chapter 3 consumer choice. chapter outline 4-2 1. preferences. 2. utility. 3. budget constraint. 4....

Chapter 3CONSUMER CHOICE

Chapter Outline4-2

1. Preferences.

2. Utility.

3. Budget Constraint.

4. Constrained Consumer Choice.

5. Behavioral Economics.

Premises of Consumer Behavior

The model of consumer behavior is based on the following premises:Individual preferences determine the amount of pleasure people derive from the goods and services they consume.Consumers face constraints or limits on their choices. Consumers maximize their well-being or pleasure from consumption, subject to the constraints they face.

Five Properties of Consumer Preferences

Completeness - when facing a choice between any two bundles of goods, a consumer can rank them so that one and only one of the following relationships is true: The consumer prefers the first bundle to the second, prefers the second to the first, or is indifferent between them.

Transitivity – a consumer’s preferences over bundles is consistent in the sense that, if the consumer weakly prefers Bundle z to Bundle y (likes z at least as much as y) and weakly prefers Bundle y to Bundle x, the consumer also weakly prefers Bundle z to Bundle x.

More Is Better - all else being the same, more of a commodity is better than less of it (always wanting more is known as nonsatiation). Good - a commodity for which more is

preferred to less, at least at some levels of consumption

Bad - something for which less is preferred to more, such as pollution

Concentrate on goods

Continuity- if a consumer prefers Bundle a to Bundle b, then the consumer prefers Bundle c to b is c is very close to a. The purpose of this assumption is to rule

out sudden preference reversals in response to small changes in the characteristics of a bundle

Strict Convexity- means that consumers prefer averages to extremes, i.e. more balanced baskets that have some of each good. For example if Bundle a and Bundle b are

distinct bundles and the consumer prefers both of these bundles to Bundle c, then the consumer prefers a weighted average of a and b, βa+(1-β)b, to Bundle c.

Preference Maps4-9

To summarize information about a consumer’s preferences is to create a graphical representation- a map-of them

Example: Each semester, Lisa, who lives for fast food, decides how many pizzas and burritos to eat.

The various bundles of pizzas and burritos she might consume are shown in panel a of Figure 3.1

Figure 3.1 Bundles of Pizzas and Burritos Lisa Might Consume

302515

Z, Pizzas per semester

302515

Which of these two bundles would be preferred by Lisa?

Lisa prefers bundle e over bundle d, since e has more of both goods: Pizza and Burritos

Lisa prefers bundle e to any bundle in area B

Which of these two bundles would be preferred by Lisa?

Lisa prefers bundle f over bundle e, since f has more of both goods: Pizza and Burritos

Lisa prefers any bundle in area A over e

If Lisa is indifferent between bundles e, a, and c …..

we can draw an indifferent curve over those three points

Indifference Curves

Indifference curve - the set of all bundles of goods that a consumer views as being equally desirable. The figure shows indifference curves that

are continuous (have no gaps). Indifference map - a complete set of

indifference curves that summarize a consumer’s tastes or preferences

Properties of Indifference Maps

1. Bundles on indifference curves farther from the origin are preferred to those on indifference curves closer to the origin. (more is better)

2. There is an indifference curve through every possible bundle.

3. Indifference curves cannot cross.4. Indifference curves slope downward.5. Indifference curves can not be thick.

Figure 3.1 Bundles of Pizzas and Burritos Lisa Might Consume

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we can draw an indifferent curve over those three points

Fig 3.2 Impossible Indifference Curves

Lisa is indifferent between e and a, and also between e and b… so by transitivity she

should also be indifferent between a and b…

but this is impossible, since b must be preferred to a given it has more of both goods. ( More-is-better)

Indifference curves can not cross: A given bundle cannot be on two indifference curves

Therefore, indifference curves must slope downward to the right

If they sloped upward, they would violate the assumption that more is preferred to less Some points that had more of both goods would be

indifferent to a basket with less of both goods

To consume more food, the consumer is willing to give up some units of clothing consumption and still get the same utility. In other words, if food consumption is decreased, the consumer needs to obtain more units of clothing to keep the same level of utility.

Impossible Indifference Curves

Lisa is indifferent between b and a since both points are in the same indifference curve… But this

contradicts the “more is better” assumption. Can you tell why?

Yes, b has more of both and hence it should be preferred over a.

Impossible Indifference Curves4-17

Solved Problem 3.14-18

Can indifference curves be thick? Answer:

Draw an indifference curve that is at least two bundles thick, and show that a preference property is violated

Consumer is indifferent between b and a since both points are in the same indifference curve… But this contradicts

the “more is better” assumption since b has more of both and hence it should be preferred over a.

Utility4-20

Utility - a set of numerical values that reflect the relative rankings of various bundles of goods.

utility function - the relationship between utility values and every possible bundle of goods.

U(B, Z)

Consumer Preferences

Utility A numerical score representing the

satisfaction that a consumer gets from a given market basket

If buying 3 copies of Microeconomics makes you happier than buying one shirt, then we say that the books give you more utility than the shirt

Utility Function: Example

Suppose that the utility Lisa gets from pizzas and burritos is

Question: Can we determine whether Lisa would be happier if she had Bundle x with 9 burritos and 16 pizzas or Bundle y with 13 of each?

Answer: The utility she gets from x is 12utils. The utility she gets from y is 13utils. Therefore, she prefers y to x.

Utility

Although we numerically rank baskets and indifference curves, numbers are ONLY for ranking

A utility of 4 is not necessarily twice as good as a utility of 2

There are two types of rankings Ordinal ranking Cardinal ranking

Ordinal Preferences

If we know only consumers’ relative rankings of bundles, our measure of pleasure is ordinal rather than cardinal

An ordinal measure is one that tells us the relative ranking of two things but does not tell us how much more one rank is than another

A cardinal measure is one by which absolute comparisons between ranks may be made

Utility measures are not unique

Willingness to Substitute between goods

Marginal Rate of Substitution- maximum amount of one good that a consumer will sacrifice (trade) to obtain one more unit of another good Slope of the indifference curve

Indifference curve is downward sloping, hence a negative MRS

We will use calculus to determine MRS at a point on Lisa’s indifference curve

Marginal Rate of Substitution

MRS at e = - slope of indifference curve at e

= - dB/dP=-dq2/dq1

Utility - Example

Food10 155

Clothing

U1 = 25

U2 = 50

U3 = 100A

Basket U = FC C 25 = 2.5(10) A 25 = 5(5) B 25 = 10(2.5)

Marginal Utility

MRS depends on how much extra utility Lisa gets from a little more of each good

marginal utility - the extra utility that a consumer gets from consuming the last unit of a good. the slope of the utility function as we hold the

quantity of the other good constant. Lisa’s utility function is:

UMU pizza

UMUburritos

Utility and Marginal Utility

As Lisa consumes more pizza, holding her consumption of burritos constant at 10, her total utility, U, increases… and her marginal

utility of pizza, MUZ, decreases (though it remains positive).

Marginal utility is the slope of the utility function as we hold the quantity of the other good constant.

l util

10987654321

(b) Marginal Utility

U = 20

Utility function, U (10, Z)

10987654321

(a) Utility

(a) MRS along an Indifference curve4-30

The MRS from bundle a to bundle b is -3. This is the same as the

slope of the indifference curve between those two points.

From b to c, MRS = -2. This is the same as the

slope of the indifference curve between those two points.

From bundle c to bundle d, Lisa is willing to give up 1 Burritos in exchange for 1 more Pizza…

From bundle a to bundle b, Lisa is willing to give up 3 Burritos in exchange for 1 more Pizza…

Indifference Curve Convex to the Origin

3 4 5 6

Marginal Rate of Substitution Indifference curves are typically convex

(bowed inward). As more of one good is consumed, a

consumer would prefer to give up fewer units of a second good to get additional units of the first one (property of diminishing MRS)

In other words, consumers generally prefer a balanced market basket

Marginal Rate of Substitution The MRS decreases as we move down

the indifference curve Along an indifference curve there is a

diminishing marginal rate of substitution. The MRS went from 3 to 2 to 1

At point a, the consumer has many units of burritos and few units of pizza and therefore, it is reasonable to assume that s/he may value pizza relatively more than burritos: s/he would give up a lot of burritos (3 units) to obtain 1 additional unit of pizza and still be able to keep the same level of utility.

However, at point c, s/he has few burritos and a lot of pizza. She’s only willing to give up a small amount of burritos for an additional unit of pizza, making the slope very flat. Therefore, it is reasonable to assume that MRS diminishes as we move down the indifference curve.

Diminishing MRS along an Indifference curve

Indifference Curve Convex to the Origin

3 4 5 6

(b) Marginal Rate of Substitution with concave indifference curves

From bundle a to bundle b, Lisa is willing to give up 2 Pizzas for 1 Burrito. Nevertheless,

from b to c she is willing to give up 3 Pizzas for 1 burrito.

This is very unlikely Could you think

(b) Indifference Curve Concave to the Origin

3 4 5 6

Diminishing marginal rate of substitution

When we have CONVEX preferences (as in the normal case) The marginal rate of substitution approaches zero as we move down and to the right along an indifference curve.

Discussion: could you imagine a good that does not exhibit this property?

Exercise:

Suppose that utility function of a consumer is give by U(F,C)= FC. Draw the indifference curve associated with a utility

level of 12 and the indifference curve associated with the utility level of 24.

Show that the indifference curves are convex. Use indifference curve for utility level 12 as an example to show this.

Find the equation for the indifference curve for utility level equal to 12 and find the MRS at (F,C) = (3,4).

Find the MRS at point (F,C) = (2,3). You will have to derive the equation for indifference curve that goes through the point first, then find the MRS at that point.

Willingness to Substitute between goodsSuppose more generally we have an indifference curve:

Then once we select a value for q1, then the point q2 is determined by the equation of the indifference curve, so we can write q2 as a function of q1, i.e. q2(q1)

(Example: U=FC; For utility=25, indifference curve is FC=25, or C=25/F)

Where U1 is MU of good 1

Marginal Utility and Consumer Choice It must be the case along an indifference

curve that

C)( MUF) (MU CF 0

No change in total utility along an indifference curve. Trade off of one good to the other leaves the consumer just as well off.

Marginal Utility and Consumer Choice Rearranging:

/MU MUMRS

MUMUFC

saycan We

Cfor F of /

Solved Problem 3.2

Suppose that Jackie has what is known as a Cobb-Douglas utility function:

where a is a positive constant, q1 is the number of CDs she buys a year and q2 is the number of movie DVDs she buys. What is her MRS?Answer:

Curvature of Indifference Curves.

Casual observation suggests that most people’s indifference curves are convex.

Exceptions:

Perfect substitutes - goods that a consumer is completely indifferent as to which to consume.

Perfect complements - goods that a consumer is interested in consuming only in fixed proportions

Figure 3.4a Perfect Substitutes

Bill views Coke and Pepsi as perfect substitutes: can you tell how his indifference curves would look like? Straight, parallel

lines with an MRS (slope) of −1.

Bill is willing to exchange one can of Coke for one can of Pepsi.

1 2 3 4

Pepsi, Cans per week

I 1 I2 I3 I 4

Figure 3.4b Perfect Complements

Pie, Slices per week

If she has only one piece of pie, she gets as much pleasure from it and one scoop of ice cream, a, as from it and two

scoops, d, or as from it and

three scoops, e.

EXERCISE

Suppose a consumer’s utility of consuming good-X and good-Y is given by

U(X,Y) = min{X,2Y} Where, X is the amount of good-X and Y is the

amount of good-Y. The function “min” is a function that chooses the smallest value in the bracket. For example min{2,3} =2, min(3,2}=2, min{100,3} =3.

Figure 3.4c Imperfect Substitutes

The standard-shaped, convex indifference curve in panel lies between these two extreme examples. Convex

indifference curves show that a consumer views two goods as imperfect substitutes.

Application: Indifference Curves Between Food and Clothing

Research has shown that at low (subsistence) levels of income (I1), there is little willingness to substitute between food and clothing.

Consumer Preferences: An Application

An analysis of consumer preferences would help to determine where to spend more on changes in car design: performance or styling

Some consumers will prefer better styling and some will prefer better performance in their car

These consumers

place a greater value on

performance than styling

Styling

Performance

These consumers place a greater value on styling

than performance

Styling

Performance

Problems: constructing indifference curves

1. Don is altruistic. Show the possible shape of his indifference curves between charity and all other goods.

2. Miguel considers tickets to the Houston Grand Opera and to Houston Astros baseball games to be perfect substitutes. Show his preference map.

3. If Joe views two candy bars and one piece of cake as perfect substitutes, what is his marginal rate of substitution between candy bars and cake?

Budget Constraint4-51

budget line (or budget constraint) - the bundles of goods that can be bought if the entire budget is spent on those goods at given prices.

opportunity set - all the bundles a consumer can buy, including all the bundles inside the budget constraint and on the budget constraint

Budget Constraint4-52

If Lisa spends all her budget, Y, on pizza and burritos, then

pBB + pZZ = Y

where pBB is the amount she spends on burritos and pZZ is the amount she spends on pizzas.

This equation is her budget constraint. It shows that her expenditures on burritos and pizza

use up her entire budget.

Budget Constraint (cont). How many burritos can Lisa buy?

To answer solve budget constraint for B (quantity of burritos):

Budget Constraint (cont). From previous slide we have:

If pZ = $1, pB = $2, and Y = $50, then:

B 25.0252$

)1($50$

Figure 3.5 Budget Constraint

B 25.0252$

)1($50$

From previous slide we have that if:

– pZ = $1, pB = $2, and Y = $50, then the budget constraint, L1, is:

Opportunity set

50 = Y /pZ

25 = Y/pB

100 30

Amount of Burritos consumed if all income is allocated for Burritos.

Amount of Pizza consumed if all income is allocated for Pizza.

Budget Constraints: Budget Line

Letting x and y be the goods on the x- and y-axis respectively: The vertical intercept, I/Py, illustrates the maximum

amount of good y that can be purchased with income I

The horizontal intercept, I/Px, illustrates the maximum amount of x that can be purchased with income I

The slope of the line measures the relative cost of food and clothing; it’s the relative price of the good on the x-axis.

The slope is the negative of the ratio of the prices of the two goods; it’s –Px/Py

The Slope of the Budget Constraint

We have seen that the budget constraint for Lisa is given by the following equation:

The slope of the budget line is also called the marginal rate of transformation (MRT) rate at which Lisa can trade burritos for pizza in the

marketplace

Slope = B/Z = MRT

Table: Allocations of a $50 Budget Between Burritos and Pizza

(a) Changes in the Budget Constraint: An increase in the Price of Pizzas.

L1 (pZ = $1)

L2 (pZ = $2)

B = YPB

- PZ = $1

If the price of Pizza doubles, (increases from $1 to $2) the slope of the budget line increases

This area represents the bundles she can no longer afford!!!

$2Slope = -$1/$2 = -0.5

Slope = -$2/$2 = -1

(b) Changes in the Budget Constraint: Increase in Income (Y)

L3 (Y = $100)

L1 (Y = $50)

B = $50PB

- PZ PB

If Lisa’s income increases by $50 the budget line shifts to the right (with the same slope!)

This area represents the new consumption bundles she can now afford!!!

Solved Problem4-61

A government rations water, setting a quota on how much a consumer can purchase. If a consumer can afford to buy 12 thousand gallons a month but the government restricts purchases to no more than 10 thousand gallons a month, how does the consumer’s opportunity set change?

Solved Problem4-62

Figure 3.6 (a) Consumer Maximization: Interior Solution

Would Lisa be able to consume any bundle along I3 (i.e. bundle f)? No! Lisa does not have

enough income to afford any bundle along I3

rr ito

5030100

I1I2I3

Would Lisa be able to consume any bundle along I1? Yes; she could afford

bundles d, c, and a.

Bundle e is called a consumer’s optimum. If Lisa is consuming this

bundle, she has no incentive to change her behavior by substituting

one good for another.

Consumer Maximization: Interior Solution

The budget constraint and the indifference curve have the same slope at the point e where they touch. Therefore, at point e:

Slope of I2

rr ito

Slope of BL

Figure 3.6 (b) Consumer Maximization: Corner Solution

Budget line

Nigel, a Brit, and Bob, a Yank, have the same tastes, and both are indifferent between a sports utility vehicle (SUV) and a luxury sedan. Each has a budget that will allow him to buy and operate one vehicle for a decade. For Nigel, the price of owning and operating an SUV is greater than that for the car. For Bob, an SUV is a relative bargain because he benefits from lower gas prices and can qualify for an SUV tax break. Use an indifference curve–budget line analysis to explain why Nigel buys and operates a car while Bob chooses an SUV.

Figure 3.7 Optimal Bundles on Convex Sections of Indifference Curves

Maximizing utility subject to a constraint using calculus

Lisa’s objective is to maximize her utility, U(q1, q2), subject to (s.t.) her budget constraint:

Here the control variables are q1 and q2. Lisa has no control over the prices she

faces, p1 and p2, or her income, Y. Two methods of solving the problem. We’ll

focus on the substitution method only.

Substitution

First, we can substitute the budget constraint into the utility function. Using algebra we can rewrite the budget constraint as q1 = (Y-p2q2)/p1 and substitute this expression for q1 in the utility function

Using standard maximization techniques we can solve this problem. (i.e. take the first derivative of the utility function with respect to q2 and set it equal to zero)

Substitution

By rearranging terms in the above equation, we get the same condition for an optimum that we obtained using a graphical approach.

When we combine the MRS=MRT condition with the budget constraint we have two equations in two unknowns , q1 and q2. So we can solve for the optimal q1 and q2 as function of prices, p1 and p2, and income

Minimizing Expenditure

We have shown how Lisa chooses quantities of goods so as to maximize her utility subject to a budget constraint.

There is a related or dual constrained maximization problem where she finds the combination of goods that achieve a particular level of utility for the least expenditure.

Earlier we showed that Lisa maximized her utility by picking a bundle of q1 = 30 and q2 = 10 at the indifference curve I2

Now we see: How can Lisa make the lowest possible expenditure to maintain her utility at a particular level which corresponds to indifference curve I2?

Fig. 3.8 Minimizing Expenditure4-73

The figure shows three possible budget lines corresponding to budgets or expenditures E1, E2 and E3.E1 lies below I2. E2 and E3 both cross I2. However the BL with E2 is the least expensive way for her to stay on I2.

The rule for minimizing expenditure while achieving a given level of utility is to choose the lowest expenditure such that the budget line touches-is tangent to-the relevant indifference curve

Minimizing Expenditure

Solving either of the two problems yields the same optimal values.

More useful to use the expenditure minimizing approach

We can use calculus to solve the expenditure minimizing problem

The solution of this problem gives us the expenditure function: the relationship showing the minimal expenditures necessary to achieve a specific utility level for a given set of prices.

Food Stamps4-75

Nearly 11% of U.S. households worry about having enough money to buy food and 3.3% report that they suffer from inadequate food (Sullivan and Choi, 2002).

Households that meet income, asset, and employment eligibility requirements receive coupons that can be used to purchase food from retail stores.

Food Stamps (cont).4-76

The Food Stamps Program is one of the nation’s largest social welfare programs with expenditures of $33.1 billion for nearly 29.1 million people in 2006.

Would a switch to a comparable cash subsidy increase the well-being of food stamp recipients? Would the recipients spend less on food

and more on other goods?

Food Stamps Versus Cash

Y Y + 100

Y + 100

Food per month

Budget line withfood stamps

Budget line with cash

Originalbudget line

Behavioral Economics4-78

behavioral economics - by adding insights from psychology and empirical research on human cognition and emotional biases to the rational economic model, economists try to better predict economic decision making

chapter 3 consumer choice. chapter outline 4-2 1. preferences. 2. utility. 3. budget constraint. 4....

bundle e

bundle b

bundle c

bundle z

bundle y

bundle f

bundle d

bundles e

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