buteverything else that might influence the decision was the same?’. Theseceteris paribus assumptions, when used well, can clarify the picture withoutdistorting the key facts.
In scientific experiments and in the experiments conducted by eco-nomists that we have considered in previous units, the experimental designholds many things constant in order to uncover the effect of X on Y. Theceteris paribus assumption refers to holding things constant in thoughtexperiments.
Incentives matterWhy did the water in Fisher’s hydraulic economy machine in Figure3.17 (page 151) (Unit 3) move when he changed the quantity of ‘supply’ or‘demand’ for one or more of the goods, so that the prices were no longer inequilibrium?
• Gravity acts on the water so it finds the lowest level.• Channels allow the water to seek out the lowest level, but restrict the
ways in which it can flow.
All economic models have something equivalent to gravity, and adescription of the kinds of movements that are possible. The equivalentof gravity is the assumption that, by taking one course of action overanother, people are attempting to do as well as they can (according tosome standard).
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The analogy to the free movement of water in Fisher’s machine is thatpeople are free to select different courses of action, rather than simplybeing told what to do. This is where economic incentives affect thechoices we make. But not every channel is open to us: we can’t doeverything we want to do.
Like many economic models, the one we use to explain the trade-offbetween free time and work is based on the idea that people respond toeconomic incentives. As we have seen in Units 2 and 3, people aremotivated not only by the desire for material gain but also by love, hate,sense of duty, and desire for approval. But material comfort is an importantmotive, and economic incentives appeal to this motive.
When owners or managers of firms decide how many workers to hire,or when shoppers decide what and how much to buy, prices are going to bean important factor determining their decision. If prices are a lot lower inthe discount supermarket than in the corner shop, and it is not too far away,then this will be a good argument for buying our food in the supermarketrather than the corner shop.
Relative pricesA third characteristic of many economic models is that we are ofteninterested in ratios of things, rather than their absolute level. Economicsfocuses attention on alternatives and choices. If you are deciding where toshop, it is not the corner shop prices alone that matter, but rather theprices relative to those in the supermarket and relative to the costs ofreaching the supermarket. If all of these were to rise by 5%, your decisionprobably wouldn’t change.
Relative prices are simply the price of one option relative to another. Weoften express relative price as the ratio of two prices. We will see that theymatter a lot in explaining not just what shoppers (or consumers, as we usuallycall them) decide to buy, but why firms make the choices that they do.
4.2 MAKING DECISIONS WHEN THERE ARE TRADE-OFFSAs a student, you choose how many hours to spend studying every day.There may be many factors influencing your choice—how much youenjoy studying, how difficult you find it, how much studying your friendsdo, and so on. Perhaps part of the motivation to devote time to studyingcomes from your belief that, the more time you spend studying, thehigher the grade you will obtain at the end of the course. In this unit, wewill construct a simple model of a student’s choice of how many hours towork, based on the assumption that the more time spent working, thebetter the final grade will be.
We assume a positive relationship between hours worked and finalgrade, but is there any evidence to back this up? A group of educationalpsychologists looked at the study behaviour of 84 students at Florida StateUniversity to identify the factors that affected their performance.
At first sight, there seems to be only a weak relationship between theaverage number of hours per week the students spent studying and theirGrade Point Average (GPA) at the end of the semester. This is in Figure 4.4.
The 84 students have been split into two groups of 42 students each,according to their hours of study. The average GPA for those with highstudy time is 3.43—only slightly more than the GPA of those with lowstudy time.
Elizabeth Ashby Plant, Karl AndersEricsson, Len Hill, and Kia Asberg.2005. ‘Why study time does notpredict grade point average acrosscollege students: Implications ofdeliberate practice for academicperformance’ (http://tinyco.re/7875663). ContemporaryEducational Psychology 30 (1): pp.96–116.
EXERCISE 4.2 CETERIS PARIBUSASSUMPTIONSYou have been asked to conduct aresearch study at your university,similar to the one done at FloridaState University.1. What factors do you think
should be held constant in amodel of the relationshipbetween study hours and finalgrade?
2. What other information aboutthe students, in addition tostudy environment, would youwant to collect?
Using the ceteris paribus assumptionLooking more closely, we discover this study is an interesting illustration ofwhy we should be careful when we make ceteris paribus assumptions. Withineach group of 42 students, there are many potentially important differ-ences. The conditions in which they study would be an obvious differenceto consider—an hour working in a busy, noisy room may not be as useful asan hour spent in the library.
In Figure 4.5, we see that students studying in poor environments aremore likely to study longer hours. Of these 42 students, 31 of them havehigh study time, compared with only 11 of the students with good environ-ments. Perhaps they are distracted by other people around them, so it takesthem longer to complete their assignments than those students who workin the library.
Now look at the average GPAs in the top row—if the environment isgood, students who study longer do better. You can see in the bottom rowthat high study time pays off for those who work in poor environments too.This relationship was not as clear when we didn’t consider the effect of thestudy environment.
After considering environment and other relevant factors (including thestudents’ past GPAs and the hours they spent in paid work or partying), thepsychologists estimated that an additional hour of study time per weekraised a student’s GPA at the end of the semester by 0.24 points on average.If we take two students who are the same in all respects except for studytime, we predict that the one who studies for longer will have a GPA that is0.24 points higher for each extra hour—in other words, study time raisesGPA by 0.24 per hour, ceteris paribus.
QUESTION 4.3 CHOOSE THE CORRECT ANSWER(S)CHOOSE THE CORRECT ANSWER(S)Based on Figure 4.5, which of the following statements are true?
More students choose to spend a longer time studying in a badenvironment than in a good environment.High study time is associated with a better grade.All students who spend a longer time studying attain a higher gradeon average than those who study fewer hours.The amount of time spent studying is important, while the environ-ment has no effect on the results.
High study time (42 students) Low study time (42 students)
Average GPA 3.43 3.36
Figure 4.4 Study time and grades.
Plant et al. 2005. ‘Why study time doesnot predict grade point average acrosscollege students.’ pp. 96–116. Additionalcalculations were conducted by AshbyPlant, Florida State University, in June2015.
High study time Low study time
Good environment 3.63 (11 students) 3.43 (31 students)
Figure 4.5 Average GPA in good and poor study environments.
Plant et al. ‘Why study time does notpredict grade point average acrosscollege students’, ibid.
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production function A graphical ormathematical expressiondescribing the amount of outputthat can be produced by any givenamount or combination of input(s).The function describes differingtechnologies capable of producingthe same thing.
marginal product The additionalamount of output that is producedif a particular input was increasedby one unit, while holding all otherinputs constant.
diminishing marginal product Aproperty of some production func-tions according to which eachadditional unit of input results in asmaller increment in total outputthan did the previous unit.
Introducing the production functionNow imagine Alexei is a student who can vary the number of hours hespends studying. We will assume that, as in the Florida State Universitystudy, the hours he spends studying over the semester will increase thepercentage grade that he will receive at the end, ceteris paribus. This rela-tionship between study time and final grade is represented in the table inFigure 4.6. In this model, study time refers to all the time that Alexei spendslearning, whether in class or individually, measured per day (not per week,as for the Florida students). The table shows how his grade will vary if hechanges his study hours, if all other factors—his social life, for example—are held constant.
This is Alexei’s production function. In general, a production functiontells us how much of a good or service is produced, given the inputs into theproduction process. In Alexei’s case, it translates the number of hours perday spent studying (his input of labour) into a percentage grade (his output).In reality, the final grade might also be affected by unpredictable events (ineveryday life, we normally lump the effect of these things together and callit ‘luck’). You can think of the production function as telling us what Alexeiwill get under normal conditions, if he is neither lucky nor unlucky.
If we plot this relationship on a graph, we get the curve in Figure 4.6.Alexei can achieve a higher grade by studying more, so the curve slopesupward. At 15 hours of work per day he gets the highest grade he is capableof, which is 90%. Any further time spent studying does not affect his examresult (he will be so tired that studying more each day will not achieveanything), and the curve becomes flat.
Alexei’s marginal product is the increase in his grade from increasingstudy time by one hour. Follow the steps in Figure 4.6 to see how tocalculate the marginal product.
At each point on the production function, the marginal product is theincrease in the grade from studying one more hour. The marginal productcorresponds to the slope of the production function.
The concept of diminishing returnsAlexei’s production function in Figure 4.6 gets flatter the more hours hestudies, so the marginal product of an additional hour falls as we movealong the curve. The marginal product is diminishing. The modelcaptures the idea that an extra hour of study helps a lot if you are notstudying much, but if you are already studying a lot, then studying evenmore does not help very much.
Notice that, if Alexei was already studying for 15 hours a day, the mar-ginal product of an additional hour would be zero. Studying more wouldnot improve his grade. As you might know from experience, a lack of eithersleep or time to relax could even lower Alexei’s grade if he worked morethan 15 hours a day. If this were the case, then his production functionwould start to slope downward, and Alexei’s marginal product wouldbecome negative.
Marginal change is an important and common concept in economics.You will often see it marked as a slope on a diagram. With a productionfunction like the one in Figure 4.6, the slope changes continuously as wemove along the curve. We have said that when Alexei studies for 4 hours aday the marginal product is 7, the increase in the grade from one more hourof study. Because the slope of the curve changes between 4 and 5 hours onthe horizontal axis, this is only an approximation of the actual marginal
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product. More precisely, the marginal product is the rate at which the gradeincreases, per hour of additional study. In Figure 4.6, the true marginalproduct is the slope of the line that just touches the curve at 4 hours. In thisunit, we will use approximations so that we can work in whole numbers,but you may notice that sometimes these numbers are not quite the same asthe slopes.
Study hours 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 or more
Figure 4.6 How does the amount of time spent studying affect Alexei’s grade?
1. Alexei’s production functionThe curve is Alexei’s production func-tion. It shows how an input of studyhours produces an output, the examgrade.
2. Four hours of study per dayIf Alexei studies for 4 hours, his gradewill be 50.
3. Ten hours of study per dayIf he studies for 10 hours, he willachieve a grade of 81.
4. Alexei’s maximum gradeAt 15 hours of study per day, Alexeiachieves his maximum possible grade,90. After that, further hours will makeno difference to his result—the curve isflat.
5. Increasing study time from 4 to 5hoursIncreasing study time from 4 to 5 hoursraises Alexei’s grade from 50 to 57.Therefore, at 4 hours of study, the mar-ginal product of an additional hour is 7.
6. Increasing study time from 10 to 11hoursIncreasing study time from 10 to 11hours raises Alexei’s grade from 81 to84. At 10 hours of study, the marginalproduct of an additional hour is 3. Aswe move along the curve, the slope ofthe curve falls, so the marginal productof an extra hour falls. The marginalproduct is diminishing.
7. The marginal productThe marginal product is the slope ofthe line that just touches but does notcross the production function. The mar-ginal product at four hours of study isapproximately 7, which is the increasein the grade from one more hour ofstudy. More precisely, the marginalproduct is the slope of the line at thatpoint, which is slightly higher than 7.
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preferences A description of thebenefit or cost we associate witheach possible outcome.
utility A numerical indicator of thevalue that one places on an out-come, such that higher valuedoutcomes will be chosen overlower valued ones when both arefeasible.
QUESTION 4.4 CHOOSE THE CORRECT ANSWER(S)CHOOSE THE CORRECT ANSWER(S)Based on Figure 4.6, which of the following statements are true?
The marginal product at 4 hours of study is 7.The marginal product decreases beyond 15 hours of study.The horizontal production function beyond 15 hours means thatstudying for more than 15 hours is detrimental to Alexei’sperformance.The marginal product at 7 hours of study is higher than at 10 hoursof study.
4.3 PREFERENCESIf Alexei has the production function shown in Figure 4.6, how many hoursper day will he choose to study? The decision depends on his preferences.The term preferences describes the benefit or cost that we associate witheach possible outcome. In this case, his preferences describe the benefits (ahigher grade) and the cost (less free time) associated with studying anyparticular number of hours. If he cared only about grades, he should studyfor 15 hours a day. But, like other people, Alexei also values his free time—he likes to sleep, go out or watch TV. So he faces a trade-off—how manypercentage points is he willing to give up in order to spend time on thingsother than study?
Introducing indifference curvesWe illustrate his preferences using Figure 4.7, with free time on the horizontalaxis and final grade on the vertical axis. Free time is defined as all the time thathe does not spend studying. Every point in the diagram represents a differentcombination of free time and final grade. Given his production function, notevery combination that Alexei would want will be possible, but for themoment we will only consider the combinations that he would prefer.
We can assume:
• For a given grade, he prefers a combination with more free time to onewith less free time. Therefore, even though both A and B in Figure 4.6correspond to a grade of 84, Alexei prefers A because it gives him morefree time.
• Similarly, if two combinations both have 20 hours of free time, heprefers the one with a higher grade.
• But compare points A and D in the table. Would Alexei prefer D (lowgrade, plenty of time) or A (higher grade, less time)? One way to find outwould be to ask him.
Suppose he says he is indifferent between A and D, meaning he would feelequally satisfied with either outcome. We say that these two outcomeswould give Alexei the same utility. And we know that he prefers A to B, soB provides lower utility than A or D.
A systematic way to graph Alexei’s preferences would be to start bylooking for all the combinations that give him the same utility as A and D.We could ask Alexei another question, ‘Imagine that you could have thecombination at A (15 hours of free time, 84 points). How many pointswould you be willing to sacrifice for an extra hour of free time?’. Supposethat, after due consideration, he answers ‘9’. Then we know that he is
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indifference curve A curve of thepoints which indicate the combina-tions of goods that provide a givenlevel of utility to the individual.
indifferent between A and E (16 hours, 75 points). Then we could ask thesame question about combination E, and so on until point D. Eventually, wecould draw up a table like the one in Figure 4.7. Alexei is indifferentbetween A and E, between E and F, and so on, which means he is indifferentbetween all the combinations from A to D.
The combinations in the table are plotted in Figure 4.7 and joined togetherto form a downward-sloping curve, called an indifference curve, which joinstogether all the combinations that provide equal utility or ‘satisfaction’.
If you look at the three curves drawn in Figure 4.7, you can see that theone through A gives higher utility than the one through B. The curvethrough C gives the lowest utility of the three. To describe preferences, wedon’t need to know the exact utility of each option; we only need to knowwhich combinations provide more or less utility than others.
A E F G H D
Hours of free time 15 16 17 18 19 20
Final grade 84 75 67 60 54 50
Figure 4.7 Mapping Alexei’s preferences.
1. Alexei prefers more free time to lessfree timeCombinations A and B both deliver agrade of 84, but Alexei will prefer Abecause it has more free time.
2. Alexei prefers a high grade to a lowgradeAt combinations C and D, Alexei has 20hours of free time per day, but heprefers D because it gives him a highergrade.
3. IndifferenceWe don’t know whether Alexei prefersA or E, so we ask him—he says he isindifferent.
4. More combinations giving the sameutilityAlexei says that F is another combina-tion that would give him the sameutility as A and E.
5. Constructing the indifference curveBy asking more questions, we discoverthat Alexei is indifferent between allthe combinations between A and D.
6. Constructing the indifference curveThese points are joined together toform an indifference curve.
7. Other indifference curvesIndifference curves can be drawnthrough any point in the diagram, toshow other points giving the sameutility. We can construct other curves,starting from B or C in the same way asbefore, by finding out which combina-tions give the same amount of utility.
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consumption good A good orservice that satisfies the needs ofconsumers over a short period.
marginal rate of substitution (MRS)The trade-off that a person iswilling to make between twogoods. At any point, this is the slopeof the indifference curve. See also:marginal rate of transformation.
Summary of indifference curvesThe curves we have drawn capture our typical assumptions about people’spreferences between two goods. In other models, these will often be con-sumption goods, such as food or clothing, and we refer to the person as aconsumer. In our model of a student’s preferences, the goods are ‘finalgrade’ and ‘free time’. Notice that:
• Indifference curves slope downward due to trade-offs: Since resources (suchas time or money) are limited, to get more of one good usually meansgiving up some of the other good(s). Therefore, if you are indifferentbetween two combinations, the combination that has more of one goodmust have less of the other good.
• Higher indifference curves correspond to higher utility levels: As we move upand to the right in the diagram, further away from the origin, we moveto combinations with more of both goods.
• Indifference curves are usually smooth: Small changes in the amounts ofgoods don’t cause big jumps in utility.
• Indifference curves do not cross: Work through Exercise 4.3 below tounderstand why.
• As you move to the right along an indifference curve, it becomes flatter.
QUESTION 4.5 CHOOSE THE CORRECT ANSWER(S)CHOOSE THE CORRECT ANSWER(S)Based on Figure 4.7, which of the following statements is correct?
A is the student’s most preferred choice as she would be attainingthe highest grade.At A, the student is willing to give up 34 grade points for 5 extrahours of free time.If at B the number of free hours is 10, then the student is 50%happier at A than at B.The student strictly prefers a grade of 54 with 19 hours of free timeto a grade of 67 with 18 hours of free time.
Introducing the marginal rate of substitution (MRS)Look at Alexei’s indifference curves, which are plotted again in Figure 4.8.If he is at A, with 15 hours of free time and a grade of 84, he would bewilling to sacrifice 9 percentage points for an extra hour of free time, takinghim to E (remember that he is indifferent between A and E). We say that hismarginal rate of substitution (MRS) between grade points and free timeat A is nine; it is the reduction in his grade that would keep Alexei’s utilityconstant following a one-hour increase of free time.
We have drawn the indifference curves as becoming gradually flatterbecause it seems reasonable to assume that, the more free time and thelower the grade he has, the less willing he will be to sacrifice furtherpercentage points in return for free time, so his MRS will be lower. InFigure 4.8, we have calculated the MRS for some combinations along theindifference curve. You can see that, when Alexei has more free time and alower grade, the MRS—the number of percentage points he would give upto gain an extra hour of free time—gradually falls.
The MRS is the slope of the indifference curve; it falls as we move to theright along the curve. If you move from one point to another in Figure 4.7,you can see that the indifference curves get flatter if you increase the
amount of free time, and steeper if you increase the grade. When free timeis scarce relative to grade points, Alexei is less willing to sacrifice an hourfor a higher grade—his MRS is high and his indifference curve is steep.
As the analysis in Figure 4.8 shows, if you move up the vertical linethrough 15 hours, the indifference curves get steeper—the MRS increases.For a given amount of free time, Alexei is willing to give up more gradepoints for an additional hour when he has a lot of points compared to whenhe has few (for example, if he was in danger of failing the course). By thetime you reach A, where his grade is 84, the MRS is high; grade points areso plentiful here that he is willing to give up 9 percentage points for anextra hour of free time.
Figure 4.8 The marginal rate of substitution.
1. Alexei’s indifference curvesThe diagram shows three indifferencecurves for Alexei. The curve furthest tothe left offers the lowest satisfaction.
2. Point AAt A, he has 15 hours of free time andhis grade is 84.
3. Alexei is indifferent between A and EHe would be willing to move from A toE, giving up 9 percentage points for anextra hour of free time. His marginalrate of substitution is 9. The indiffer-ence curve is steep at A.
4. Alexei is indifferent between H and DAt H he is only willing to give up 4points for an extra hour of free time.His MRS is 4. As we move down theindifference curve, the MRS diminishes,because points become scarce relativeto free time. The indifference curvebecomes flatter.
5. All combinations with 15 hours offree timeLook at the combinations with 15 hoursof free time. On the lowest curve, thegrade is low and the MRS is small.Alexei would be willing to give up onlya few points for an hour of free time. Aswe move up the vertical line, theindifference curves are steeper—theMRS increases.
6. All combinations with a grade of 54Now look at all the combinations with agrade of 54. On the curve furthest to theleft, free time is scarce and the MRS ishigh. As we move to the right along thered line, he is less willing to give uppoints for free time. The MRS decreases,the indifference curves get flatter.
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EXERCISE 4.3 WHY INDIFFERENCE CURVES NEVER CROSSIn Figure 4.9, IC1 is an indifference curve joining all the combinations thatgive the same level of utility as A. Combination B is not on IC1.
Figure 4.9 The trade-off between grades and work.
1. Does combination B give higher or lower utility than combination A?How do you know?
2. Draw a sketch of the diagram, and add another indifference curve, IC2,that goes through B and crosses IC1. Label the point at which they crossas C.
3. Combinations B and C are both on IC2. What does that imply abouttheir levels of utility?
4. Combinations C and A are both on IC1. What does that imply abouttheir levels of utility?
5. According to your answers to (3) and (4), how do the levels of utility atcombinations A and B compare?
6. Now compare your answers to (1) and (5) and explain how you knowthat indifference curves can never cross.
You can see the same effect if you fix the grade and vary the amount offree time. If you move to the right along the horizontal line for a grade of54, the MRS becomes lower at each indifference curve. As free timebecomes more plentiful, Alexei becomes less and less willing to give upgrade points for more time.
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EXERCISE 4.4 YOUR MARGINAL RATE OF SUBSTITUTIONImagine that you are offered at job at the end of your university coursethat requires you to work for 40 hours per week. This would leave you with128 hours of free time per week. Estimate the weekly pay that you expectto receive (be realistic!).
1. Draw a diagram with free time on the horizontal axis and weekly payon the vertical axis, and plot the combination corresponding to yourjob offer, calling it A. Assume you need about 10 hours a day forsleeping and eating, so you may want to draw the horizontal axis with70 hours at the origin.
Now imagine you were offered another job requiring 45 hours of work perweek.
2. What level of weekly pay would make you indifferent between this andthe original offer?
3. By asking yourself more questions about the trade-offs you wouldmake, plot an indifference curve through A to represent your prefer-ences.
4. Use your diagram to estimate your marginal rate of substitutionbetween pay and free time at A.
QUESTION 4.6 CHOOSE THE CORRECT ANSWER(S)CHOOSE THE CORRECT ANSWER(S)Based on Figure 4.7, which of the following statements are true?
Alexei prefers C to B because at C he has more free time.Alexei is indifferent between the grade of 84 with 15 hours of freetime, and the grade of 50 with 20 hours of free time.Alexei prefers D to C, because at D he has the same grade for morefree time.At G, Alexei is willing to give up 2 hours of free time for 10 extragrade points.
QUESTION 4.7 CHOOSE THE CORRECT ANSWER(S)CHOOSE THE CORRECT ANSWER(S)The marginal rate of substitution (MRS) is:
The ratio of the amounts of the two goods at a point on the indiffer-ence curve.The amount of one good that the consumer is willing to trade forone unit of the other.The change in the consumer’s utility when one good is substitutedfor another.The slope of the indifference curve.
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opportunity cost When taking anaction implies forgoing the nextbest alternative action, this is thenet benefit of the foregonealternative.
AccountAnt:
Economist:
economic cost The out-of-pocketcost of an action, plus the oppor-tunity cost.
economic rent A payment or otherbenefit received above and beyondwhat the individual would havereceived in his or her next bestalternative (or reservation option).See also: reservation option.
AccountAnt:
Economist:
4.4 DECISION MAKING, TRADE-OFFS, ANDOPPORTUNITY COSTSAlexei faces a dilemma. We know from looking at his preferences that hewants both his grade and his free time to be as high as possible. But givenhis production function, he cannot increase his free time without getting alower grade in the exam. Another way of expressing this is to say that freetime has an opportunity cost—to get more free time, Alexei has to forgothe opportunity of getting a higher grade.
In everyday decision making, opportunity costs are relevant wheneverwe consider choosing between alternative and mutually exclusive coursesof action. When we consider the cost of taking action A, we include the factthat if we do A, we cannot do B. So ‘not doing B’ becomes part of the cost ofdoing A. This is called an opportunity cost because doing A means forgoingthe opportunity to do B.
Accountants think differently about costs. Imagine that an accountantand an economist have been asked to report the cost of going to a concert Ain a theatre, which has a $25 admission cost. In a nearby park, there isconcert B, which is free but happens at the same time.
The cost of concert A is your ‘out-of-pocket’ cost—you paid$25 for a ticket, so the cost is $25.
But what do you have to give up to go to concert A? You giveup $25, plus the enjoyment of the free concert in the park. So thecost of concert A for you is the out-of-pocket cost plus the oppor-tunity cost.
Suppose that the most you would have been willing to pay to attend (if itwasn’t free) was $15. The benefit of your next best alternative to concert Awould be $15 of enjoyment in the park. This is the opportunity cost ofgoing to concert A.
The total economic cost of concert A is $25 + $15 = $40. If the pleasureyou anticipate from being at concert A is greater than the economic cost,say $50, then you will forego concert B and buy a ticket to the theatre. (Thebenefit of an action minus the economic cost is called its economic rent.)
On the other hand, if you anticipate $35 worth of pleasure from concertA, then the economic cost of $40 means you will not choose to go to thetheatre. In simple terms, given that you have to pay $25 for the ticket, youwill instead opt for concert B, pocketing the $25 to spend on other thingsand enjoying $15 worth of benefit from the free park concert.
Why don’t accountants think this way? Because it is not their job.Accountants are paid to keep track of money, not to provide decision ruleson how to choose among alternatives, some of which do not have a statedprice. But making sensible decisions and predicting how sensible peoplewill make decisions involve more than keeping track of money. Anaccountant might argue that the park concert is irrelevant.
Whether or not there is a free park concert does not affectthe cost of going to the concert A. The cost to you is always $25.
But whether or not there is a free park concert can affectwhether you go to concert A or not, because it changes your avail-able options. If your enjoyment from concert A is $35 and your nextbest alternative is staying at home, with enjoyment of $0, you will
choose concert A. However, if concert B is available, you will chooseit rather than concert A.
The table in Figure 4.10 summarizes the example of your choice of whichconcert to attend.
EXERCISE 4.5 OPPORTUNITY COSTSThe British government introduced legislation in 2012 that gaveuniversities the option to raise their tuition fees. Most chose to increaseannual tuition fees from £3,000 to £9,000.
From the viewpoint of an accountant, does this mean that the cost ofgoing to university has tripled? What would an economist’s viewpoint be?
QUESTION 4.8 CHOOSE THE CORRECT ANSWER(S)CHOOSE THE CORRECT ANSWER(S)You are a taxi driver in Melbourne who earns A$50 for a day’s work.You have been offered a one-day ticket to the Australian Open forA$40. Being a big tennis fan, you value the experience at A$100. Basedon this information, which of the following statements is true?
The opportunity cost of the day at the Open is A$40.The economic cost of the day at the Open is A$40.The enjoyment minus economic cost of the day at the Open is A$10.You would be willing to pay up to A$100 for the ticket.
4.5 THE FEASIBLE SETNow we return to Alexei’s problem of how to choose between highgrades and free time. Free time has an opportunity cost in the form oflost percentage points in his grade (equivalently, we might say thatpercentage points have an opportunity cost in the form of the free timeAlexei gives up to obtain them). But before we can describe how Alexeiresolves his dilemma, we need to work out precisely which alternativesare available to him.
A high value on thetheatre choice (A)
A low value on thetheatre choice (A)
Out-of-pocket cost (price of ticketfor A)
$25 $25
Opportunity cost (foregonepleasure of B, park concert)
$15 $15
Economic cost (sum of out-of-pocket and opportunity cost)
$40 $40
Enjoyment of theatre concert (A) $50 $35
Enjoyment minus economic cost $10 −$5
Decision A: Go to the theatreconcert.
B: Go to the parkconcert.
Figure 4.10 Opportunity costs and decision making: Which concert will you choose?
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feasible frontier The curve made ofpoints that defines the maximumfeasible quantity of one good for agiven quantity of the other. Seealso: feasible set.
feasible set All of the combinationsof the things under considerationthat a decision-maker could choosegiven the economic, physical orother constraints that he faces. Seealso: feasible frontier.
marginal rate of transformation(MRT) The quantity of some goodthat must be sacrificed to acquireone additional unit of anothergood. At any point, it is the slope ofthe feasible frontier. See also: mar-ginal rate of substitution.
From the production function to the feasible setTo answer this question, we look again at the production function. Thistime, we will show how the final grade depends on the amount of free time,rather than study time. There are 24 hours in a day. Alexei must divide thistime between studying (all the hours devoted to learning) and free time (allthe rest of his time). Figure 4.11 shows the relationship between his finalgrade and hours of free time per day—the mirror image of Figure 4.6 (page165). If Alexei studies solidly for 24 hours, that means zero hours of freetime and a final grade of 90. If he chooses 24 hours of free time per day, weassume he will get a grade of zero.
In Figure 4.11, the axes are ‘final grade’ and ‘free time’, the two goodsthat give Alexei utility. If we think of him choosing to consume a combina-tion of these two goods, the curved line in Figure 4.11 shows the boundaryof what is feasible. The line is his feasible frontier—the highest grade hecan achieve given the amount of free time he takes, and the area inside thefrontier is the feasible set.
Follow the analysis of Figure 4.11 to see which combinations of gradeand free time are feasible, and which are not, and how the slope of thefrontier represents the opportunity cost of free time.
Any combination of free time and final grade that is on or inside thefrontier is feasible. Combinations outside the feasible frontier are said to beinfeasible given Alexei’s abilities and conditions of study. On the otherhand, even though a combination lying inside the frontier is feasible,choosing it would imply Alexei has effectively thrown away something thathe values. If he studied for 14 hours a day, then according to our model, hecould guarantee himself a grade of 89. But he could obtain a lower grade(70, say), if he just stopped writing before the end of the exam. It would befoolish to throw away points like this for no reason, but it would bepossible. Another way to obtain a combination inside the frontier might beto sit in the library doing nothing—Alexei would be taking less free timethan is available to him, which again makes no sense.
By choosing a combination inside the frontier, Alexei would be givingup something that is freely available—something that has no opportunitycost. He could obtain a higher grade without sacrificing any free time, orhave more time without reducing his grade.
The feasible frontier is a constraint on Alexei’s choices. It represents thetrade-off he must make between grade and free time. At any point on thefrontier, taking more free time has an opportunity cost in terms of gradepoints foregone, corresponding to the slope of the frontier.
Introducing the marginal rate of transformation (MRT)Another way to express the same idea is to say that the feasible frontiershows the marginal rate of transformation (MRT)—the rate at whichAlexei can transform free time into grade points. Look at the slope of thefrontier between points A and E in Figure 4.11.
• The slope of AE: This is the vertical distance from A to E divided by hori-zontal distance from A to E. It is −3.
• At point A: Alexei could get 1 more unit of free time by giving up 3 gradepoints. The opportunity cost of a unit of free time is 3.
• At point E: Alexei could transform 1 unit of time into 3 grade points. Themarginal rate at which he can transform free time into grade points is 3.
Figure 4.11 How does Alexei’s choice of free time affect his grade?
1. The feasible frontierThis curve is called the feasiblefrontier. It shows the highest final examgrade Alexei can achieve, given theamount of free time he takes. With 24hours of free time, his grade would bezero. By having less free time, Alexeican achieve a higher grade.
2. A feasible combinationIf Alexei chooses 13 hours of free timeper day, he can achieve a grade of 84.
3. Infeasible combinationsGiven Alexei’s abilities and conditionsof study, under normal conditions hecannot take 20 hours of free time andexpect to get a grade of 70 (remember,we are assuming that luck plays nopart). Therefore, B is an infeasible com-bination of hours of free time and examgrade.
4. A feasible combinationThe maximum grade Alexei canachieve with 19 hours of free time perday is 57.
5. Inside the frontierCombination D is feasible, but Alexei iswasting time or points in the exam. Hecould get a higher grade with the samehours of study per day, or have morefree time and still get a grade of 70.
6. The feasible setThe area inside the frontier, togetherwith the frontier itself, is called thefeasible set. (A set is a collection ofthings–in this case, all the feasiblecombinations of free time and grade.)
7. The opportunity cost of free timeAt combination A, Alexei could get anextra hour of free time by giving up 3points in the exam. The opportunitycost of an hour of free time at A is 3points.
8. The opportunity cost variesThe more free time he takes, the higherthe marginal product of studying, sothe opportunity cost of free timeincreases. At C, the opportunity cost ofan hour of free time is higher than atA—Alexei would have to give up 7points instead of 3.
9. The slope of the feasible frontierThe opportunity cost of free time at C is7 points, corresponding to the slope ofthe feasible frontier. At C, Alexei wouldhave to give up 7 percentage points(the vertical change is −7) to increasehis free time by 1 hour (the horizontalchange is 1). The slope is −7.
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Note that the slope of AE is only an approximation to the slope of thefrontier. More precisely, the slope at any point is the slope of the line thatjust touches the frontier, and this represents both the MRT and the oppor-tunity cost at that point.
The two trade-offsNote that we have now identified two trade-offs:
• The marginal rate of substitution (MRS): In the previous section, we sawthat the MRS measures the trade-off that Alexei is willing to makebetween exam grade and free time.
• The marginal rate of transformation (MRT): In contrast, the MRTmeasures the trade-off that Alexei is constrained to make by the feasiblefrontier.
As we shall see in the next section, the choice Alexei makes between hisgrade and his free time will strike a balance between these two trade-offs.
QUESTION 4.9 CHOOSE THE CORRECT ANSWER(S)CHOOSE THE CORRECT ANSWER(S)Figure 4.11 shows Alexei’s production function, which describes howhis final grade (the output) depends on the number of hours spentstudying (the input). Free time per day is given by 24 hours minus thenumber of hours of study. Based on this information and the figure,which of the following statements is true?
To find the feasible set, one needs to know the number of hours thatAlexei sleeps per day.The feasible frontier is a mirror image of the production function.If the production function is horizontal after 15 hours of study perday, the feasible frontier is horizontal between 0 and 10 hours offree time per day.The marginal product at 10 hours of study equals the marginal rateof transformation at 14 hours of free time.
QUESTION 4.10 CHOOSE THE CORRECT ANSWER(S)CHOOSE THE CORRECT ANSWER(S)Consider a student whose final grade increases with the number ofhours spent studying. Her choice is between more free time and highergrades, both of which are ‘goods’. Which of the following are the sameas her marginal rate of transformation between the two goods?
the opportunity cost of free timethe number of percentage points the student would gain by givingup another hour of free timethe slope of the student’s feasible frontierthe number of percentage points the student would lose by takinganother hour of free time
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4.6 DECISION MAKING AND SCARCITYThe final step in this decision-making process is to determine the combina-tion of final grade and free time that Alexei will choose. Figure 4.12a bringstogether his feasible frontier (Figure 4.11) and indifference curves (Figure4.7). Recall that the indifference curves indicate what Alexei prefers, andtheir slopes show the trade-offs that he is willing to make; the feasiblefrontier is the constraint on his choice, and its slope shows the trade-off heis constrained to make.
Figure 4.12a shows four indifference curves, labelled IC1 to IC4. IC4represents the highest level of utility because it is the furthest away fromthe origin. No combination of grade and free time on IC4 is feasible, how-ever, because the whole indifference curve lies outside the feasible set.Suppose that Alexei considers choosing a combination somewhere in thefeasible set, on IC1. By looking at the analysis of Figure 4.12a, you will seethat he can increase his utility by moving to points on higher indifferencecurves until he reaches a feasible choice that maximizes his utility.
Alexei maximizes his utility at point E, at which the slope of his indiffer-ence curve is equal to the slope of the feasible frontier. The model predictsthat Alexei will:
• choose to spend 5 hours each day studying, and 19 hours on otheractivities
• obtain a grade of 57 as a result
We can see from Figure 4.12a that at E, the feasible frontier and the highestattainable indifference curve IC3 touch but do not cross. At E, the slope ofthe indifference curve is the same as the slope of the feasible frontier.Remember that the slopes represent the two trade-offs facing Alexei:
• The slope of the indifference curve is the MRS: It is the trade-off he iswilling to make between free time and percentage points.
• The slope of the frontier is the MRT: It is the trade-off that he isconstrained to make between free time and percentage points because itis not possible to go beyond the feasible frontier.
Alexei achieves the highest possible utility where the two trade-offs justbalance (E). His optimal combination of grade and free time is at the pointwhere the marginal rate of transformation is equal to the marginal rate ofsubstitution.
Figure 4.12b lists the MRS (slope of indifference curve) and MRT (slopeof feasible frontier) at the points shown in Figure 4.12a. At B and D, thenumber of points Alexei is willing to trade for an hour of free time (MRS) isgreater than the opportunity cost of that hour (MRT), so he prefers toincrease his free time. At A, the MRT is greater than the MRS so he prefersto decrease his free time. And, as expected, at E the MRS and MRT areequal.
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Figure 4.12a How many hours does Alexei decide to study?
B D E A
Free time 13 15 19 22
Grade 84 78 57 33
MRT 2 4 7 9
MRS 20 15 7 3
Figure 4.12b How many hours does Alexei decide to study?
1. Which point will Alexei choose?The diagram brings together Alexei’sindifference curves and his feasiblefrontier.
2. Feasible combinationsOn the indifference curve IC1, all com-binations between A and B are feasiblebecause they lie in the feasible set.Suppose Alexei chooses one of thesepoints.
3. Could do betterAll combinations in the lens-shapedarea between IC1 and the feasiblefrontier are feasible, and give higherutility than combinations on IC1. Forexample, a movement to C wouldincrease Alexei’s utility.
4. Could do betterMoving from IC1 to point C on IC2
increases Alexei’s utility. Switchingfrom B to D would raise his utility by anequivalent amount.
5. The best feasible trade-offAlexei can raise his utility by movinginto the lens-shaped area above IC2. Hecan continue to find feasible combina-tions on higher indifference curves,until he reaches E.
6. The best feasible trade-offAt E, he has 19 hours of free time perday and a grade of 57. Alexeimaximizes his utility—he is on thehighest indifference curve obtainable,given the feasible frontier.
7. MRS = MRTAt E, the two curves touch but do notcross. The marginal rate of substitution(the slope of the indifference curve) isequal to the marginal rate oftransformation (the slope of thefrontier).
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constrained choice problem Thisproblem is about how we can dothe best for ourselves, given ourpreferences and constraints, andwhen the things we value arescarce. See also: constrainedoptimization problem.
EXERCISE 4.6 EXPLORINGSCARCITYIn our model of decision making,grade points and free time arescarce. Describe a situation inwhich Alexei’s grade points andfree time would not be scarce.Remember, scarcity depends onboth his preferences and the pro-duction function.
We have modelled the student’s decision on study hours as what we calla constrained choice problem—a decision-maker (Alexei) pursues anobjective (utility maximization in this case) subject to a constraint (his feas-ible frontier).
In our example, both free time and points in the exam are scarce forAlexei because:
• Free time and grades are goods: Alexei values both of them.• Each has an opportunity cost: More of one good means less of the other.
In constrained choice problems, the solution is the individual’s optimalchoice. If we assume that utility maximization is Alexei’s goal, the optimalcombination of grade and free time is a point on the feasible frontier atwhich:
The table in Figure 4.13 summarizes Alexei’s trade-offs.
QUESTION 4.11 CHOOSE THE CORRECT ANSWER(S)CHOOSE THE CORRECT ANSWER(S)Figure 4.12a shows Alexei’s feasible frontier and his indifference curvesfor final exam grade and hours of free time per day. Suppose that allstudents have the same feasible frontier, but their indifference curvesmay differ in shape and slope depending on their preferences.
Use the diagram to decide which of the following statements are true.
Alexei will choose a point where the marginal rate of substitutionequals the marginal rate of transformation.C is below the feasible frontier, but D is on the feasible frontier.Therefore, Alexei may select point D as his optimal choice.All students with downward-sloping indifference curves, whateverthe slope, would choose point E.At E, Alexei has the highest ratio of final exam mark per hour of freetime per day.
The trade-off Where it ison thediagram
It isequalto …
MRS Marginal rate of substitution: The number ofpercentage points Alexei is willing to tradefor an hour of free time
The slopeof theindifferencecurve
MRT, oropportunitycost of freetime
Marginal rate of transformation: The numberof percentage points Alexei would gain (orlose) by giving up (or taking) another hour offree time
average product Total outputdivided by a particular input, forexample per worker (divided by thenumber of workers) or per workerper hour (total output divided bythe total number of hours of labourput in).
4.7 HOURS OF WORK AND ECONOMIC GROWTHNew technologies raise the output produced per hour of labour. This iscalled the average product or labour productivity. We now have the toolsto analyse the effects of increased productivity on living standards,specifically on incomes and free time.
A farmer’s production functionSo far, we have considered Alexei’s choice between studying and free time.We now apply our model of constrained choice to Angela, a self-sufficientfarmer who chooses how many hours to work. We assume that Angelaproduces grain to eat and does not sell it to anyone else. If she produces toolittle grain, she will starve.
What is stopping her producing more than enough grain? Like thestudent, Angela also values free time—she gets utility from both free timeand consuming grain.
As a result, her choice is constrained. Producing grain takes labour time,and each hour of labour means Angela foregoes an hour of free time. Thehour of free time sacrificed is the opportunity cost of the grain produced.Like Alexei, Angela faces a problem of scarcity. She has to make a choicebetween her consumption of grain and her consumption of free time.
Technological progressTo understand her choice and how it is affected by technological progress (asin Unit 1), we need to model her production function and her preferences.
Figure 4.14 shows the initial production function before the change occurs,which is the relationship between the number of hours worked and theamount of grain produced. Notice that the graph has a similar concave shapeto Alexei’s production function. The marginal product of an additional hour’swork, shown by the slope, diminishes as the number of hours increases.
A technological improvement—such as seeds with a higher yield, orbetter equipment that makes harvesting quicker—will increase the amountof grain produced in a given number of hours. The analysis in Figure 4.14demonstrates the effect on the production function.
Notice that the new production function is steeper than the original onefor every given number of hours. The new technology has increasedAngela’s marginal product of labour. At every point, an additional hour ofwork produces more grain than under the old technology.
QUESTION 4.12 CHOOSE THE CORRECT ANSWER(S)CHOOSE THE CORRECT ANSWER(S)Based on Figure 4.14, which of the following statements about mar-ginal and average product are true?
The marginal product and average product are approximately thesame for the initial hour.For 2 hours of work, the average product is less than the marginalproduct.The average product is the same for 11 and 12 hours of work.Both the average product and marginal product are diminishing.
Figure 4.14 How technological change affects the production function.
1. The initial technologyThe table shows how the amount ofgrain produced depends on the numberof hours worked per day. For example,if Angela works for 12 hours a day, shewill produce 64 units of grain. This ispoint B on the graph.
2. A technological improvementAn improvement in technology meansthat more grain is produced for a givennumber of working hours. The productionfunction shifts upward, from PF to PFnew.
3. More grain for the same amount ofworkIf Angela works for 12 hours per day, shecan produce 74 units of grain (point C).
4. Same amount of grain, less workAlternatively, by working 8 hours a day,she can produce 64 units of grain (pointD), which previously took 12 hours.
5. The average product of labourThe average product at a particularpoint is the slope of the ray from thatpoint to the origin. For example, atpoint B, Angela’s average product is 64/12 = 5.33 units per hour.
6. Technological improvement raisesthe average productAfter technological improvement,Angela’s average product from workingthe same number of hours is now 74/12= 6.17 units per hour.
From the production function to the feasible frontierFigure 4.15 shows Angela’s feasible frontier, which is just the mirrorimage of the production function, for the original technology (FF), andthe new one (FFnew).
As before, what we call free time is all the time that is not spentworking to produce grain—it includes time for eating, sleeping, andeverything else that we don’t count as farm work, as well as her leisuretime. The feasible frontier shows how much grain can be consumed foreach possible amount of free time. Points B, C, and D represent the samecombinations of free time and grain as in Figure 4.14. The slope of thefrontier represents the MRT (the marginal rate at which free time can betransformed into grain) or, equivalently, the opportunity cost of free time.
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You can see that technological progress expands the feasible set, givingher a wider choice of combinations of grain and free time.
The two trade-offs againNow we add Angela’s indifference curves to the diagram, representing herpreferences for free time and grain consumption, in order to find whichcombination in the feasible set is best for her. Figure 4.16 shows that heroptimal choice under the original technology is to work for 8 hours a day,giving her 16 hours of free time and 55 units of grain. This is the point oftangency, where her two trade-offs balance out—her marginal rate of sub-stitution (MRS) between grain and free time (the slope of the indifferencecurve) is equal to the MRT (the slope of the feasible frontier). We can thinkof the combination of free time and grain at point A as a measure of herstandard of living.
Follow the analysis of Figure 4.16 to see how her choice changes as aresult of technological progress.
Technological change raises Angela’s standard of living—it enables herto achieve higher utility. Note that in Figure 4.16, she increases both herconsumption of grain and her free time.
It is important to realize that this is just one possible result. Had wedrawn the indifference curves differently, Angela’s trade-offs would havebeen different. We can say that the improvement in technology definitelymakes it feasible to both consume more grain and have more free time,but whether Angela will choose to have more of both depends on herpreferences between these two goods, and her willingness to substituteone for the other.
To understand why, remember that technological change makes the pro-duction function steeper—it increases Angela’s marginal product of labour.This means that the opportunity cost of free time is higher, giving her agreater incentive to work. But also, now that she can have more grain foreach hour of free time, she may be more willing to give up some grain formore free time—that is, to reduce her hours of work.
Figure 4.15 An improvement in technology expands Angela’s feasible set.
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These two effects of technological progress work in opposite directions.In Figure 4.16, the second effect dominates and she chooses point E, withmore free time as well as more grain.
EXERCISE 4.7 YOUR PRODUCTION FUNCTIONThink back to the constrained choice problem of final grade and studyhours.
1. What could bring about a technological improvement in your and yourfellow students’ production functions?
2. Draw a diagram to illustrate how this improvement would affect yourfeasible set of grades and study hours.
3. Analyse what might happen to your choice of study hours, and thechoices that you might make.
Figure 4.16 Angela’s choice between free time and grain.
1. Maximizing utility with the originaltechnologyThe diagram shows the feasible setwith the original production functionand Angela’s indifference curves forcombinations of grain and free time.The highest indifference curve she canattain is IC3 at point A.
2. Her optimal choice is point A on thefeasible frontierShe enjoys 16 hours of free time perday and consumes 55 units of grain. AtA, her MRS is equal to the MRT.
3. Technological progressAn improvement in technologyexpands the feasible set. Now she cando better than at A.
4. Angela’s new optimal choiceWhen the technology of farming hasimproved, Angela’s optimal choice ispoint E, where FFnew just touchesindifference curve IC4. She has morefree time and more grain than before.
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normal good A good for whichdemand increases when a person’sincome rises, holding pricesunchanged.
QUESTION 4.13 CHOOSE THE CORRECT ANSWER(S)CHOOSE THE CORRECT ANSWER(S)The following diagram shows a farmer’s choice between free time andgrain before and after an improvement in technology.
Figure 4.17 A farmer’s choice between free time and grain.
Based on this information, which of the following statements arecorrect?
If the MRS of the indifference curve at B is larger than the MRS ofthe indifference curve at A, then the farmer will have an incentiveto take more free time after the technology improvement.The MRT of the new feasible frontier at B is larger than the MRT ofthe old feasible frontier at A. This gives the farmer an incentive totake more free time after the technology improvement.The farmer may choose a point on either side of B after the techno-logy improvement.The farmer will definitely choose a point to the right of B after thetechnology improvement.
4.8 EXPLAINING OUR WORKING HOURS: CHANGESOVER TIMEWe can think through how the technological change and rising incomesdescribed in Unit 1 affected the trade-off faced by workers. Higherwages meant it was possible to have both higher consumption and morefree time. And, like Angela, workers wanted more of both. In economics,the term normal good is used when more of something is demanded asincome rises. Using this definition, both consumption and free time arenormal goods.
We use the idea of the two effects of technological progress onAngela’s choice of free time to explore what has happened to workinghours over the past 250 years.
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income effect The effect that theadditional income would have ifthere were no change in the priceor opportunity cost.
substitution effect The effect thatis only due to changes in the priceor opportunity cost, given the newlevel of utility.
• Income effect: The higher income from every hour of work has madeworkers better off. This is called the income effect—it means thatworkers want to have more hours of free time (as well as more con-sumption).
• Substitution effect: The higher reward from working an extra hour hasincreased the incentive to work. This is called the substitution effect—it has the effect of reducing hours of free time.
Before 1870Let’s consider first the period before 1870 in Britain, when both wages andworking hours rose.
• Income effect: At this time, there was a relatively low level of consump-tion. Workers’ willingness to substitute free time for goods did notincrease much when rising wages made higher consumption possible.The income effect resulting in the choice of more free time was small.
• Substitution effect: Technology improved. Workers were more productiveand paid more, so each hour of work brought more rewards than beforein the form of goods, increasing the incentive to work longer hours. Thesubstitution effect resulting in the choice of less free time was large.
• The substitution effect dominated: Work hours rose, which can beinterpreted as saying that the substitution effect (free time falls) wasbigger than the income effect (free time rises).
During the twentieth centuryDuring the twentieth century, we saw rising wages but falling workinghours. Using the same concepts, we can account for this change as follows:
• Income effect: By the late nineteenth century, workers had a higher levelof consumption and valued free time relatively more, so the incomeeffect of a wage increase was larger.
• Substitution effect: This was consistent with the period before 1870.• The income effect dominated: When the income effect began to outweigh
the substitution effect, working time fell.
The futureWhat about the future?
The high-income economies will continue to experience a majortransformation—the declining role of work in the course of ourlifetimes. We start working at a later age, stop working at an earlier age,and spend fewer hours at work during our working years. Robert Fogel,an economic historian, estimated the total working time in the past,including travel to and from work and housework. He made projectionsfor the year 2040, defining what he called ‘discretionary time’ in a day as24 hours minus the amount we all need for biological maintenance(sleeping, eating, and personal hygiene). Fogel calculated leisure time asdiscretionary time minus working time.
Fogel estimated that, in 1880, lifetime leisure time was just a quarter oflifetime work hours. In 1995, lifetime leisure time exceeded lifetime workingtime. He predicted that lifetime leisure would be three times lifetimeworking hours by the year 2040. His estimates are shown in Figure 4.18.
To see how to use a diagram torepresent the income and substitu-tion effects, see Section 3.7 of TheEconomy (http://tinyco.re/8736282).
Robert William Fogel. 2000. TheFourth Great Awakening and theFuture of Egalitarianism: The Polit-ical Realignment of the 1990s andthe Fate of Egalitarianism.Chicago: University of ChicagoPress.
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Figure 4.18 Estimated lifetime hours of work and leisure (1880, 1995, 2040).
Robert William Fogel. 2000. The FourthGreat Awakening and the Future ofEgalitarianism. Chicago: University ofChicago Press.
It is possible that Fogel overstated the future decline in working time, asKeynes once did. But he raises the challenging possibility that one of thegreat changes brought about by the technological revolution could be avastly reduced role of work in the life of an average person.
QUESTION 4.14 CHOOSE THE CORRECT ANSWER(S)CHOOSE THE CORRECT ANSWER(S)In the period before 1870 in Britain, both wages and hours workedrose, while in the twentieth century, working hours fell even thoughwages continued to rise. Based on this information, which of thefollowing statements are correct?
The marginal rate of transformation between consumption and freetime rose from the pre-1870s to the twentieth century.In the period before 1870, the positive substitution and incomeeffects of rising wages led to workers taking less free time.From the pre-1870s to the twentieth century, the substitution effectof a rise in the wage rate on the hours of free time changed fromnegative to positive.In the twentieth century, the substitution effect dominated theincome effect, so that hours of free time rose.
4.9 EXPLAINING OUR WORKING HOURS: DIFFERENCESBETWEEN COUNTRIES
Figure 4.3 (page 160) showed that, in countries withhigher income (GDP per capita), workers tend tohave more free time; it also showed that there arebig differences in annual hours of free time betweencountries with similar income levels. The table inFigure 4.19 shows our calculations of the disposableincome of an average employee per hour worked,his or her free time per day, and the maximumamount that could be consumed per day. The figuresare shown for five countries.
Brian Burgoon and Phineas Baxandall explore the differencesbetween the average hours that people spend at work in dif-ferent developed countries, and argue that cultural andeconomic differences have created three different ‘worlds’ inthis paper: Brian Burgoon and Phineas Baxandall. 2004. ‘ThreeWorlds of Working Time: The Partisan and Welfare Politics ofWork Hours in Industrialized Countries.’ Politics & Society 32(4): 439–73.
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From the data in Figure 4.19, we see that average free time in Mexicoand South Korea was virtually the same, although the wage was muchhigher in South Korea than in Mexico. South Koreans, Americans andDutch people have about as much to spend per day, but South Koreans havebetween one and two hours less of free time.
Could it be that South Koreans have the same preferences as Americans,so that, if the wage increased in South Korea, they would make the samechoice? This seems unlikely—the substitution effect would lead them toconsume more goods and take less free time; it is implausible to supposethat the income effect of a wage increase would lead them to consumefewer goods. More plausible is the hypothesis that South Koreans andAmericans (on average) have different preferences.
In particular, the idea that South Koreans work exceptionally hard isconsistent with the hypothesis that the average American is willing to giveup more units of daily goods for an hour of free time than the averageSouth Korean.
4.10 IS THIS A GOOD MODEL?We have looked at three different contexts in which people decide how longto spend working—a student (Alexei), a farmer (Angela), and wage earnersin different countries. We have used a model of preferences and feasible setsin which their best (utility-maximizing) choice is the level of working hoursat which the slope of the feasible frontier is equal to the slope of theindifference curve.
You may have been thinking that this is not what people do in real life!Billions of people organize their working lives without knowing
anything about MRS and MRT (if they did make decisions that way,perhaps we would have to subtract the hours they would spend makingcalculations). And even if they did make their choice using mathematics,most of us can’t just leave work whenever we want to. So how can thismodel be useful?
Remember that models help us ‘see more by looking at less’. Lack ofrealism is an intentional feature of any model.
Does it matter that people (mostly) do not really optimize?Is it possible that a model that ignores how we think is a good model ofhow we choose?
Milton Friedman, an economist, explained that, when economists usemodels in this way, they do not claim that we actually think through thesecalculations (such as equating MRS to MRT) each time we make a decision.
Country Wage (disposable incomeper hour worked)
Free timeper day
The most that could beconsumed per day
US 20.54 19.10 100.65
South Korea 18.35 18.07 108.73
Netherlands 29.05 20.21 110.06
Turkey 9.23 18.92 46.90
Mexico 4.96 17.90 30.26
Figure 4.19 Free time and consumption per day across countries (2013).
OECD. Average annual hours actuallyworked per worker (http://tinyco.re/6892498). Accessed June 2016. Netincome after taxes calculated in USdollars using PPP exchange rates.
Instead, we each try various choices (sometimes not even intentionally) andwe tend to adopt habits, or rules of thumb, that make us feel satisfied andnot regret our decisions.
In his book, Essays in Positive Economics, Friedman described this assimilar to playing billiards (pool):
Consider the problem of predicting the shots made by an expertbilliard player. It seems not at all unreasonable that excellentpredictions would be yielded by the hypothesis that the billiard playermade his shots as if he knew the complicated mathematical formulasthat would give the optimum directions of travel, could estimateaccurately by eye the angles, etc., describing the location of the balls,could make lightning calculations from the formulas, and could thenmake the balls travel in the direction indicated by the formulas.
Similarly, if we see a person regularly choosing to go to the library afterlectures instead of going out, or not putting in much work on their farm, orasking for longer shifts after a pay rise, we do not need to suppose that thisperson has done the calculations we set out. If that person later regretted thechoice, next time they might go out a bit more, work harder on the farm, orcut their hours back. Eventually, we could speculate they might end up with adecision on work time that is close to the result of our calculations.
This is why economic theory can help to explain—and sometimes evenpredict—what people do, even though those people are not performing themathematical calculations that economists make in their models.
The influence of culture and politicsA second unrealistic aspect of the model is that employers typically chooseworking hours, not individual workers, and employers often impose alonger working day than workers prefer. As a result, the hours that manypeople work are regulated by law, so that neither the employee nor theemployer can choose to work beyond the maximum amount. In this case,the government has limited the feasible set of hours and goods.
Although individual workers often have little freedom to choose theirhours, workers’ preferences may nevertheless be reflected by changes inworking hours over time and differences between countries. If many indi-vidual workers in a democracy wish to lower their hours, they may ‘choose’this indirectly as voters, if not individually as workers. Or they may bargainas members of a trade union for contracts requiring employers to payhigher overtime rates for longer hours.
This explanation stresses culture (meaning changes in preferences ordifferences in preferences among countries) and politics (meaning differ-ences in laws, or trade union strength and objectives). Culture and politicscertainly help to explain differences in working hours between countries:
Cultures differ. Some northern European peoples highly value theirvacation times, while South Korea is famous for the long hours thatemployees put in. Legal limits on working time differ. In Belgium and
Milton Friedman. 1953. Essays inPositive Economics. (7th ed.)Chicago: University of ChicagoPress.
Our confidence in this hypothesis is not based on the belief thatbilliard players, even expert ones, can or do go through the processdescribed. It derives rather from the belief that, unless in some wayor other they were capable of reaching essentially the same result,they would not in fact be expert billiard players.
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external effect A positive or neg-ative effect of a production,consumption, or other economicdecision on another person orpeople that is not specified as abenefit or liability in a contract. It iscalled an external effect becausethe effect in question is outside thecontract. Also known as:externality. See also: incompletecontract, market failure, externalbenefit, external cost.
France, the normal work week is limited to 35–39 hours, while in Mexicothe limit is 48 hours, and in Kenya even longer.
Employers have an incentive to take account of these differences. Forexample, employers who advertise jobs with the working hours that mostpeople prefer may find they have more applicants than other employersoffering too many (or too few) hours.
Remember, we also judge the quality of a model by whether it providesinsight into something that we want to understand. You can make ajudgement as to whether our model of the choice of hours of work helps usunderstand why working hours differ so much between countries and whythey have changed over time.
EXERCISE 4.8 ANOTHER DEFINITION OF ECONOMICSLionel Robbins, an economist, wrote in 1932 that ‘Economics is the sciencethat studies human behaviour as a relationship between given ends andscarce means which have alternative uses.’
1. Give an example from this unit to illustrate the way that economicsstudies human behaviour as a relationship between ‘given ends andscarce means with alternative uses’.
2. Are the ‘ends’ of economic activity—that is, the things we desire—fixed? Use examples from this unit (study time and grades, or workingtime and consumption) to illustrate your answer.
3. The subject matter that Robbins refers to—doing the best you can in agiven situation—is an essential part of economics. But is economicslimited to the study of ‘scarce means which have alternative uses’? Inanswering this question, include a contrast between Robbins’ definitionof economics and the one given in Section 2.11 (page 101). Note thatRobbins wrote this passage at a time when 15% of the British workforcewas unemployed.
4.11 WORK, FREE TIME, AND WELLBEING: A SOCIALDILEMMAWe have analysed what we termed Alexei’s and Angela’s optimal choice ofworking hours, which sounds like a pretty good thing. But like ‘equilibrium’,‘social preferences’, and ‘efficient’, all of which sound positive, ‘optimal’choices by individuals may lead to social problems that public policiesshould address.
An optimal choice for an individual simply means doing the best that heor she can under the circumstances. But as you already know, if this meansignoring the positive or negative external effects that one’s choices imposeor convey to others, what is optimal for Alexei or Angela may result in asocial dilemma. So far, we have not considered Alexei’s or Angela’sneighbours and friends; they have been acting in isolation.
But one of the reasons why a person may choose to work longer hours isto be able to show off their material success to others. Some goods—such asexpensive cars, watches, and clothes—may be desired as status symbols.Their owners value these or other luxuries partly because ownership raisestheir status above that of other people.
Lionel Robbins. 1984. An Essay onthe Nature and Significance of Eco-nomic Science (http://tinyco.re/4615466). (3rd ed.) New York: NewYork University Press.
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conspicuous consumption Thepurchase of goods or services topublicly display one’s social andeconomic status.
positional good A good—such ashigh status, conspicuous consump-tion, or power—which, if enjoyedby one member of a community isexperienced negatively by others.The more one person benefits fromthis good, the more others areharmed.
Veblen effect A negative externaleffect that arises from the con-sumption of a positional good.Examples include the negativeexternal effects imposed on othersby the consumption of luxuryhousing, clothing, or vehicles.
Conspicuous consumptionPerhaps one of your motives when you buy a car, or a coat, is todemonstrate your wealth and superior style. Or perhaps you settle for acheaper second-hand coat but feel envious, embarrassed, or disadvantagedat a job interview. Thorstein Veblen (1857–1929), an economist andsociologist, described buying luxury items as a public display of social andeconomic status as conspicuous consumption. The process is morecommonly described as ‘keeping up with the Joneses’.
Veblen made an important point—when we work, buy, save, and engagein other economic activities, we are not only attempting to get things; weare also trying to be someone consistent with our own aspirations and therespect of others.
Expensive goods are a good way to communicate high income for thesimple reason that poor people will not be able to compete on this terrain.The rich are the ‘Joneses’, whom people want to emulate.
Goods that are valued more because they are a signal of status or incomeare an example of a larger class called positional goods. They arepositional because they are based on status or power, which can be rankedas high or low. Our positions in this ranking, like the rungs of a ladder, maybe higher or lower. But there is only a fixed amount of a positional good togo around. If Jo is on a higher rung of the ladder because of her new coat,somebody must now be on a lower rung.
Positional goods are sometimes called ‘public bads’. Like public goods,they are ‘available’ to everyone—nobody in the neighbourhood can escapethe fact that one of the neighbours is driving a BMW. But instead of a posit-ive external effect on others, the effect is negative.
To see how this leads to a social dilemma, consider the case of SueSmith and her sister Jo Jones, each moving with their families to a newtown. Each family has a choice between buying a luxury house or a moremodest one. Their payoffs are represented in Figure 4.20. Since bothfamilies have limited funds, they would be better off if both boughtmodest houses than if both bought luxury ones, squeezing the rest oftheir budgets. But Sue is status-conscious and the two families are com-petitive when it comes to lifestyle. If the Smiths buy a modest house, theJoneses can benefit from feeling superior if they choose a luxury house.The Smiths, in turn, will feel miserable.
In short, Sue is trying to keep up with the Joneses, and Jo is trying tokeep up with the Smiths.
You can see that this problem has the structure of a prisoners’ dilemma.Whatever the Joneses do, the Smiths are better off with a luxury house. Forboth couples, choosing Luxury is a dominant strategy. They will achieve apayoff of 1 each, and the outcome is Pareto inefficient, because both wouldbe better off if they each bought modest houses.
The root of this problem is the external effect that one family imposes onthe other by choosing a luxury house. The price of the luxury house that Sue’sfamily will buy does not include the positional externalities inflicted on hersister’s family. If it did, Sue would not buy the luxury house, given the payoffsin the table.
What can they do to avoid the Pareto-inefficient outcome? We knowfrom Unit 2 that altruism would help, but Sue and Jo are more moved bysibling rivalry—these families are not altruistic about houses.
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Figure 4.20 Keeping up with the Joneses.
The ‘keeping up with the Joneses’ problem that Sue and Jo face arisesbecause people care not only about what they have, but also about whatthey have relative to what other people have. This is sometimes called aVeblen effect.
Taxing a positional good to address a social dilemmaThe Nash equilibrium that is the outcome of this social dilemma will bethat both families purchase a luxury house, when both would have beenbetter off with more modest accommodation. If the only people trapped inthe ‘keeping up with the Joneses’ dilemma were really sisters, we mightexpect them to contain their sibling rivalry sufficiently to agree that bothwould buy a modest house. But our story about the sisters is really a parableabout entire communities, even on a global level; a face-to-faceconversation, eye contact, and a handshake might have worked amongsisters, but will not solve the problem.
A government policymaker might devise a policy that would address thesocial dilemma, however. Recall from the previous unit that policies changeoutcomes by altering the Nash equilibrium of the relevant interaction. So,in this case, the policymaker would have to think of a way to make bothfamilies buying a modest home into a Nash equilibrium.
The policymaker could do this simply by passing a law prohibitingluxury housing. A more acceptable policy might be to impose a tax onluxury housing. You can see from the payoff matrix in Figure 4.20 that inorder to make (Modest, Modest) a Nash equilibrium, a tax of just a littlemore than 0.5 on luxury housing would accomplish the objective. (This issimilar to imposing a tax on placing additional cows on the pasture in thetragedy of the commons game in Section 3.6 (page 132).) Be sure that youunderstand what the new payoff matrix (with the tax) would look like, andwhy it would solve the social dilemma.
Positional goods, inequality and the overwork rat raceVeblen effects can be especially important in economies in which ‘theJoneses’ are very rich, so that keeping up with them requires people to worklong hours or to shift their expenditure away from necessities—like foodconsumed privately—and into conspicuous consumption.
Veblen effects help to explain two facts about modern economies:
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Figure 4.21 The relationship between average annual work hours and incomeshare of the very rich (twentieth century).
• People work longer hours in countries in which the very rich receive a largerfraction of the income: Figure 4.21 shows some of the data for a largenumber of rich countries over the entire twentieth century. For example,the US has both higher hours of work and a higher income share of thevery rich than Germany, France, Sweden and the Netherlands. A centuryago, American workers worked fewer hours than workers in all thesecountries. But over the past 100 years, the share of income going to thevery rich declined in all these countries. Sweden, for example, went fromone of the most unequal countries (by this measure) to one of the moreequal. (For more on this topic, watch Juliet Schor’s ‘Economist in action’video (http://tinyco.re/8362335).)
• As a nation gets richer, its citizens often do not become happier: When an indi-vidual gets a wage increase or loses a job, there is a large effect on howhappy that individual claims to be. But economists have also found that achange in our income has a much smaller effect if most of our acquaint-ances also got the same rise, or also lost their job. When an entire nationgets richer, the effect on individual happiness is small, if there is one at all.
Another reason that, as a nation gets richer, its citizens may not becomehappier is that people may become habituated to their recent standard ofliving, and so their happiness reverts back to previous levels if they do notkeep becoming ever richer.
The situation in which nations become richer but their citizens becomeno happier—due either to the effects of income relativities or ofhabituation, or adaptation, as it is often known—is known as the ‘EasterlinParadox’, in honour of the economist who made the argument in 1974.
Betsey Stevenson and Justin Wolfers, among other economists, producealternative evidence that the link between happiness and higher incomes isnot broken, even for the most developed countries.
When Veblen effects are present, the conspicuous consumption of the well-off is a positional good, which has a negative external effect. If conspicuousconsumption is experienced by everyone, reducing their satisfaction with theirown situation, it is a public bad.
Richard A. Easterlin. 1974. ‘Doeseconomic growth improve thehuman lot?’ (http://tinyco.re/7453951) In M Abramovitz, PDavid, & M Reder (Eds.). Nationsand Households in EconomicGrowth: Essays in Honor of MosesAbramovitz. New York: AcademicPress.
Betsey Stevenson and JustinWolfers. (2008) Economic growthand subjective well-being:Reassessing the Easterlin paradox(http://tinyco.re/7219387).Brookings Papers on EconomicActivity, pp. 1–87.
EXERCISE 4.9 USING EXCEL: CORRELATION OR CAUSATION?Figure 4.21 is a scatterplot of average annual work hours and incomeshare of the top 1%, using data from 10 OECD countries. Download andsave the spreadsheet (https://tinyco.re/4012073) containing the data forFigure 4.21.
1. Make a scatterplot similar to Figure 4.21, showing data for eachcountry in a different colour. Follow the walk-through in Figure 4.22below on how to compile a scatterplot diagram in Excel. Are there anypatterns you see for particular countries that are different from theoverall pattern shown in Figure 4.21?
1. The dataThis is what the data looks like. Column A has country names, Column B hasyears, Column C has the percentage of total income earned by the top 1% in thepopulation, and Column D has average annual working hours.
2. Draw a scatterplot with data for one countryAfter step 3, you scatter chart will look like the one shown above.
4.11 WORK, FREE TIME, AND WELLBEING: A SOCIAL DILEMMA
3. Add the other countries to the scatterplotThe scatterplot currently has data for Australia only. Now we will add the othercountries to the scatterplot one by one, so they will each be shown in a differentcolour.
4. Add the other countries to the scatterplotThe section on the left lists all the data series currently plotted on the chart. Weneed to add the other countries as separate data series, so they will appear indifferent colours.
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5. Add the other countries to the scatterplotAfter step 8, the data for the country added will appear on the scatterplot in adifferent colour.
6. Add the other countries to the scatterplotAfter completing step 9, your scatterplot will look like the one shown above,with each country represented by a different colour.
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7. Add axis titles and a chart titleAfter step 13, your chart will look similar to Figure 4.21.
8. Add a chart legendWe will add a legend so it is easy to see which colour represents each country.You can see that the relationship between average annual working hours (ver-tical axis) and income share owned by the top 1% is positive for all countries,but clearer for some countries compared to others.
2. Calculate the correlation coefficient between average annual workhours and income share of the top 1%, using data from all countries.What does this coefficient tell us about the strength of the associationbetween these two variables?
3. Now calculate the correlation coefficient for each country separately.Which country has the highest correlation coefficient, and whichcountry has the lowest? Suggest some explanations for why the rela-tionship between income share and work hours differs in strengthbetween countries.
4. In this unit, we presented one explanation for what we observe inFigure 4.21, namely that the conspicuous consumption of the top 1%may motivate people to work more (‘keep up with the Joneses’). Canyou think of an explanation for why higher average annual workinghours would lead to a higher income share of the top 1%? What otherfactors could be responsible for the observed relationship? Based on
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Juliet Schor: Why do we work sohard? http://tinyco.re/8362335
your answers, discuss whether we can conclude from Figure 4.21 that ahigher income share of the top 1% causes higher average annual workhours.
Changing preferencesWhen interpreting changes in working hours, we should also consider thepossibility that preferences change over time. If you look carefully at Figure4.1 (page 158), you can see that, in the last part of the twentieth century,hours of work rose in the US, even though wages hardly increased. Hoursof work also rose in Sweden during this period.
Why? Perhaps Swedes and Americans came to value consumptionmore over these years. In other words, their preferences changed (in dia-grammatic terms, this would be a flattening of the indifference curves.)This may have occurred because, in both the US and Sweden, the shareof income gained by the very rich increased considerably and the lavishconsumption habits of the rich set a higher standard for everyone else.According to this explanation, Swedes and Americans were ‘keeping upwith the Joneses’ and the Joneses got richer, leading everyone else tochange their preferences.
The combined political, cultural and economic influences on ourchoices may produce some surprising trends. In our ‘Economist inaction’ video, Juliet Schor, a sociologist and economist who has writtenabout the paradox that many of the world’s wealthiest people areworking more despite gains in technology, asks what this means for ourquality of life, and for environment sustainability.
EXERCISE 4.10 VEBLEN EFFECTS AND POLICY1. The example of Veblen effects above concerns houses. Can you think of
any other examples where Veblen effects are present?2. Why do Veblen effects cause inefficiency?3. Describe in what way Veblen effects are similar to (or different from)
pollution?4. Discuss whether the government should adopt policies to address this
market failure and, if so, what might they be?
QUESTION 4.15 CHOOSE THE CORRECT ANSWER(S)CHOOSE THE CORRECT ANSWER(S)Watch the ‘Economist in action’ video of Juliet Schor. Which of thefollowing statements were not mentioned in the video?
Technological advancement does not necessarily mean shorterworking days.Workers can choose jobs but not their working hours.There has been a definite divergence recently in working hoursacross countries.Countries with longer working hours tend to have higher carbonfootprints.
4.11 WORK, FREE TIME, AND WELLBEING: A SOCIAL DILEMMA
4.12 CONCLUSIONTechnological improvements have enabled people to increase their con-sumption of goods and services and also to enjoy more free time. Theextent to which higher wages have led to decreased working hours variesacross time and between countries, reflecting the fact that preferences maychange over time and that they are shaped by different cultural factors.
Mindful of three key concepts in economic modelling (ceteris paribus,incentives, and relative prices), we have built a constrained choicemodel to study an individual’s choice between different combinations ofconsumption and free time.
Constraint: The feasible set Preferences: Indifference curves
The production function translates inputs (likehours of work) into outputs (like grades orgrain.) Diminishing marginal product meansthat, for each additional unit of input, theresulting increase in output becomes smaller.For some given level of input, the marginalproduct is the slope of the production function,while the average product is the slope of the rayfrom the origin to a given point on theproduction function.
The feasible frontier gives the maximumamount of one good (grain) that can be obtainedfor a given amount of another (free time). Itsslope, the marginal rate of transformation(MRT), represents the opportunity cost of, forexample, increasing free time by one hour interms of the grain the individual must forgo.
Indifference curves join together allcombinations of goods (like free time andconsumption) that provide the same levelof utility. Indifference curves are basedon our preferences, that is on the benefitor cost that we associate with eachpossible outcome. To reflect the trade-offbetween two things that we valuepositively ('goods'), indifference curvesslope downwards.
The slope of an indifference curve iscalled the marginal rate of substitution(MRS), and it represents the trade-offbetween the two goods, namely, howmuch more of one good would berequired to offset the subtraction of oneunit of the other good.
Optimal choice: MRT = MRS
Technological progress can be modelled as an upward shift of the produc-tion function.
This expands the feasible set (in this case just the mirror image of theproduction function).
We have distinguished between two effects of a wage increase:
• The substitution effect: The amount by which leisure hours fall due totheir higher opportunity cost in terms of foregone income.
• The income effect: The amount by which free time increases as a result ofhigher income, assuming that, like income, free time is a normal good.
Finally, we have considered how the conspicuous consumption ofpositional goods as a status symbol may lead to a Pareto-inefficient out-come in which one person’s luxury consumption inflicts negative externaleffects, called Veblen effects, on others.
UNIT 4 WORK, WELLBEING, AND SCARCITY
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4.13 DOING ECONOMICS: MEASURING WELLBEINGIn Unit 1 and in this unit, we have used GDP per capita to compare livingstandards across countries or measure progress in living standards overtime. The rationale is that higher income/expenditure means a greaterability to spend on goods and services, which in turn increases materialwellbeing. Since material wellbeing can contribute to non-materialwellbeing, we might also expect countries with higher GDP per capita tohave higher non-material wellbeing. But how do we measure non-materialwellbeing? And does a higher GDP per capita necessarily mean a highernon-material wellbeing?
In the Doing Economics Empirical Project 4 we answer these questions.The project shows how different variables can be summarized into an indexby looking at GDP and its components. We will then learn how indices ofnon-material wellbeing are constructed, and compare an index of materialwellbeing (GDP per capita) with an index of non-material wellbeing (theHuman Development Index).
Go to Doing Economics Empirical Project 4 (http://tinyco.re/4523278) towork on this problem.
Learning objectivesIn this project you will:
• check datasets for missing data• generate new variables using cell formulae• sort data and assign ranks based on values• distinguish between time series and cross sectional data, and plot
appropriate charts for each type of data• calculate the geometric mean and explain how it differs from the
arithmetic mean• construct indices using the geometric mean, and use index values to
rank observations• explain the difference between two measures of wellbeing (GDP per
capita and the Human Development Index).
4.14 REFERENCESEasterlin, Richard. 1974. ‘Does economic growth improve the human lot?’
(http://tinyco.re/7453951) In M Abramovitz, P David & M Reder(Eds.), Nations and Households in Economic Growth: Essays in Honor ofMoses Abramovitz. New York: Academic Press.
Fogel, Robert William. 2000. The Fourth Great Awakening and the Future ofEgalitarianism: The Political Realignment of the 1990s and the Fate ofEgalitarianism. Chicago: University of Chicago Press.
Friedman, Milton. 1953. Essays in Positive Economics. (7th ed.) Chicago: Uni-versity of Chicago Press.
Harford, Tim. 2015. ‘The rewards for working hard are too big for Keynes’svision’ (http://tinyco.re/5829245). The Undercover Economist.
Keynes, John Maynard. 1963. ‘Economic Possibilities for ourGrandchildren’ (http://tinyco.re/8213530). In Essays in Persuasion.New York, NY: W. W. Norton & Co.
Plant, E. Ashby, Karl Anders Ericsson, Len Hill, and Kia Asberg. 2005. ‘Whystudy time does not predict grade point average across college
students: Implications of deliberate practice for academicperformance’ (http://tinyco.re/7875663). Contemporary EducationalPsychology 30 (1): pp. 96–116.
Robbins, Lionel. 1984. An Essay on the Nature and Significance of EconomicScience (http://tinyco.re/4615466). (3rd ed.) New York: New YorkUniversity Press.
Stevenson, Betsey, and Justin Wolfers. 2008. ‘Economic growth andsubjective well-being: Reassessing the Easterlin paradox’(http://tinyco.re/7219387). Brookings Papers on Economic Activity,pp. 1–87.
Whaples, Robert. 2001. ‘Hours of work in U.S. History’ (http://tinyco.re/1660378). EH.net Encyclopedia.
preferences A description of the benefit or cost we associatewith each possible outcome.ceteris paribus Economists often simplify analysis by settingaside things that are thought to be of less importance to thequestion of interest. The literal meaning of the expression is‘other things equal’. In an economic model it means ananalysis ‘holds other things constant’.incentive Economic reward or punishment, which influencesthe benefits and costs of alternative courses of action.relative price The price of one good or service compared toanother (usually expressed as a ratio).constrained choice problem This problem is about how wecan do the best for ourselves, given our preferences and con-straints, and when the things we value are scarce. See also:constrained optimization problem.production function A graphical or mathematical expressiondescribing the amount of output that can be produced by anygiven amount or combination of input(s). The functiondescribes differing technologies capable of producing thesame thing.diminishing marginal product A property of some productionfunctions according to which each additional unit of inputresults in a smaller increment in total output than did theprevious unit.average product Total output divided by a particular input,for example per worker (divided by the number of workers)or per worker per hour (total output divided by the totalnumber of hours of labour put in).indifference curve A curve of the points which indicate thecombinations of goods that provide a given level of utility tothe individual.utility A numerical indicator of the value that one places onan outcome, such that higher valued outcomes will bechosen over lower valued ones when both are feasible.preferences A description of the benefit or cost we associatewith each possible outcome.feasible frontier The curve made of points that defines themaximum feasible quantity of one good for a given quantityof the other. See also: feasible set.
marginal rate of transformation (MRT) The quantity of somegood that must be sacrificed to acquire one additional unit ofanother good. At any point, it is the slope of the feasiblefrontier. See also: marginal rate of substitution.opportunity cost When taking an action implies forgoing thenext best alternative action, this is the net benefit of theforegone alternative.marginal rate of substitution (MRS) The trade-off that aperson is willing to make between two goods. At any point,this is the slope of the indifference curve. See also: marginalrate of transformation.technological progress A change in technology that reducesthe amount of resources (labour, machines, land, energy,time) required to produce a given amount of the output.conspicuous consumption The purchase of goods or servicesto publicly display one’s social and economic status.positional good A good—such as high status, conspicuousconsumption, or power—which, if enjoyed by one member ofa community is experienced negatively by others. The moreone person benefits from this good, the more others areharmed.substitution effect The effect that is only due to changes inthe price or opportunity cost, given the new level of utility.income effect The effect that the additional income wouldhave if there were no change in the price or opportunity cost.external effect A positive or negative effect of a production,consumption, or other economic decision on another personor people that is not specified as a benefit or liability in acontract. It is called an external effect because the effect inquestion is outside the contract. Also known as: externality.See also: incomplete contract, market failure, external bene-fit, external cost.Veblen effect A negative external effect that arises from theconsumption of a positional good. Examples include the neg-ative external effects imposed on others by the consumptionof luxury housing, clothing, or vehicles.
