Unit3_Feb2015.pdf

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3SCARCITY, WORK AND PROGRESS

HOW INDIVIDUALS DO THE BEST THEY CAN GIVEN THE CONSTRAINTS THEY FACE, AND HOW THEIR CHOICE OF WORK HOURS IS AFFECTED BY TECHNOLOGICAL CHANGE.You will learn:

What an opportunity cost is.

A general framework for studying decision-making when your choices are limited by a scarcity of resources available to meet your objectives.

How individuals choose work hours when there is a trade-off between their objective of more free time and their objective of consuming more goods.

How an individuals choices are constrained by a technology that determines the feasible set of outcomes for the individual.

How technological improvement expands this feasible set and influences the amount of hours an individual chooses to work.

What complements and substitutes are, and how decisions over work hours are affected by whether free time and consumption are substitutes or complements.

Some reasons why the rapid economic growth in successful capitalist societies was associated with a relatively small increase in free time, and a much larger increase in income and consumption.

February 2015 beta

See www.core-econ.org for the full interactive version of The Economy by The CORE Project. Guide yourself through key concepts with clickable figures, test your understanding with multiple choice

questions, look up key terms in the glossary, read full mathematical derivations in the Leibniz supplements, watch economists explain their work in Economists in Action and much more.

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coreecon | Curriculum Open-access Resources in Economics 2

imagine that you are working in a job in London that is paying you 10 an hour for a 40-hour working week: so your earnings are 400 per week. There are 24 hours in a day and 168 hours in a week so, after 40 hours of work, you are left with 128 hours of free time to allocate across all non-work activities, including leisure and sleep.

Suppose, by some happy stroke of luck, you are offered a job at a much higher wagesix times higher. Your new hourly wage is 60. Not only that, your prospective employer asks you to choose how many hours you will work each week.

Will you carry on working 40 hours per week? If you do, your weekly pay will be six times higher than before: it will be 2,400. Or will you decide that you are satisfied with the goods you can buy with your weekly earnings of 400? You can now earn this by cutting your weekly hours to just 6 hours and 40 minutes (a six-day weekend!) If this were your choice, you would enjoy an additional 33 hours and 20 minutes (about 26%) more free time than previously.

How did we calculate these numbers? EINSTEIN 1 shows you.

EINSTEIN 1

Suppose you are happy earning just 400 per week, and so convert any hourly pay increase into more free time. At an hourly wage rate of 60 per hour you can earn 400 by working just 400/60 = 6.67 hours: that is, 6 hours and 40 minutes. Hence your consumption of free time will rise by 33 hours and 20 minutes from 7 x 24 40 = 128 hours to 7 x 24 6.67 = 161.33 hours: that is, by ((161.33 128)/128) x 100 = 26%.

Or would you use the greater hourly wage rate to raise both your weekly earnings and your free time?

The idea of receiving, overnight, a six-fold increase in your hourly wage, and being able to choose your own hours of work, might seem fanciful. But the data presented in Figure 3 in Unit 1 shows between 1870 and 2000 the real wage rose from a base of 100 in 1870 to 627 in 2000; in other words, people were earning more than six times as much in 2000 as they were 130 years earlier, even allowing for inflation. And while employees ordinarily cannot just tell their employer how many hours they want to work, over long periods the typical hours that we work will change. In part this is a response to how much we prefer to work: we choose part-time work or legislation imposing maximum hours of work, or trade union contracts requiring employers to pay a higher hourly rate for longer hours.

UNIT 3 | SCARCITY, WORK AND PROGRESS 3

So an important question is: has economic progress of the type illustrated in the past two units, taken the form of more goods, more free time, or both? The amount of goods we consume, and our free time, have both increased. But has the increase in free time been relatively large or small compared to the increases in wages and living standards?

The number of annual days worked per person in Britain has been calculated to be about 266 around the year 1600 and it did not change much until the industrial revolution, rising to 318 days in 1870. From 1870, however, there have been reductions in the numbers of days and of hours worked per year. Figure 1 shows data on real wages in London (using the same data on which Figure 3 in Unit 1 is based) and annual hours worked in the UK, between 1870 and 2000.

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Figure 1. Real wages and annual hours worked in the UK, 1870-2000.

Source: Allen, R. C. 2001. The Great Divergence in European Wages and Prices from the Middle Ages to the First World War. Explorations in Economic History 38, pp. 411-447. Huberman, M. 2003. Working Hours of the World Unite? New International Evidence of Worktime, 1870-2000, working paper.

While real wages in London increased by a factor of six in that period, average work hours fell by only 40% (from around 2,700 hours in 1870 to just over 1,600 hours in 2000). In other words, people enjoyed more than a 600% increase in their ability to buy goods and services, and a much smaller increase of about 18%, or slightly less than one-fifth, in their free time (We show you how to calculate this percentage in EINSTEIN 2).How does this compare with the hours you would have chosen when our hypothetical employer offered a six-fold increase in your wage?


EINSTEIN 2

There are 24 hours per day that can be allocated to work or to free time. So the maximum amount of free time in a year is 365 x 24 = 8,760 hours. With 2,743 hours worked in 1870 and 1,653 in 2000, free time rose from 8,760 2,743 = 6,017 hours to 8,760 1,653 = 7,107 hours between 1870 and 2000: that is, by ((7,107-6,017)/6,017) x 100 = 18.1%.

The result for British workers was a huge increase in living standards, largely in the form of more goods and services to consume, rather than more free time. Why did this occur? That is, why was the increase in wages converted mostly into more goods and services? We will provide some answers to this question by studying a basic problem of economicsscarcityand how we make choices when we cannot have all of everything that we want, such as goods and free time.

TEST YOUR UNDERSTANDING

Test yourself using multiple choice questions in the full interactive version at www.core-econ.org.

3.1 LABOUR AND PRODUCTION

in unit 2 we saw that labour can be thought of as an input in the production of goods and services. Labour is work; in the Unit 1 example of making a cake, it is stirring, mixing, and preparing ingredients. In making a car it is welding, assembling, testing and similar activities. Work activity is often difficult to measure, which will be important in later units because employers find it difficult to determine the amount of work that individual workers are doing. Because we cannot measure the effort required by different activities in a comparable way (compare baking a cake to building a car), economists often measure labour simply as the number of hours worked by individuals engaged in production and assume that, as the number of hours worked increases, the amount of goods produced also increases.


As a student, you make a choice every day: how many hours to spend studying. The motivation to devote time to studying comes from your belief that the more time you spend studying, the higher mark you will be able to obtain at the end of the course. The curve in Figure 2 shows the relationship between the hours a student spends studying per day and the final exam mark that the student receives. After spending zero hours studying per day the student would be completely unprepared for the final exam and would get a mark of zero. The student is able to achieve a higher mark by studying, so the curve slopes upward. At 15 hours of work per day the student gets the highest mark that he or she is capable of, which is 90 out of 100. Any time spent studying beyond that does not affect the students exam result (think about tiredness), and the curve becomes flat.

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Figure 2. How does the amount of time spent studying affect the final exam mark the student receives?

INTERACT

Follow figures click-by-click in the full interactive version at www.core-econ.org.

The curve shown in Figure 2 can be thought of as the students production function, as it shows how the amount of hours spent studying (the students input) translates into final exam marks (the students output).


We can see that the curve in Figure 2 gets flatter as we approach the maximum mark that is possible for the student. What does this mean? If the student is studying for four hours per day, then the student will get a mark of 50 in the final exam. The student can increase the mark from 50 to 57 by being willing to put in one more hour of study per day. The extra effort gains the student seven marks in the final exam. In other words, at this point on the curve the marginal product of the additional hour of study per day is seven. Now, imagine the student is much more diligent and is currently studying for 10 hours per day. An additional hours study is now less useful, raising the students final exam mark by only three marks, from 81 to 84. The marginal product has fallen to three. The example shows that if the students curve, or production function, becomes flatter the more hours spent studying, then the marginal product of an additional hour of study falls as the student moves along the curve. The marginal product is diminishing. What this means in simple terms is that studying helps a lot if you are not studying much; while if you are already studying a lot, then studying even more does not help very much.

If the student is working hard and studying for 15 hours a day, then this means a mark of 90 in the final exam. At this point, what is the marginal product of an additional hours study? It is zero; studying more does not improve the students mark. In reality, a lack of sleep or down time could result in the students mark deteriorating if he or she works more than 15 hours a day. If this were the case then the students production function would start to slope downward as it approached 24 hours, and the marginal product would be negative.

DISCUSS 1: THE STUDENTS PRODUCTION FUNCTION

What would it mean if the students production function became steeper the more hours of work that the student put in?

We have looked at the effect on the students exam mark of studying for one more hour at different points on the production function. But, how does the average amount of marks the student gets per hour of study vary along the production function? At four hours of study per day the student gets 50 in the final exam, so each hour of study is equivalent to 12.5 marks. In other words, the average product of studying is 12.5 when the student studies for four hours per day. The average product can also be calculated by finding the slope of a ray from the origin to the curve at the chosen number of hours of study. At four hours of study per day the slope of the ray (slope = height/width) is 50/4 = 12.5. If the student increases their daily hours of study to 10, then the average product will fall to 81/10 = 8.1. The rays from the origin at four and 10 hours of study per day are shown as blue dotted lines on Figure 2. We can see that the slope of the rays is decreasing as we move along the curve; similar


to the marginal product, the average product falls as we move along the students production function. We can also see that each ray from the origin is steeper than the curve itself (each ray cuts the curve from below) so that average product is always greater than the marginal product with a production function of this shape. LEIBNIZ 2 shows you how to model the production function algebraically, and find the properties of the average and marginal product of labour using calculus.

LEIBNIZ

For mathematical derivations of key concepts, download the Leibniz boxes from www.core-econ.org.

3.2 CHOICES

on the basis of the production function shown in Figure 2, how many hours might an ambitious student choose to study? We assume that all students prefer to get a high mark in the final exam (holding everything else constant). An ambitious student maximises the final mark by studying for 15 hours per day. No student, however ambitious, would choose to work more than 15 hours because extra study will not improve the final mark. Given the high exam mark that can be achieved, will an ambitious student choose to study for 15 hours per day? Almost certainly not, because the student has to give up free time, which the student also values, for every hour spent studying. Put another way, there is an opportunity cost to studying for one more hour: the hour of free time that is sacrificed. There are only 24 hours in a day, and the student has to choose how to divide those hours between studying and doing other activities. The student values both high marks and free time, but cannot have more of one without having less of the other (unless the student in question is studying more than 15 hours, in which case its possible to reduce study time without sacrificing marks).

In thinking about how the student chooses to split time between studying and doing other activities, it is useful to have a way of measuring how much the student values different things. Economists use the word utility to mean how much a person values something. In our example, the student derives utility from both high marks and free time. Utility provides a way to compare how much the student values different combinations of exam marks and free time. For example, if the combination of 14


hours of free time and a mark of 81 has less utility to the student than 20 hours of free time and a mark of 50, then the student will choose the latter (if there are no other choices).

Figure 3 shows how the utility of the student varies with their final exam mark. In order to isolate the effect of the students exam mark on utility we hold all other things constant. In this simple example that just means that free time is held constant at 20 hours (we note from Figure 2 that 4 hours of study are associated with a final exam mark of 50). We can see that the curve is upward sloping; the students utility increases as the exam mark increases, holding free time constant. The curve is referred to as the students partial utility function. The term partial is used because only one of the students outputs is allowed to vary (exam marks) whilst all other outputs are kept constant (free time).

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Figure 3. How much does the student value higher exam marks, holding free time constant at 20 hours a day?

Figure 4. How much does the student value free time, holding the exam mark constant at 50?

Notice that, like the students production function, the partial utility function becomes flatter as the exam mark increases. This implies that, as the students mark increases, each additional mark creates a smaller increase in utility. Exactly as in the case of the production function in Figure 2, we can use a numerical example to highlight this property of the partial utility function. What is the increase in the students utility of moving from a final exam mark of 30 to a mark of 40? Utility increases from 6.1 to 7.4; the marginal utility of an additional 10 exam marks is 1.3. What is the increase in the students utility of moving from a final exam mark of 70 to a mark of 80? Utility increases from 9.5 to 9.8; the marginal utility of an additional 10 marks is 0.3. The numerical example shows that marginal utility is falling as we move along the partial utility function. In other words, there is diminishing marginal utility in the mark achieved.


Figure 4 shows the other side of the coin; how the students utility varies with free time, holding the exam mark constant at 50. Again, the partial utility function is upward-sloping, showing that if the student knew he or she would get the same mark at the end of the course, then the student would prefer to have as much free time as possible. We can also see that there is diminishing marginal utility in free time. The shape of the partial utility functions in Figures 3 and 4 expresses the fact that the more you have of something you value, the less highly you value any additional (marginal) amount of it.

DISCUSS 2: VARIETIES OF UTILITY FUNCTIONS

The partial utility functions need not get flatter as the student moves along them; they could get steeper for greater levels of final exam mark or hours of free time per day. Other shapes are also possible. Suppose, for example, that an academic programme the student highly values will only admit applicants if they get a mark of at least 50. Any mark lower that this is not worth much to the student. Any mark higher than the minimum for admission is not worth much more. What would the students partial utility function look like in this case?

3.3 TRADE-OFFS

we can see from Figures 3 and 4 that the student faces a dilemma: by choosing to give up an extra hour of free time to study an additional hour, the student can achieve a higher mark in the final exam. A higher exam mark increases the students utility. But the hour of free time the student loses lowers that same utility. What should the student do? How should students choose to divide time between studying and other activities? What is termed a trade-off occurs in cases like this: something of which you want more has an opportunity costbecause getting it means getting less of something else that you also value. The student must trade off marks in the final exam against free time. How does the student do this?

To answer this question, it helps to look again at Figure 2, but this time to show the relationship between final exam marks and free time, rather than that between final exam marks and study time. There are 24 hours in a day. The student must divide this time between studying and free time. Figure 5 shows the relationship between final exam marks and hours of free time per day. The figure is the mirror image of Figure


2. If the student studies solidly for 24 hours, that means zero hours of free time and a final exam mark of 90. Likewise, choosing 24 hours of free time per day implies a mark of zero.

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Figure 5. How does the amount of free time the student takes affect the exam mark?

In Figure 5, the axes are final exam mark and free time, the two things that give the student utility. In a more general setting, the things that give people utility are often consumption goods such as food or clothing. In our example, we can think of the student choosing to consume either final exam marks or free time. We therefore call the curved line in Figure 5 the feasible consumption frontier. It plots the highest final exam mark achievable given the amount of free time that the student takes. For example, if the student takes 14 hours of free time per day, and hence studies for 10 hours each day, the highest possible mark in the final exam is 81. A combination of free time and final exam mark lying outside the feasible consumption frontier, such as point A, is said to be infeasible given the students abilities and conditions of study. The student cannot have 20 hours of free time per day and still achieve a final exam mark of 70. In fact, the maximum mark they can achieve with 20 hours of free time per day is just 50. The curve is called a frontier because all combinations outside it are infeasible.

On the other hand the combination at point B, lying inside the frontier, is feasible; but it would imply the student achieving a lower mark than is possible given the amount of hours spent studying each day; perhaps as a result of bad luck during the revision period. At point B, the student obtains a mark of 70 in the final exam by studying 14 hours per day. Without bad luck during their revision period, then this amount of time spent studying would have yielded a mark of 89. At combinations inside the frontier the student can obtain higher marks without sacrificing any free time. The frontier is shown as downward-sloping in Figure 5 because of the diminishing marginal product of study time, as explained earlier. The area inside the


frontier is called the feasible set; it shows all the combinations of final exam mark and hours of free time per day that are obtainable given the students abilities and conditions of study.

The feasible consumption frontier represents the trade-off the student must make between exam marks and free time. An additional hour of free time reduces the exam mark the student can achieve. The trade-off gets steeper as we move along the feasible consumption frontier; it is equal to the slope of the frontier. The marginal product of each hour of study is very high when the student is enjoying a lot of free time, and study time is correspondingly low. More formally, we can define the slope of the feasible consumption frontier as the marginal rate of transformation between final exam marks and hours of free time per day. The marginal rate of transformation shows how much it would increase the students final exam mark if they give up an additional hour of free time per day. Another way to think about this is how the student can transform an hour of free time into extra marks.

The feasible consumption frontier constrains the student in the choice between exam marks and free time. The student will, of course, want to be somewhere on the frontier, getting the highest grade possible for any given amount of free timebut which combination on the frontier will the student choose? A high final exam mark and little free time, or a lower mark and more free time?

The answer will depend on the trade-off the student is willing to make between exam marks and free time. In other words, it will depend on how much the student values each additional hour of free time relative to the increase in the mark that an additional hour of study can yield. The choice the student makes involves balancing what is feasible (defined by the feasible consumption frontier) with what the student values most. The first trade-off the student faces is how the final exam mark rises with an extra hour of study, and the resulting opportunity cost of one less hour of free time. The second trade-off is the students willingness to give up a little more free time to gain a higher mark. The latter trade-off reflects the students preferences between free time and exam marks.

To understand the second trade-off more clearly, we need to develop the analysis of the partial utility functions introduced in Figures 3 and 4. We can see that the amount of free time is held constant at 20 hours in Figure 3. Similarly, the final exam mark is kept constant at 50 in Figure 4. In this case, the two figures tell a consistent story: the students utility level is 8.3. We can see this by using the partial utility functions to find the utility associated with 50 marks in Figure 3 and with 20 hours in Figure 4.

In Figure 6, the combination at point A is associated with 50 final exam marks and 20 hours of free time. We know from Figures 3 and 4 this gives the student a utility of 8.3. Now, assume the mark is constant at 50 but the student is studying for one extra hour, as shown by point B. The student will have one hour less free time but is not rewarded with a higher exam mark. This outcome is worse than point A, so the students utility must have fallen. We can see this from Figure 4; when the student


has 19 hours of free time per day, holding the exam mark constant at 50, utility falls to 8.275. What would the student need for utility to be restored to its original level of 8.3? It would need the lost hour of free time per day to be offset with a higher exam mark. This combination is shown at point C in Figure 6, with 19 hours of free time per day and an exam mark of 53.

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Figure 6. How is the student willing to trade off exam marks against free time?

We have just shown that the students utility at points A and C in Figure 6 is the same. In other words, the student is equally happy with the combinations of hours and free time at points A and C. When the student is equally happy with two alternatives, we say that the student is indifferent. Indifference means not preferring point A to point C, nor preferring point C to point A; the student values points A and C the same. If both points were feasible, and there were no other choices available, the student would not care which one occurred. It is not just points A and C that give a utility of 8.3, there are a whole range of combinations of exam marks and free time that yield this level of utility. The student is indifferent between all these combinations. The set of all such combinations is shown in Figure 6 as the curve passing through points A and C: it is called an indifference curve.

There will also be an indifference curve passing through point B linking all combinations of final exam marks and free time that yield utility of 8.275. Indeed, for any combination of exam marks and free time, there will be an associated utility level and a corresponding indifference curve. Indifference curves further from the origin represent higher levels of utility, because utility is assumed to be increasing in both exam marks and free time. We know this because of the upward-sloping partial utility functions in Figures 3 and 4.


What should a student do to obtain the highest utility possible? Clearly, the student should try to reach the furthest indifference curve from the origin. This gives the student the highest exam mark and the largest amount of free time that is feasible. As we will see in Figure 7, the feasible consumption frontier will limit the indifference curve the student can reach.

The indifference curves in Figure 6 are downward-sloping and become flatter as we move along them. The shapes of the curves are related to the properties of the underlying partial utility functions and the extent to which the marginal utilities are diminishing (see Figures 3 and 4). For an insight, consider the combination at point D in Figure 6; the student is enjoying only 16 hours of free time per day but the obtainable final exam mark is now 72. The student can increase this mark further by giving up some more free time. We know from Figure 4 that when the student does not have a lot of free time, the partial utility function is steep and the marginal utility of an extra hour of free time per day is large. Therefore, a large increase in final exam mark is needed to offset the utility lost from reducing free time at this point on the indifference curve. By reducing free time per day from 16 to 15 hours, the student moves from point D to point E on the indifference curve. The obtainable exam mark rises from 72 to 84, which is enough to offset the utility lost from the one-hour reduction in free time. We know from Figure 3 that the marginal utility of an additional exam mark is much smaller when the students exam marks are already high. This is why the student would be willing to give up many exam marks for a small gain in free time in the section of the indifference curve between points E and D.

At point A on the students indifference curve in Figure 6, we know that a rise of only three marks is necessary for the student to maintain utility at 8.3 after giving up an hour of free time. We say that the marginal rate of substitution between final exam marks and free time from A is three; it is defined as the additional number of exam marks required to keep utility constant following a reduction in free time of one hour. The marginal rate of substitution is just the slope of the indifference curve. If the student studies for longer and chooses the combination at point D, then we can see that the marginal rate of substitution rises to 84 72 = 12. The marginal rate of substitution is therefore diminishing as we move along the indifference curve from left to right. This is because when consuming a lot of free time, the student needs only a small increase in exam marks to offset any given reduction in free time. This property of the students indifference curves is related to the shape of the underlying partial utility functions shown in Figures 3 and 4. LEIBNIZ 3 shows you how to find the find the marginal rate of transformation and the marginal rate of substitution algebraically, using calculus.

As we have seen, the feasible consumption frontier represents the trade-off that constrains student choice over exam marks and free time: it determines the highest mark the student is able to achieve for a given amount of time spent studying. In this way, the frontier takes into account the marking scheme, the students abilities and the study conditions. The indifference curves also represent a trade-off: the trade-off the student is willing to make between exam marks and free time. Therefore


the indifference curves reflect the students preferences. As we shall see in the next section, the choice the student makes between exam marks and free time will balance these trade-offs against each another.

3.4 DECISION-MAKING AND SCARCITY

the next step is to think about the combination of exam marks and free time that the student will choose. Figure 7 brings together the students feasible consumption frontier (Figure 5) and indifference curves (Figure 6). It therefore shows both the constraint trade-off and the preference trade-off of the student. The figure enables us to draw conclusions about the decisions the student will make. Here the feasible consumption frontier (or the boundary of the feasible set) is shown in red, while indifference curves derived from the individuals utility function are shown in blue. The indifference curves (blue) indicate where the student would like to go and the frontier (red) is the constraint on the students choice.

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Figure 7. How many hours does the student decide to study?

Figure 7 shows five indifference curves. We labelled them IC0 to IC4 to make the figure less cluttered. IC4 represents the highest level of utility because it is the furthest away from the origin. No combinations of exam mark and free time on IC4 are feasible; the whole indifference curve lies outside the feasible consumption frontier. First, focus on IC1. All combinations of exam mark and free time on this indifference curve between points A and B are feasible. In addition, all combinations between A and B in the lens-shaped area created by the intersection of IC1 and the


feasible consumption frontier are feasible. Would the student want to choose the combination at either point A or point B? No, because the student could achieve a higher level of utility by picking a different combination of exam marks and free time. For example, a movement to point C would increase the students utility. We know this must be true because point C is on a higher indifference curve than points A or B. Similarly, switching from point B to point D raises the students utility by an equivalent amount. The student could continue switching the choice of exam marks and free time, all the time raising utility, by moving along the feasible consumption frontier and reaching successively higher indifference curves until the student finds the combination at point E. At this point, the student is on the highest indifference curve obtainable given the position of the feasible consumption frontier.

This example of a students constrained choice over free time and study (and hence final exam mark) tells us that, under the assumptions we have made, the student will choose to spend five hours of the day studying, 19 hours of the day doing other activities, and will be able to obtain a mark of 57 in the final exam.

We can see from Figure 7 that at point E the feasible consumption frontier and the highest attainable indifference curve IC3, are tangent to each other, meaning they touch but do not cross. This means that the two trade-offs the student has to manage just balance. More formally, at point E the marginal rate of transformation is equal to the marginal rate of substitution. To find out how to determine the optimal combination of final marks and free time using calculus, see LEIBNIZ 4.

Figure 7 also highlights point F, where the student is not studying at all. The indifference curve that passes through this point is said to be the reservation indifference curve, which we labelled IC0. We can see that it will be at a lower level of utility than any of the other indifference curves in the figure; it will be closer to the origin. The reservation indifference curve shows the level of utility the student gets by deciding not to study (and hence receiving a mark of zero). The student would never choose a combination of exam mark and free time that is on a lower indifference curve than the reservation indifference curve.

This example of a students constrained choice has many useful applications: it is a way of thinking rigorously about how we can do the best we can for ourselves, given our preferences and the constraints we face, when the things we value are scarce. In our example, both exam marks and free time are scarce for the student because:

1. The student values both of them.2. The student cannot have more of one without having less of the othereach has

an opportunity cost.

But do people really act like this, finding the work hours that equates the slope of their feasible consumption frontier with the slope of their indifference curve? If we did wed have to factor in all the time it would take making the calculations.


The economist Milton Friedman explains that economics does not claim that we actually think through these calculations each time we make a decision. Instead we try out various choices (sometimes not even intentionally) and we tend to adopt those that worked well (made us feel satisfied and not regretful about our decisions) as habits, or rules of thumb.

He described it as similar to playing billiards (pool):

Consider the problem of predicting the shots made by an expert billiard player. It seems not at all unreasonable that excellent predictions would be yielded by the hypothesis that the billiard player made his shots as if he knew the complicated mathematical formulas that would give the optimum directions of travel, could estimate accurately by eye the angles, etc., describing the location of the balls, could make lightning calculations from the formulas, and could then make the balls travel in the direction indicated by the formulas. Our confidence in this hypothesis is not based on the belief that billiard players, even expert ones, can or do go through the process described. It derives rather from the belief that, unless in some way or other they were capable of reaching essentially the same result, they would not in fact be expert billiard players.

Similarly, if we see a person regularly choosing to study a lot, or to not put in much work on a farm (see the example in section 3.5), we do not need to suppose that this person has done the calculations we set out. But, if the result of these decisions led to regret, the person would have tried something else, eventually ending up with some work time close to that which would have resulted from the calculations we have just done.

That is why economic theory can help to explain, and sometimes even predict, what people doeven though the student or the farmer is not performing the kind of calculations that we use to make our predictions.

DISCUSS 3: EXPLORING SCARCITY

Using this definition of scarcity, define a situation in which exam marks and free time would not be scarce. Remember scarcity is defined by both the students utility function and the production function for exam marks.


3.5 HOURS OF WORK AND ECONOMIC GROWTH

one of the aims of this unit is to examine how rising wages and living standards might affect the choices people make about how many hours they want to work. We now have the tools to solve this problem. More generally, these tools (built on concepts relating to opportunity costs and preferences) will prove useful in a variety of situations in which choices have to be made in conditions of scarcity.

Up to this point, we have looked at a students choice between studying and free time. We now use our model of constrained choice to look at a self-sufficient farmer who chooses how many hours to work. We assume that the farmer produces grain to eat and does not sell it to anyone else. If the farmer produces less than a certain amount of grain, the farmer will starve. What is stopping the farmer producing the most grain possible? Just like the student, the farmer values free time. Formally, the farmer gets utility from both free time and consuming grain. The farmer also faces the problem of scarcity: grain can be consumed only if it is produced, but production takes labour time, and each hour of labour means the farmer foregoes an hour of free time. The hour of free time sacrificed is the opportunity cost of working for one hour. Scarcity implies the farmer has to make a choice between the consumption of grain and the consumption of free time.

We are interested in two questions:

1. Given the production function, how many hours will the farmer choose to work?2. How will the farmers choice change after a technological improvement that

can produce the same amount of grain with fewer hours of workthat is, while enjoying more free time?

We begin by considering the relationships in Figures 8 and 9.

Figure 8 shows how the amount of hours the farmer works per day affects the amount of grain produced. The production function shows the relationship between hours worked and grain production for the initial technology. We can see that the farmers production function has a similar property to the students production function: the marginal product of an additional hours work is diminishing as we move along the curve.

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Figure 8. A grain technology: the farmers production function for grain


Figure 9 shows the farmers feasible consumption frontier, which is just the mirror image of the production function. It shows how much grain can be consumed for each possible amount of free time, given the initial technology. Reflecting the diminishing marginal product of labour in the farmers production function, the feasible consumption frontier gets steeper as hours of free time increase; the marginal rate of transformation between free time and quantity of grain produced increases as we move along the curve. In simple terms, this means the additional amount of grain that can be produced from giving up an hour of free time is higher when the farmer has a lot of free time already.

In Figure 9 we can see that the highest indifference curve the farmer can attain given the feasible consumption frontier is IC1. The farmer will therefore maximise utility at point A, enjoying 16 hours of free time per day and consuming 55 units of grain. We can also pin down the farmers reservation indifference curve (this will be useful in Unit 5) by plotting the indifference curve that goes through point B. At this point, the farmer does not work at all, no grain is produced, and free time is the only source of utility.

Next, we want to think about how the farmers choice between free time and grain responds to an improvement in technology. A technological improvement will increase the amount of grain the farmer can produce in a given number of hours of work (apart from when the farmer is not working at all). The improvement could involve using better seeds that yield more grain, or better equipment that makes harvesting quicker. In the previous example of the student, we could think of an improvement in technology as being the refurbishment of the university library, or the introduction of a higher-quality revision guide. Both these improvements would increase the students final exam mark for a given amount of hours spent studying. In our model of constrained choice, an improvement in technology shifts the production function upward as shown in Figure 10. As before, we abbreviate the labels, and denote the initial production function as PF and the production function after the improvement in technology as PFnew.

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Figure 9. The farmers choice between free time and grain.


If the farmer worked for 12 hours per day before the introduction of the new technology, then the farmer would be at point A on the production function and would be able to produce 64 units of grain. After the technological improvement, the farmer is able to produce 74 units of grain by working for 12 hours (point B). Alternatively, reducing the hours of work to just eight per day still produces the 64 units of grain the farmer was producing before the improvement in technology (point C). To find out how to model technical change algebraically, see LEIBNIZ 5.

The new technology has therefore given the farmer the option of a number of combinations of free time and grain that were not previously available. In our model this means an upward shift in the feasible consumption frontier as shown in Figure 11. We label the initial feasible consumption frontier as FCF and the feasible consumption frontier after the improvement in technology as FCFnew. The figure is a mirror image of Figure 10; the points A, B and C in the two figures represent exactly the same combinations of free time and grain.

What combination of free time and grain will the farmer choose after the improvement in technology? To answer this question, we return to the farmers choice before the technological improvement. As shown by point A in Figure 12 the farmer is enjoying 16 hours of free time per day and is consuming 55 units of grain. The improvement in technology shifts the feasible consumption set upward to FCFnew. The farmer can now reach an indifference curve further from

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Figure 10. The farmers production function after an improvement in technology.

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Figure 11. The farmers feasible consumption frontier after an improvement in technology.

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Figure 12. The farmers choice between free time and grain after an improvement in technology.


the origin because the feasible set has expanded. The farmer moves to point B on indifference curve IC2, consuming 61 units of grain and enjoying 17 hours of free time per day.

The result is that the farmer has responded to the technological improvement by taking some additional free time and consuming more grain. It is important to realise that this is just one possible result. Had we drawn the indifference curves or the consumption frontier differently, the trade-off would have been different. So far we have assumed that the indifference curves are smooth, and become flatter as free time increases. Put another way, we have assumed the farmers marginal rate of substitution between grain and free time is diminishing. In Figures 13 and 14 we will examine extreme examples of possible indifference curves to get a deeper understanding of what lies behind the farmers response to an improvement in technology.

In an economy with just two goods, such as our examples of free time and exam marks and free time and grain, downward-sloping indifference curves describe the case in which an increase in the consumption of either good raises utility. When we think about points on an individuals indifference curve, we know that utility is constant; a rise in consumption of one good offsets a fall in consumption of the other good. This is why the individuals indifference curves are downward-sloping. But what if the individual increased utility from additional amounts of one good only when there was more of the other good as well? If, for example, the two goods in the economy are cream and cake, and the individual does not like cake without cream (or cream without cake). In this case, the individuals utility will not increase with more of only one of the two goods. The indifference curves will be L-shaped.

We now return to the example of the farmer and show how technological improvement affects the farmers choices when preferences between free time and grain are described by L-shaped indifference curves. Indifference curves of this shape imply that the farmers utility rises with additional free time only if the farmer also has more grain, and vice-versa. Why might this be the case? If the farmers enjoyment of leisure requires a lot of energy (playing sport rather than watching it on television), then the farmer might need more food to enjoy extra free time. Similarly, the farmer might enjoy more food only when there is also more free time in which to expend the additional energy the food provides.


Figure 13 shows the feasible consumption frontier facing the farmer before the improvement in technology, plus a set of L-shaped indifference curves. The highest indifference curve that the farmer can attain is IC2. At point A, the farmer is consuming 55 units of grain and is enjoying 16 hours of free time. To understand why the farmers indifference curves are L-shaped, look at points B, C and D on IC1. Compared to point B, point C represents a combination in which the farmer enjoys more free time and the same consumption of grain; and yet the farmer is indifferent between points B and C as they both lie on the same indifference curve. Now, if we compare points B and D, the farmer gets the same amount of free time but consumes more grain at point D; again, the farmer is indifferent between these two combinations.We have shown that the farmers utility does not increase as a result of consuming more grain or free time, holding the other good constant. The only way the farmer can get more utility and jump onto an indifference curve further from the origin is to increase consumption of both goods. Point A is on a higher indifference curve than point B precisely because the combination contains both more free time and more grain.

When an individuals preferences for two goods are described by L-shaped indifference curves, we say that the two goods are complementary: as in our example of cream and cake. In our example of the farmer, the L-shaped indifference curves represent a situation in which the farmer regards the two goods, grain and free time, as perfect complements in consumption. Of course, this is an extreme case. In real life we rarely see two goods that are perfect complements: for example, a badminton racquet is not much use without a shuttlecock, and vice versa.

DISCUSS 4: EXPLORING ISOQUANTS

Explain in words the meaning of the L-shaped isoquants in Unit 2, and the L-shaped indifference curves in this unit, using the concept of perfect complementarity.

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Figure 13. The farmers choice between free time and grain when they are perfect complements (L-shaped indifference curves).


How will the farmer, for whom grain and free time are perfect complements, react to an improvement in technology? The technological improvement shifts the feasible consumption frontier upward to FCFnew and the farmer can reach a higher indifference curve. The farmer chooses point E on IC4, enjoying 17 hours of free time per day and consuming 61 units of grain. The advance in technology has increased the farmers consumption of both grain and free time, as we would expect given the farmers preferences. The complementarity in the relationship between consumption of grain and of free time implies that technological improvements will have a disincentive effect on work: the farmer will choose to take some of the rewards of technological advance by choosing more free time.

Now we look at the extreme case at the other end of the scale, when the farmers indifference curves are downward-sloping straight lines. This means that grain and free time are substitutes. Having more grain means the farmer is happy to forgo some free time. When the farmer has more free time,having less grain might be a sacrifice the farmer is happy to make. Cookies and cakes are likely to be substitutes. The indifference curves shown in Figure 12 are downward-sloping and so grain and free time are substitutes for the farmer in that case. But in Figure 12 the indifference curves are not straight linesthey become flatter as free time increases. We have explained previously that this is because of the diminishing marginal rate of substitution: the more the farmer has of one good, the less highly the farmers values it relative to the other good. In the case of straight-line indifference curves, the marginal rate of substitution between grain and free time is not diminishing: it is constant. Regardless of how much free time the farmer has, the amount of grain the farmer is willing to give up for one more unit of free time remains constant (and vice versa). Straight-line indifference curves are special: they are an extreme example in which the two goods are perfect substitutes.

DISCUSS 5: SUBSTITUTES AND COMPLEMENTS

You could think of the indifference curves shown in Figure 12 as being intermediate between the extreme case of L-shaped indifference curves on one hand, and downward sloping straight indifference curves on the other. In other words, they mix the characteristics of substitutability and of complementarity. Some pairs of goods that you buy will be better described as complements (for example, pen and paper) and others as substitutes (a pen and a pencil). Try to categorise some of the goods you buy in this way.


Figure 14 shows the feasible consumption frontier facing the farmer at the initial technology, with a set of downward-sloping straight indifference curves. The highest indifference curve that the farmer can attain is IC2. At point A, the farmer is consuming 55 units of grain and is enjoying 16 hours of free time. The farmer chooses this combination with L-shaped indifference curves in Figure 13. But the response of the farmer to the technological change will be different because grain and free time are regarded as perfect substitutes rather than perfect complements.

How will the farmer, for whom grain and free time are now perfect substitutes, react to an improvement in technology? The technological improvement shifts the feasible consumption frontier upward to FCFnew and the farmer is able to reach a higher indifference curve. The farmer chooses point B on IC3, enjoying 15 hours of free time per day and consuming 68 units of grain.

How does the farmers new choice compare to that when grain and free time were perfect complements? When the goods are perfect substitutes the farmer responds to the technological improvement by reducing the amount of free time consumed. This is the opposite response to the case of perfect complements presented in Figure 13, in which the farmer increased the consumption of free time.

In both Figures 13 and 14, the technological shift results in the feasible consumption frontier becoming steeper at each value of free time. In other words, in the trade-off that has to be made between grain and free time, each additional hour of free time incurs a greater opportunity cost in forgone consumption of grain than was the case prior to the improvement in technology. Taken on its own, this means that the technological improvement generates an increased incentive for the farmer to work. This case is captured in Figure 14 and leads us to expect that, as technology progresses over time, we should see an increase in hours worked. However, Figure 13 shows that when there is complementarity in the consumption of free time and grain the farmer chooses to work less. In other words, complementarity between grain and free time generates a disincentive to work. Treating the goods as complements shows that there is also an offsetting tendency for people to enjoy more free time, alongside higher consumption of other goods, when technology improves.

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Figure 14. The farmers choice between free time and grain when they are perfect substitutes (downward-sloping straight indifference curves).


We saw in Unit 2 how a change in relative prices changes incentives and leads to changed behaviour: specifically, we observed that if wages became more expensive relative to the cost of coal, new technologies would be adopted so that relatively less labour and relatively more coal are used. In other words, as the relative price of labour rises, there is an incentive to use less of it.

DISCUSS 6: A WAGE WORKER CHOOSES HER HOURS

How would the analysis in Figure 9 change if the individual considering how many hours to work were paid a fixed wage, and so could choose how many hours to work at that wage? The individual values free time and uses the wage to buy goods, which she also enjoys consuming.

What is the opportunity cost of free time in this new situation? How is the workers feasible set now defined?

Draw a new figure like the previous ones, but with the feasible set indicated, and show (using indifference curves) the hours of work that the individual will choose.

Now consider how many hours this person would choose if the wage were higher. Would the individual work more or less, and on what would that depend?

In Unit 3 we have seen a similar mechanism: if the opportunity cost (equivalently, the relative price of free time) rises, then the farmer in our example has an incentive to change behaviourconsuming less free time. This is shown in Figure 14. The relative price of free time rises because technological progress results in the feasible consumption frontier becoming steeper at each value of free time, as we have noted. In Unit 3 we have seen that choices are affected both by relative prices (in this case, reflected in the marginal rate of transformation, MRT) and by preferences (reflected in the marginal rate of substitution, MRS).


3.6 CONCLUSION

let us recap on what the evidence shows, about hours of work over time. We know from Unit 1 that real wages of London craftsmen increased more than six-fold between 1870 and 2000. Over this time period, the dramatic improvements in living standards that this real wage rise made possible have taken the form of an increase in the amount of free time enjoyed by workers. With hours worked in Great Britain falling by about 40%, the consumption of free time has risen by approximately 18%. This increase is small compared to the change in real wages, and hence the consumption of goods.

Why has the huge increase in wages been converted disproportionately into the consumption of goods rather than free time?

One reason is that employers typically choose working hours, not individual workers, and employers often prefer a longer working day. In many countries the reduction in working hours resulted from legislation imposing maximum hours of work, and trade union negotiations requiring employers to pay higher overtime rates for longer hours. The spread of television and mass communication may have influenced the choice by workers to reduce their working hours even when they were able to do sobecause even people with little money had glimpse into the lifestyles and consumption habits of the very well off. The phrase keeping up with the Joneses captures the idea that our preferences could be affected by observing the consumption of others.

Economic theory can supply a fresh look at this old question. We developed an analysis in which technological improvement raises the opportunity cost of free time. In isolation this is likely to lead people to choose less free time. If goods and free time are perfect substitutes, workers will respond to the technological change by working more. However, we have also seen that if workers preferences are such that there is complementarity in the consumption of goods and free time, then they are likely to respond to technological improvement by raising their consumption of both goods and free time.

The fact that free time consumed has risen over time indicates that goods and free time are not perfect substitutes. That the increase in free time is small relative to the change in real wages, however, suggests that goods and free time are far from perfect complements.


DISCUSS 7: WORKING HOURS ACROSS COUNTRIES AND TIME

To see what has happened to work hours in many countries over the 20th century, look at this data: LINK.

1. How would you describe what happened?2. How are the countries in Panel A of the figure different from those in Panel B?3. What possible explanations can you suggest for why the decline in work hours was

greater in some countries than in others?4. Why do you think that the decline in work hours is faster in most countries in the

first half of the century?5. In recent years, is there any country in which working hours have increased? Why

do you think this happened?


UNIT 3 KEY POINTS

1. Goods and free time are both scarce. Because people value both we have to trade off one against the other: more free time means fewer hours worked, which means a lower consumption of goods.

2. The opportunity cost of an additional hour of free time is equal to the consumption of goods forgone as a result of less work time.

3. In deciding how many hours to work, the worker has to balance a trade-off based on the relative desirability of each (represented by the marginal rate of substitution, the slope of the indifference curve) against a trade-off based on the feasibility of combinations of the two (represented by the marginal rate of transformation, the slope of the feasible consumption frontier).

4. Technological improvement is likely to alter the marginal rate of transformation between goods and free time, raising the opportunity cost of free time.

If workers regard consumption of goods and of free time as perfect substitutes, they will work longer hours following a technological improvement.

If workers regard consumption of goods and of free time as perfect complements, then technological improvement will be associated with workers choosing more free time.

5. Since 1870 real wages in the UK have risen approximately six-fold. Over the same time annual hours worked per worker has fallen by less than half. In most countries the percentage increase in free time has been much less than the percentage increase in consumption of goods.


UNIT 3: READ MORE

3.6 CONCLUSION

The leisure classThe economist Thorsten Veblen (1857-1929) invented the term conspicuous consumption in his explanation of why people of lesser means try to mimic the consumption habits of the rich. Veblen, T. 1934. The Theory of the Leisure Class. New York: Modern Library (first published in 1899).

Juliet Schor continues the Veblen tradition.Schor, J. 1993. The Overworked American: The Unexpected Decline of Leisure. New York City: Basic Books.

Robert Fogel has studied the change in free time in the very long run.Fogel, R. 2000. The Fourth Great Awakening and the Future of Egalitarianism. Chicago and London: The University of Chicago Press.

Three worlds of working timeBurgoon, B. and Baxandall, P. 2004. Three worlds of working time: the partisan and welfare politics of work hours in industrialized countries. Politics and Society 32 (4), p. 439.

MORE

Essays in positive economicsFriedman, M. 1953. Essays in Positive Economics. Chicago: University of Chicago Press.

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