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Perloff Reference Chapters: Chapter 4: pp. 92-105, Chapter 5: pp. 112-128
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AgendaConsumer EquilibriumChange in EquilibriumIncome and Substitution EffectsDemandTastes and Preferences Affects on DemandConsumer Surplus
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Consumer EquilibriumConsumer equilibrium is comprised of two
concepts:The utility functionThe budget constraint
Consumer equilibrium can be defined as a consumption bundle that is feasible given a particular budget constraint and maximizes total utility.
3
Consumer Equilibrium Cont.If there was no budget constraint, a
person would consume each good to the point where marginal utility of consumption for each good is zero.Why?
Given a budget constraint, the consumer maximizes total utility by consuming a bundle that is feasible.A feasible bundle is one that lies either on or
inside the budget constraint.
4
Consumer Equilibrium Cont.In graphical terms, consumer equilibrium is
defined as the point where the highest utility function touches the budget constraint.
5
Consumer Equilibrium ExampleSuppose we have the following utility
function:U = u(x1,x2) = x1 * x2
Where x1 is equal to the number of hotdogs consumed Where x2 is equal to the number of sodas consumed
Suppose we have the following budget constraint:I = p1*x1 + p2*x2
Where pi is equal to the price of hotdogs consumed Where pj is equal to the price of sodas consumed
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Consumer Equilibrium Example Cont.Now consider that you have a price of
hotdogs equal to $2 and a price of soda is a $1.
Also suppose that our income is $10.Examine the different indifference curves of
U = 1, U=12.5, and U = 25
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8
Con
sum
ptio
n of
sod
as
Consumption of hotdogs
U = 11
1
10
5
5
2.5
U = 12.5
U = 25
x2
x1
Consumer Equilibrium Cont.Intuitively what we have done in the graph is
equate the tradeoff from prices to the tradeoff in utility.I.e., (p2/p1) = (MU2/MU1)
Where p2 is the price of good 2 and p1 is the price of good 1
Where MU2 is the marginal utility of consuming good 2 and MU1 is the marginal utility of consuming good 1
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Consumer Equilibrium Cont.(p2/p1) = (MU2/MU1) can be rewritten as:
(MU2 / p2) = (MU1 / p1)This says that you are normalizing the change
in utility by the price of the good and then equating it to the normalized marginal utility of the other good.
Another way to look at this is to say that the marginal utility derived from the last dollar spent for each good is equal.
What happens if one side is greater than the other?
10
Changes in EquilibriumThere are many things that can change
consumer equilibrium.The major two items that we will examine
that can change consumer equilibrium, ceteris paribus:IncomePrice of each good
Note: Ceteris paribus means that we hold everything else fixed.
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Mathematical Side Note on Ceteris ParibusThere are many things that enter our
utility function which we can represent with the following utility function:U = u(x1, x2, x3, …, xn)
When we say that we want to examine utility with respect to x1 and x2, ceteris paribus, what we are saying is that we hold constant the values for all other goods.
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Mathematical Side Note on Ceteris Paribus Cont.Mathematically, we can represent holding
things constant in the following two manners:U = u(x1, x2; x3, …, xn) or
U = u(x1, x2| x3, …, xn) Where it is understood using this notation that
goods x3 through xn are held at some constant level.
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Change in Equilibrium ExampleSuppose Dr. Hurley is consuming a basket of
goods that only has two items, chips and soda.
Assume for the moment that the price is held constant for chips at $1.00 and the price for soda is held constant at $1.00.
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Change in Equilibrium Example Cont.Also assume that Dr. Hurley has $10 for this
basket of goods and his utility function is represented by U = u(soda, chips) = soda * chips.
What is Dr. Hurley’s initial consumer equilibrium?
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Change in Equilibrium ExampleMathematically we can represent Dr.
Hurley’s problem as the following:Dr. Hurley’s utility function:
U = u(x1, x2) = x1 * x2
Dr. Hurley’s budget constraint: M = p1*x1 + p2*x2 10 = 1*x1 + 1*x2
Where x1 is the quantity of soda consumed
Where x2 is the quantity of chips consumed
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Change in Equilibrium Example
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Consumption of soda
1
1
10
10
5
5
U = 25
Con
sum
ptio
n of
Chi
ps
QuestionHow did Dr. Hurley know that consuming 5
chips and 5 sodas will maximize utility?He used advance math that you will learn in Ag
Bus 313?But there is another way you can find the
answer.
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Graphically Finding the Maximum Utility To find the maximum utility we can make
the following argument:We know that are maximum utility point must
lie on the budget line assuming all the consumption goods are desirable and we are non-satiated, i.e.,utility is always increasing.
This being the case we can examine the points on the budget line to see which provides the highest utility.
Once we have found the maximum utility on the budget curve, we can hold our utility fixed and draw the utility function.
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Graphically Finding the Maximum Utility
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10 = x1 + x2, U = u(x1,x2) = x1 * x2
Consumption of x1 Consumption of x2 Total Utility from consumption
0
1
2
3
4
5
6
7
8
10
9
8
7
6
5
4
3
2
0 = 0 * 10
9 = 9 * 1
16 = 2 * 8
21 = 3 * 7
24 = 4 * 6
25 = 5 * 5
24 = 6 * 4
21 = 7 * 3
16 = 8 * 2
Maximum
Change in Equilibrium Example Cont.What happens if we change the price of soda
from $1 to $2 holding the price of the chips constant.
What happens if we change the price of soda from $1 to $0.50 holding the price of the chips constant.
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22Consumption of soda
2.5
10
10
5
5
U = 50
Con
sum
ptio
n of
Chi
ps
U = 25U = 12.5
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Observations on Changing EquilibriumCoincidently, the consumption of chips did
not change.This is a property of the function we used, it is
not always true.
The line/curve that connected all three equilibrium points is considered a price consumption curve.This curve relates the quantity of chips and
soda consumed when changing the price of soda.
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Observations on Changing Equilibrium Cont.As price went down for soda, more was
consumed and when price went up for soda less was consumed.
There are two effects at work when price changes:The income effectThe substitution effect
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Income and Substitution EffectsSubstitution Effect
It is the change in the quantity consumed due to a change in the price of the good, while holding other prices for goods constant and utility constant.
Income EffectIt is the change in the quantity consumed due
to a relative increase in a change of income while holding prices constant.
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Graphical ExampleAssume that the price for soda has
decreased.To find the substitution effect graphically,
we examine what quantities would be consumed if the consumer had to stay on her original indifference curve facing the new prices.This is equivalent to taking a parallel line to the
new budget line and setting it tangent, i.e., just touching at one point, to the old utility level.
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Income Effect
Substitution Effect
Qua
ntit
y of
Chi
ps
Quantity of Soda
Original consumption level
New consumption level
I1
I2
Original Budget line
New Budget Line
Notes on Income and Substitution EffectsThe total effect of a price change is the
summation of the substitution and income effect.
The substitution and income effect can work in opposite direction of each other.
The income effect defines whether the good is an inferior good or a normal good.
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Inferior and Normal GoodsA normal good can be defined as a good
whose consumption has a positive correlation with the income effect.
An inferior good can be defined as a good whose consumption has a negative correlation with the income effect.
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Deriving DemandBy changing the price
of soda and examining the new equilibrium point, we can derive the demand curve for soda for an individual.
Summarizing the changing equilibrium example gives the following demand schedule for soda:
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Price of Soda Quantity Demanded of Soda
$0.50
$1.00
$2.00
10
5
2.5
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Price of Soda
Quantity of Soda
$0.50
$1.00
$2.00
2.5 5 10
•
•
•
Deriving Demand Cont.Now suppose we
change the price for soda on a continuous basis.Instead of points
on the graph, you would begin to see a curve like the following:
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P
Q
Demand curve for soda
Notes on DemandWe have seen that using the idea of a budget
constraint and utility function, we can derive a person’s demand schedule or curve.A demand schedule is a table that shows the
relationship between the quantity demanded of a good and its corresponding price.
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Notes on Demand Cont.When we derived demand, we only change
the price of the good we were investigating and the change in the quantity demanded for the good.Prices of the other good(s) and income were
held fixed.Any other variable that might affect the utility
function were held fixed also.
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Notes on Demand Cont.We can mathematically represent demand
for good i as the following:D(pi) = d(price of good i| price of all other
goods and income)D(pi) = d(pi| p1, p2, …, pi-1, pi+1, …, pn, M)
Where d(·) is a functional relationship that maps prices to quantities.
pi is the price of good i pj for j = 1,2, …, i-1, i+1, …, n are the prices of all
other good except good i M is the persons income.
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Other Demand DeterminantsBeside the price of the good, there are three
other major items that affect the demand curve:Income (M)Prices of other goods (pj)Tastes and preferences
This can either show up as a variable in the demand function or it can change the function altogether.
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How Income Affects DemandRemember that an increase in income shifts
the budget curve out, while a decrease in income shifts the budget curve in.
Does an increase in income imply that you will always increase demand for a good?No. It depends on whether the good is a
inferior or normal good.
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Inferior and Normal Goods RevisitedA good can be classified as a normal good if
the consumption for it has a positive correlation with income.I.e., when income increases, you consume
more of the good and when income decreases you consume less.
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Inferior and Normal Goods Revisited Cont.A good can be classified as an inferior good if
the consumption for it has a negative correlation with income.I.e., when income increases, you consume less
of the good and when income decreases you consume more.
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Inferior and Normal Goods Revisited Cont.A good can be both a normal good and an
inferior good.It all depends on where you are on the level of
consumption of the good and your income. Suppose you have $10 to use for buying food each
week. You might try living off spaghetti because you cannot afford steak.
What happens when your income doubles, you might find yourself eating more spaghetti and still no steak.
What happens if you have $100 to spend, you might begin to eat less spaghetti and start consuming steak.
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Engel’s CurveEngel’s curve tells you what happens to your
consumption of a good as you change your level of income.
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How Price Changes of Other Goods Change DemandThe demand curve for a particular good may
shift if the price of another good changes.How the demand curve shifts will depend on
whether the goods are substitutes, complements, or have no correlation.
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Substitute GoodGood j is said to be a substitute of good i if an
increase in the price of good j causes you to consume more of good i.
Good j is also said to be a substitute of good i if a decrease in the price of good j causes you to consume less of good i.I.e., the demand for product i is positively
correlated with the price of product j.
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Complementary GoodGood j is said to be a complement of good
i if an increase in the price of good j causes you to consume less of good i.
Good j is also said to be a complement of good i if a decrease in the price of good j causes you to consume more of good i.I.e., the demand for product i is negatively
correlated with the price of product j.
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Other Items that Affect the Demand CurveComposition of the PopulationAttitudes toward Nutrition and HealthFood SafetyLifestylesTechnological ForcesAdvertising
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Consumer SurplusConsumer surplus is a measure of the
difference between the amount of money a person was willing to pay to buy a quantity of good and the actual price they paid.
This measure is used as a tool in policy analysis.
Consumer surplus is represented graphically as the area underneath the demand curve above the price paid for the goods.
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P
Q
p = 5
q = 5
Consumer Surplus