平狄克微观经济学第六版第三章课后答案

PART II

PRODUCERS, CONSUMERS, AND COMPETITIVE MARKETS

CHAPTER 3

CONSUMER BEHAVIOR

Chapter 3 builds the foundation for deriving the demand curve in Chapter 4. In order to

understand demand theory, students must have a firm grasp of indifference curves, the marginal rate

of substitution, the budget line, and optimal consumer choice. It is possible to discuss consumer choice

without going into extensive detail on utility theory. Many students find utility functions to be a more

abstract concept than preference relationships. However, if you plan to discuss uncertainty in Chapter

5, you will need to cover marginal utility (section 3.5). Even if you cover utility theory only briefly,

make sure students are comfortable with the term utility because it appears frequently in Chapter 4.

When introducing indifference curves, stress that physical quantities are represented on the

two axes. After discussing supply and demand, students may think that price should be on the vertical

axis. To illustrate the indifference curves, pick an initial bundle on the graph and ask which other

bundles are likely to be more preferred and less preferred to the initial bundle. This will divide the

graph into four quadrants, and it is then easier for students to figure out the set of bundles between

which the consumer is indifferent. It is helpful to present a lot of examples with different types of

goods and see if the class can figure out how to draw the indifference curves. The examples are also

useful for explaining the significance of the assumptions made about preferences. In presenting

different examples, you can ask which assumption would be violated.

Explaining utility follows naturally from the discussion of indifference curves. Though an

abstract concept, it is possible to get students to understand the basic idea without spending too much

time on the topic. You might point out that we as consumers have a goal in life, which is to maximize

our utility subject to our budget constraint. When we go to the store we pick the basket that we like

best and that stays within our budget. From this we derive demand curves. Emphasize that it is the

ranking that is important and not the utility number, and point out that if we can graph an indifference

curve we can certainly find an equation to represent it. Finally, what is most important is the rate at

which consumers are willing to exchange goods (the marginal rate of substitution) and this is based on

the relative satisfaction that they derive from each good at any particular time.

The marginal rate of substitution, MRS, can be confusing to students. Some confuse the MRS

with the ratio of the two quantities. If this is the case, point out that the slope is equal to the ratio of the rise, ?Y, and the run, ?X. This ratio is equal to the ratio of the intercepts of a line just tangent to the indifference curve. As we move along a convex indifference curve, these intercepts and the MRS

change. Another problem is the terminology “of X for Y.” This is confus ing because we are not

substituting “X for Y,” but Y for one unit of X. You may want to present a variety of examples in class

to explain this important concept.

1. What are the four basic assumptions about individual preferences? Explain the

significance or meaning of each.

(1) Preferences are complete: this means that the consumer is able to compare and

rank all possible baskets; (2) Preferences are transitive: this means that preferences

are consistent, in that if bundle A is preferred to bundle B and bundle B is preferred

to bundle C, then we should be able to conclude that bundle A is preferred to bundle

C; (3) More is preferred to less: this means that all goods are desirable, and that the

consumer will always prefer to have more of a good; (4) Diminishing marginal rate

of substitution: this means that indifference curves are convex, and that the slope of

the indifference curve increases (becomes less negative) as we move down along the

curve. As a consumer moves down along her indifference curve she is willing to give

up fewer units of the good on the vertical axis in exchange for one more unit of the

good on the horizontal axis. This assumption also means that balanced market

baskets are preferred to baskets that have a lot of one good and very little of the

other good.

2. Can a set of indifference curves be upward sloping? If so, what would this tell you about the two goods?

A set of indifference curves can be upward sloping if we violate assumption number

three; more is preferred to less. When a set of indifference curves is upward sloping,

it means one of the goods is a “bad” in that the consumer prefers less of the good

rather than more of the good. The positive slope means that the consumer will

accept more of the bad good only if she also receives more of the other good in return.

As we move up along the indifference curve the consumer has more of the good she

b.Draw a set of indifference curves for Jon.

Since Jon is always willing to trade one can of coke for one can of sprite, his

indifference curves are linear with a slope of –1.

c.Draw two budget lines with different slopes and illustrate the satisfaction-

maximizing choice. What conclusion can you draw?

Jon’s indifference curves are linear with a slope of –1. Jon’s budget line is also

linear, and will have a slope that reflects the ratio of the two prices. If Jon’s budget

line is steeper than his indifference curves then he will choose to consume only the

good on the vertical axis. If Jon’s b udget line is flatter than his indifference curves

then he will choose to consumer only the good on the horizontal axis. Jon will

always choose a corner solution, unless his budget line has the same slope as his

indifference curves. In this case any combination of Sprite and Coke that uses up

his entire income with maximize his satisfaction.

5. What happens to the marginal rate of substitution as you move along a convex indifference curve? A linear indifference curve?

The MRS measures how much of a good you are willing to give up in exchange for one

more unit of the other good, keeping utility constant. The MRS diminishes along a

convex indifference curve in that as you move down along the indifference curve, you

are willing to give up less and less of the one good in exchange for the other. The

MRS is also the slope of the indifference curve, which increases (becomes less

negative) as you move down along the indifference curve. The MRS is constant

along a linear indifference curve, since in this case the slope does not change. The

consumer is always willing to trade the same number of units of one good in

exchange for the other.

6. Explain why an MRS between two goods must equal the ratio of the price of the goods for the consumer to achieve maximum satisfaction.

The MRS describes the rate at which the consumer is willing to trade one good for

another to maintain the same level of satisfaction. The ratio of prices describes the

trade-off that the market is willing to make between the same two goods. The

tangency of the indifference curve with the budget line represents the point at which

the trade-offs are equal and consumer satisfaction is maximized. If the MRS between

two goods is not equal to the ratio of prices, then the consumer could trade one good for

another at market prices to obtain higher levels of satisfaction. For example, if the

slope of the budget line (the ratio of the prices) is –4 then the consumer can trade 4

units of good 2 for one unit of good 1. If the MRS at the current bundle is –6, then the

consumer is willing to trade 6 units of good 2 for one unit of good 1. Since the two

slopes are not equal the consumer is not maximizing her satisfaction. The consumer is

willing to trade 6 but only has to trade 4, so she should make the trade. This trading

continues until the highest level of satisfaction is achieved. As trades are made, the

MRS will change and become equal to the price ratio.

7. Describe the indifference curves associated with two goods that are perfect substitutes. What if they are perfect complements?

Two goods are perfect substitutes if the MRS of one for another is a constant number.

Given the MRS is a constant number, the slope of the indifference curves will be

constant, and the indifference curves are therefore linear. If two goods are perfect

complements, the indifference curves are L-shaped. In this case the consumer

wants to consume the two goods in a fixed proportion, say one unit of good 1 for every

1 unit of good 2. If she has more of one good but not more of the other then she does

not get any extra satisfaction.

8. What is the difference between ordinal utility and cardinal utility? Explain why the assumption of cardinal utility is not needed in order to rank consumer choices.

Ordinal utility implies an ordering among alternatives without regard for intensity of

preference. For example, if the consumer’s first choice is preferred to their second

choice, then utility from the first choice will be higher than utility from the second

choice. How much higher is not important. An ordinal utility function generates a

ranking of bundles and no meaning is given to the utility number itself. Cardinal

utility implies that the intensity of preferences may be quantified, and that the utility

number itself has meaning. An ordinal ranking is all that is needed to rank consumer

choices. It is not necessary to know how intensely a consumer prefers basket A over

basket B; it is enough to know that A is preferred to B.

9. Upon merging with the West German economy, East German consumers indicated a preference for Mercedes-Benz automobiles over Volkswagens. However, when they converted their savings into deutsche marks, they flocked to Volkswagen dealerships. How can you explain this apparent paradox?

Three assumptions are required to address this question: 1) that a Mercedes costs more

than a Volkswagen; 2) that the East German consumers’ utility function comprises two

goods, automobiles and all other goods evaluated in deutsche marks; and 3) that East

Germans have incomes. Based on these assumptions, we can surmise that while East

German consumers may prefer a Mercedes to a Volkswagen, they either cannot afford a

Mercedes or they prefer a bundle of other goods plus a Volkswagen to a Mercedes alone.

While the marginal utility of consuming a Mercedes exceeds the marginal utility of

consuming a Volkswagen, the consumer will consider marginal utility per dollar for

each good. This means the marginal utility per dollar must have been higher for the

Volkswagen since consumers flocked to the Volkswagen dealerships and not the

Mercedes dealerships.

10. Draw a budget line and then draw an indifference curve to illustrate the satisfaction maximizing choice associated with two products. Use your graph to answer the following questions.

a.Suppose that one of the products is rationed. Explain why the consumer is likely

to be worse off.

When goods are not rationed, the consumer is able to choose the satisfaction-

maximizing bundle where the slope of the budget line is equal to the slope of the

indifference curve, or the price ratio is equal to the MRS. This is point A in the graph

below. If good 1 is now rationed the consumer will not be able to attain the utility

maximizing point. He or she will have to consume more of the other good instead.

This is point B below.

b.Suppose now that the price of one of the products is fixed at a level below the

current price. As a result, the consumer is not able to purchase as much as she would like of the product. Can you tell if the consumer is better off or worse off?

When the price of the good is fixed at a level below the current (equilibrium) price,

there will be a shortage of the good and the good will have to be effectively rationed.

As in the question above, the consumer is worse off because she is not able to attain

her utility maximizing point.

11. Based on his preferences, Bill is willing to trade 4 movie tickets for 1 ticket to a basketball game. If movie tickets cost $8 each and a ticket to the basketball game costs $40, should Bill make the trade? Why or why not?

No Bill should not make the trade. If he gives up the 4 movie tickets then he will

save $8 per ticket for a total of $32. However, this is not enough for a basketball

ticket. He would in fact have to give up 5 movie tickets if he wanted to buy another

basketball ticket. Notice also, that the marginal utility per dollar is higher for movie

tickets so Bill will be better off if he consumes more movie tickets and fewer

basketball tickets. To figure this out recall that what Bill is willing to do defines his

MRS. His MRS is 4 so this means that the marginal utility of a basketball game is 4

and the marginal utility of a movie is 1:

MRS=-4=-

MU

ball

MU

movie

=-

4

1

.

Now the marginal utility per dollar can be computed:

MU

ball P

ball =

4

40

=

1

10

MU

movie P

movie =

1

8

.

12. Describe the equal marginal principle. Explain why this principle may not hold if increasing marginal utility is associated with the consumption of one or both goods.

The equal marginal principle states that the ratio of the marginal utility to price must

be equal across all goods to obtain maximum satisfaction. In other words, utility

maximization is achieved when the budget is allocated so that the marginal utility per

dollar of expenditure is the same for each good. If the marginal utility per dollar is not

equal then utility can be increased by allocating more dollars to the good with the

higher marginal utility per dollar. The consumer will obtain more “bang for the buck”

if they reallocate their dollars.

If marginal utility is increasing, the consumer maximizes satisfaction by consuming

ever larger amounts of the good. Thus, the consumer would spend all income on one

good, assuming a constant price, resulting in a corner solution. With a corner solution,

the equal marginal principle cannot hold.

13. The price of computers has fallen substantially over the past two decades. Use this drop in price to explain why the Consumer Price Index is likely to overstate substantially the cost-of-living index for individuals who use computers intensively.

The consumer price index measures the cost of a typical basket of goods purchased by

the consumer in the current year relative to the cost of the basket in the base year.

Each good in the basket is assigned a weight, which reflects the importance of the good

to the consumer, and the weights are kept fixed from year to year. The problem with

fixing the weights is that consumers will shift their purchases from year to year to give

more weight to goods whose prices have fallen, and less weight to goods whose prices

have risen. The CPI will therefore give too much weight to goods whose prices have

risen, and too little weight to goods whose prices have fallen. For the individual who

uses computers intensively, the fixed weight for computers in the basket will

understate the importance of this good, and will hence understate the effect of the fall

in the price of computers. The CPI will overstate the rise in the cost of living for this

type of individual.

14. Explain why the Paasche index will generally understate the ideal cost-of-living index.

The Paasche index measures the current cost of the current bundle of goods relative

to the base year cost of the current bundle of goods. The Paasche index will

understate the ideal cost of living because it assumes the individual will buy the

current year bundle in the base period. In reality, at base year prices the consumer

would have been able to attain the same level of utility at a lower cost by altering

their consumption bundle. Since the base year cost is overstated, the denominator

will be larger and the index will be lower, or understated.

1. In this chapter, consumer preferences for various commodities did not change during the analysis. Yet in some situations, preferences do change as consumption occurs. Discuss why and how preferences might change over time with consumption of these two commodities:

a. cigarettes

The assumption that preferences do not change is a reasonable one if choices are

independent across time. It does not hold, however, when “habit-forming” or addictive

behavior is involved, as in the case of cigarettes: the consumption of cigarettes in one

period influences their consumption in the next period.

b. dinner for the first time at a restaurant with a special cuisine

This example is parallel to examples of adventure seeking. For some, a new dining

experience creates enthusiasm to seek out more exciting and different cuisines and

dishes. For others, they develop a fondness for regularity and consistency or fear of

the new and unknown. In either of these cases, choices change as consumption occurs.

2. Draw indifference curves that represent the following individuals’ preferences for hamburgers and soft drinks. Indicate the direction in which the individuals’ satisfaction (or utility) is increasing.

a.Joe has convex preferences and dislikes both hamburgers and soft drinks.

Since Joe dislikes both goods, his set of indifference curves will be bowed inwards

towards the origin instead of outwards, as in the normal case where more is preferred

to less. Given he dislikes both goods, his satisfaction is increasing in the direction of

the origin. Convexity of preferences implies his indifference curves will have the

normal shape in that they are bowed towards the direction of increasing satisfaction.

Convexity also implies that given any two bundles between which the consumer is

indifferent, the “average” of the two bundles will be in the preferred set, or wi ll leave

him at least as well off.

so ft dr in k

b.Jane loves hamburgers and dislikes soft drinks. If she is served a soft drink, she

will pour it down the drain rather than drink it.

Since Jane can freely dispose of the soft drink if it is given to her, she considers it to be a

neutral good. This means she does not care about soft drinks one way or the other.

With hamburgers on the vertical axis, her indifference curves are horizontal lines. Her

so ft dr in k

c.Bob loves hamburgers and dislikes soft drinks. If he is served a soft drink, he will

drink it to be polite.

Since Bob will drink the soft drink in order to be polite, it can be thought of as a “bad”.

When served another soft drink, he will require more hamburgers at the same time

in order to keep his satisfaction constant. More soft drinks without more

hamburgers will worsen his utility. More hamburgers and fewer soft drinks will

increase his utility.

s o ft d rin k

d.Molly loves hamburgers and soft drinks, but insists on consuming exactly one soft

drink for every two hamburgers that she eats.

Molly wants to consume the two goods in a fixed proportion so her indifference curves

are L-shaped. For any given amount of one good, she gets no extra satisfaction from

having more of the other good. She will only increase her satisfaction if she has

more of both goods.

s o ft d rin k

e.Bill likes hamburgers, but neither likes nor dislikes soft drinks.

Like Jane, Bill considers soft drinks to be a neutral good. Since he does not care

about soft drinks one way or the other we can assume that no matter how many he

has, his utility will be the same. His level of satisfaction depends entirely on how

s o ft d rin k

f.Mary always gets twice as much satisfaction from an extra hamburger as she does

from an extra soft drink.

How much extra satisfaction Mary gains from an extra hamburger or soft drink tells

us something about the marginal utilities of the two goods, or about her MRS. If she

always receives twice the satisfaction from an extra hamburger then her marginal

utility from consuming an extra hamburger is twice her marginal utility from

consuming an extra soft drink. Her MRS, with hamburgers on the vertical axis, is

1/2.

so ft dr in k

3. If Jane is currently willing to trade 4 movie tickets for 1 basketball ticket then she must like basketball better than movies. True or false? Explain.

This statement is not necessarily true. If she is always willing to trade 4 movie

tickets for 1 basketball ticket then yes she likes basketball better because she will

always gain the same satisfaction from 4 movie tickets as she does from 1 basketball

ticket. However, it could be that she has convex preferences (diminishing marginal

rate of substitution) and is at a bundle where she has a lot of movie tickets relative to

basketball tickets. This would make her willing to give up more movie tickets to get

another basketball ticket. It would not mean though that she liked basketball better.

Her willingness to give up a good would in this case depend on the quantity of each

good in her current basket.

4. Janelle and Brian each plan to spend $20,000 on the styling and gas mileage features of a new car. They can each choose all styling, all gas mileage, or some combination of the two. Janelle does not care at all about styling and wants the best gas mileage possible. Brian likes both equally and wants to spend an equal amount on the two features. Using indifference curves and budget lines, illustrate the choice that each person will make.

Assume styling is on the vertical axis and gas mileage is on the horizontal axis.

Janelle has indifference curves that are vertical. If the styling is there she will take

it, but she otherwise does not care about it. As her indifference curves move over to

the right, she gains more gas mileage and more satisfaction. She will spend all

$20,000 on gas mileage. Brian has indifference curves that are L-shaped. He will

not spend more on one feature than on the other feature. He will spend $10,000 on

styling and $10,000 on gas mileage.

5. Suppose that Bridget and Erin spend their income on two goods, food (F) and clothing

(C). Bridget’s preferences are represented by the utility function U(F,C)=10FC, while Erin’s preferences are represented by the utility function U(F,C)=.20F2C2.

a.On a graph, with food on the horizontal axis and clothing on the vertical axis,

identify the set of points that give Bridget the same level of utility as the bundle (10,5). Do the same for Erin on a separate graph.

Bridget receives a utility of 10*10*5=500 from this bundle. The indifference curve is

represented by the equation 10FC=500 or FC=50. Some bundles on this indifference

curve are (5,10), (10,5), (25,2), and (2,25). Erin receives a utility

of .2*10*10*5*5=500 from the bundle (10,5). Her indifference curve is represented

by the equation 500=.2F2C2, or 50=FC. This is the same indifference curve as

Bridget. Both indifference curves have the normal, convex shape.

b.On the same two graphs, identify the set of bundles that give Bridget and Erin the

same level of utility as the bundle (15,8).

For each person, plug in F=15 and C=8 into their respective utility functions. For

Bridget, this gives her a utility of 1200, so her indifference curve is given by the

equation 10FC=1200, or FC=120. Some bundles on this indifference curve are

(12,10), (10,12), (3,40), and (40,3). For Erin, this bundle gives her a utility of 2880,

so her indifference curve is given by the equation 2880=.2F2C2, or FC=120.

This is the same indifference curve as Bridget.

c.Do you think Bridget and Erin have the same preferences or different preferences?

Explain.

They have the same preferences because for any given bundle they have the same

level of utility. This means that they will rank all bundles in the same order. Note

however, that it is not necessary that they receive the same level of utility to have the

same set of preferences. All that is necessary is that they rank the bundles in the

same order.

6. Suppose that Jones and Smith have each decided to allocate $1,000 per year to an entertainment budget in the form of hockey games or rock concerts. They both like hockey games and rock concerts and will choose to consume positive quantities of both goods. However, they differ substantially in their preferences for these two forms of entertainment. Jones prefers hockey games to rock concerts, while Smith prefers rock concerts to hockey games.

a. Draw a set of indifference curves for Jones and a second set for Smith.

Given they each like both goods and they will each choose to consume positive

quantities of both goods, we can assume their indifference curves have the normal

convex shape. However since Jones has an overall preference for hockey and Smith

has an overall preference for rock concerts, their two sets of indifference curves will

have different slopes. Suppose that we place rock concerts on the vertical axis and

hockey games on the horizontal axis, Jones will have a larger MRS than Smith.

Jones is willing to give up more rock concerts in exchange for a hockey game since he

prefers hockey games. The indifference curves for Jones will be steeper.

b. Using the concept of marginal rate of substitution, explain why the two sets of

curves are different from each other.

At any combination of hockey games and rock concerts, Jones is willing to give up more

rock concerts for an additional hockey game, whereas, Smith is willing to give up fewer

rock concerts for an additional hockey game. Since the MRS is a measure of how many

of one good (rock concerts) an individual is willing to give up for an additional unit of

the other good (hockey games), then the MRS, and hence the slope of the indifference

curves, will be different for the two individuals.

7. The price of DVDs (D) is $20 and the price of CDs (C) is $10. Philip has a budget of $100 to spend on the two goods. Suppose that he has already bought one DVD and one CD. In addition there are 3 more DVDs and 5 more CDs that he would really like to buy.

a.Given the above prices and income, draw his budget line on a graph with CDs on

the horizontal axis.

His budget line is P

D D+P

C

C=I, or 20D+10C=100. If he spends his entire income

on DVD’s he could afford to buy 5. If he spends his entire income on CD’s he could

afford to buy 10.

b.Considering what he has already purchased, and what he still wants to purchase,

identify the three different bundles of CDs and DVDs that he could choose.

Assume that he cannot purchase fractional units for this part of the question.

Given he has already purchased one of each, for a total of $30, he has $70 left. Since

he wants 3 more DVD’s he can buy these for $60 and spend his remaining $10 on 1

CD. This is the first bundle below. He could also choose to buy only 2 DVD’s for

$40 and spend the remaining $30 on 3 CD’s. He can choose the following bundles: Purchased Quantities Total Quantities

D C D C

3 1 2 6

2 3 3 4

1 5 4 2

8. Anne has a job that requires her to travel three out of every four weeks. She has an annual travel budget and can either travel by train or by plane. The airline she typically flies with has a frequent traveler program that reduces the cost of her tickets depending on the number of miles she has flown in a given year. When she reaches 25,000 miles the airline will reduce the price of her tickets by 25% for the remainder of the year. When she reached 50,000 miles, the airline will reduce the price of her tickets by 50% for the remainder of the year. Graph Anne’s budget line, with train miles on the vertical axis and plane miles on the horizontal axis.

The typical budget line is linear (with a constant slope) because the prices of the two

goods do not change as the consumer buys more or less of a particular good. In this

case, the price of airline miles will change depending on how many miles she

purchases. As the price changes, the slope of the budget line will change. Since

there are three prices, there will be three slopes, or two kinks, to the budget line.

Since the price falls as she flies more miles, the budget line will become flatter with

every price change. See the graph in the problem below.

9. Debra usually buys a soft drink when she goes to a movie theater, where she has a choice of three sizes: the 8 ounce drink costs $1.50, the 12 ounce drink, $2.00, and the 16 ounce drink, $2.25. Describe the budget constraint that Debra faces when deciding how many ounces of the drink to purchase. (Assume that Debra can costlessly dispose of any of the soft drink that she does not want.

First notice that as the size of the drink increases, the price per ounce decreases.

When she buys the 8-ounce soft drink she pays $1.50

8oz

$0.19 per oz.When she

buys the 12-ounce size she pays $0.17 per ounce, and when she buys the 16-ounce size, she pays $0.14 per ounce. Given that there are three different prices per ounce of soft drink, the budget line will have two kinks in it, as illustrated below. Notice that at each kink, the slope of the budget line gets flatter (due to the decreasing cost per ounce relative to the “other good” on the vertical axis).

O u n ces o f

S o ft D rin k 81216

10. Antonio buys 5 new college textbooks during his first year at school at a cost of $80 each. Used books cost only $50 each. When the bookstore announces that there will be a 10% increase in the price of new books and a 5% increase in the price of used books, Antonio’s father offers him $40 extra.

a.What happens to Antonio’s budget line? Illustrate the change with new books on

the vertical axis.

In the first year he spends $80 each on 5 new books for a total of $400. For the same

amount of money he could have bought 8 used textbooks. His budget line is

therefore 80*New+50*Used=400. After the price change, new books cost $88, used

books cost $52.5, and he has an income of $440. If he spends all of his income on

new books, he can still afford to buy 5 new books, but can now afford to buy 8.4 used

books if he buys only used books. The new budget line is 88*New+52.5*Used=440.

The budget line has changed its slope and become flatter if we place used books on

the horizontal axis.

b.Is Antonio worse or better off after the price change? Explain.

The first year he bought 5 books at a cost of $80 each for a total of $400. The new

price of books is $88 and the cost of 5 new books is now $440. The $40 extra income

will cover the price increase. Antonio is definitely not worse off since he can still

afford the same number of new books. He may in fact be better off if he decides to

switch to used books.

11. Consumers in Georgia pay twice as much for avocados as they do for peaches. However, avocados and peaches are equally priced in California. If consumers in both states maximize utility, will the marginal rate of substitution of peaches for avocados be the same for consumers in both states? If not, which will be higher?

The marginal rate of substitution of peaches for avocados is the amount of avocados

that a person is willing to give up to obtain one additional peach. When consumers

maximize utility, they set their marginal rate of substitution equal to the price ratio,

which in this case is

P

peach

P

avocado

.In Georgia, P

avoca do

=2P

peach

, which means that when

consumers are maximizing utility, MR S=

P

peach

P

avoca do

=

1

2

.In California,

P

avoca do =P

peach

, which means that when consumers are maximizing utility,

MRS=

P

peach

P

avoca do

=

1

1

.The marginal rate of substitution is therefore not the same in

both states, and will be higher in California.

12. Ben allocates his lunch budget between two goods, pizza and burritos.

a.Illustrate Ben’s optimal bundle on a graph with pizza on the horizontal axis.

This is the standard graph, where Ben’s budget line is linear and he consumes at the

point where his indifference curve is tangent to his budget line. This places him on

the highest possible indifference curve.

b.Suppose now that pizza is taxed, causing the price to increase by 20%. Illustrate

Ben’s new optimal bundle.

When the price of pizza increases, the budget line will pivot inwards. This will

shrink the size of Ben’s bu dget set and he will no longer be able to afford his old

bundle. His new optimal bundle is where the indifference curve is tangent to his

new budget line and this indifference curve is below his original indifference curve.

c.Suppose instead that pizza i s rationed at a quantity less than Ben’s desired

quantity. Illustrate Ben’s new optimal bundle.

Rationing the quantity of pizza that can be purchased will result in Ben not being

able to choose his optimal bundle. He will have to choose a bundle on the budget

line that is above his original bundle. This new bundle will have a lower level of

utility.

13. Brenda wants to buy a new car and has a budget of $25,000. She has just found a magazine that assigns each car an index for styling and an index for gas mileage. Each index runs from 1-10, with 10 representing either the most styling or the best gas mileage. While looking at the list of cars, Brenda observes that on average, as the style index rises by one unit, the price of the car increases by $5,000. She also observes that as the gas mileage index rises by one unit, the price of the car increases by $2,500.

a.Illustrate the various combinations of style (S) and gas mileage (G) that Brenda

could select with her $25,000 budget. Place gas mileage on the horizontal axis.

For every $5,000 she spends on style the index rises by one so the most she can

achieve is a car with a style index of 5. For every $2,500 she spends on gas mileage,

the index rises by one so the most she can achieve is a car with a gas mileage index of

10. The slope of her “budget line” is -1/2.

b.Suppose Brenda’s preferences are such that she always receives three times as

much satisfaction from an extra unit of styling as she does from gas mileage.

What type of car will Brenda choose?

If Brenda always receives three times as much satisfaction from an extra unit of

styling as she does from an extra unit of gas mileage then she is willing to trade one

unit of styling for three units of gas mileage, and still maintain the same level of

satisfaction. This is her MRS or the slope of her indifference curves, which is

constant. Since the MRS is 1/3 and the slope of her budget line is -1/2, Brenda will

choose all styling. You can also compute the marginal utility per dollar for styling

and gas mileage and note that styling will be higher. In the graph below, she will

move up to the highest possible indifference curve where she chooses all styling and

no gas mileage.

c.Suppose that Bre nda’s marginal rate of substitution (of gas mileage for styling)

was equal to

S

4G

. What value of each index would she like to have in her car?

To find the optimal value of each index, set MRS equal to the price ratio of 1/2 and

cross multiply to get S=2G. Now substitute into the budget 5000S+2500G=25000 to

get G=2 and S=4.

d.Suppose that Brenda’s marginal rate of substitution (of gas mileage for styling)

was equal to 3S

G

. What value of each index would she like to have in her car?

To find the optimal value of each index set MRS equal to the price ratio of 1/2 and

cross multiply to get G=6S. Now substitute into the budget 5000S+2500G=25000 to

get G=7.5 and S=1.25.

14. Connie has a monthly income of $200, which she allocates between two goods: meat and potatoes.

a. Suppose meat costs $4 per pound and potatoes cost $2 per pound. Draw her budget

constraint.

Let M = meat and P= potatoes. Connie’s budget constraint is

$200 = 4M + 2P, or

M = 50 - 0.5P.

As shown in the figure below, with M on the vertical axis, the vertical intercept is 50.

The horizontal intercept may be found by setting M = 0 and solving for P.

$2 per pound), she gets the next 10 pounds for free. This offer applies only to the first 20 pounds she buys. All potatoes in excess of the first 20 pounds (excluding bonus potatoes) are still $2 per pound. Draw her budget constraint.

Assume that potatoes are on the horizontal axis. Connie’s budget constraint has a

slope of –1/2 until Connie has purchased twenty pounds of potatoes, is then flat from 20

to 30 pounds of potatoes, since the ten next pounds of potatoes are free, and then has a

slope of –1/2 until it intercepts the potato axis at 110.

d. An outbreak of potato rot raises the price of potatoes to $4 per pound. The

supermarket ends its promotion. What does her budget constraint look like now?

What combination of meat and potatoes maximizes her utility?

With the price of potatoes at $4, Connie may buy either 50 pounds of meat or 50 pounds

of potatoes, or some combination in between. See Figure 3.14.d. She maximizes

utility at U = 100 at point A when she consumes 50 pounds of meat and no potatoes.

This is a corner solution.

Choose combinations of D and F whose product is 120 to find a few bundles.

b.Graph Jane’s budget line on the same graph.

If Jane spends all of her budget on domestic travel she can afford 40 days. If she

spends all of her budget on foreign travel she can afford 10 days.

c.Can Jane afford any of the bundles that give her a utility of 800? What about a

utility of 1200?

Yes she can afford some of the bundles that give her a utility of 800 as part of this

indifference curve lies below the budget line. She cannot afford any of the bundles

that give her a utility of 1200 as this whole indifference curve lies above the budget

line.

d.Find Jane’s utility maximizing choice of days spent traveling domestically and

days spent in a foreign country.

The optimal bundle is where the slope of the indifference curve is equal to the slope

of the budget line, and Jane is spending her entire income. The slope of the budget

line is

-P

D

P

F

=-

1

4

.

The slope of the indifference curve is

MRS =-MU

D

MU F =-10F 10D =-F D .

Setting the two equal we get:

F D =144F =D .

We now have two equations and two unknowns:

4F =D

100D +400F =4000.

Solving the above two equations gives D=20 and F=5. Utility is 1000.

This bundle is on an indifference curve between the two you had previously drawn.

16. Julio receives utility from consuming food (F) and clothing (C) as given by the utility function U (F ,C )=FC . In addition, the price of food is $2 per unit, the price of clothing is $10 per unit, and Julio’s weekly income is $50.

a. What is Julio’s marginal rate of substitution of food f or clothing when utility is

maximized? Explain.

Utility is maximized when MRS (food for clothing) equals P C /P F , the price ratio.

Given that clothing is on the horizontal axis and food is on the vertical axis, then the

price ratio is the slope of the budget line, which is price of clothing divided by the

price of food or -5.

b. Suppose instead that Julio is consuming a bundle with more food and less clothing

than his utility maximizing bundle. Would his marginal rate of substitution of food for clothing be greater than or less than your answer in part a? Explain.

In absolute value terms, the slope of his indifference curve at this non-optimal bundle

is greater than the slope of his budget line. He is willing to give up more food than

he has to at market prices to obtain one more unit of clothing. He will therefore find

17. The utility that Meredith receives by consuming food F and clothing C is given by u(F,C) = FC. Su ppose that Meredith’s income in 1990 is $1,200 and the prices of food and clothing are $1 per unit for each. However, by 1995 the price of food has increased to $2 and the price of clothing to $3. Let 100 represent the cost of living index for 1990. Calculate the ideal and the Laspeyres cost-of-living index for Meredith for 1995. (Hint: Meredith will spend equal amounts on food and clothing with these preferences.)

First, we need to calculate F and C, which make up the bundle of food and clothing which maximizes Meredith’s utility given 1990 prices and her income in 1990. Use the hint to simplify the problem: Since she spends equal amounts on both goods, P F F = P C C. Or, you can derive this same equation mathematically: With this utility function, MU C = ?U/?C = F,

and MU F = ?U/?F = C. To maximize utility, Meredith chooses a consumption bundle such that MU F /MU C = P F /P C , which again yields P F F = P C C.

From the budget constraint, we also know that:

P F F +P C C = Y.

Combining these two equations and substituting the values for the 1990 prices and income yields the system of equations:

C = F and C + F = 1,200.

Solving these two equations, we find that:

C = 600 and F = 600.

Laspeyres Index

The Laspeyres index represents how much more Meredith would have to spend in 1995 versus 1990 if she consumed the same amounts of food and clothing in 1995 as she did in 1990. That is, the Laspeyres index for 1995 (L) is given by:

L = 100 (Y ')/Y

where Y’ represents the amount Meredith would spend at 1995 prices consuming the same amount of food and clothing as in 1990. In 1995, 600 clothing and 600 food would cost ($3)(600)+($2)(600)=$3000.

Therefore, the Laspeyres cost-of-living index is:

L = 100($3000/$1200) = 250.

Ideal Index

The ideal index represents how much Meredith would have to spend on food and clothing in 1995 to get the same amount of utility as she had in 1990. That is, the ideal index for 1995 (I) is given by:

I = 100(Y'')/Y, where Y'' = P'F F' + P'C C' = 2F' + 3C'

where F' and C' are the amount of food and clothing that give Meredith the same utility as she had in 1990. F' and C' must also be such that Meredith spends the least amount of money at 1995 prices to attain the 1990 utility level.

The bundle (F',C') will be on the same indifference curve as (F,C) so F'C'=FC=360,000 in utility. If Meredith’s income is adjusted in 1995 so that the bundle (F',C') is maximizing her utility given her income, then the indifference curve at this point will be tangent to the budget line with slope -(P'F /P'C ), where P'F and P'C are the prices of food and clothing in 1995. Using MU F '/MU C ' = P F '/P C ' we know that 2F' = 3C'.

We now have two equations: F'C'=360,000 and 2F' = 3C'.

Solving for F' yields: F'[(2/3)F'] = 360,000 or F' =

[(/),)]32360000 = 734.8.

From this, we obtain C':

C' = (2/3)F' = (2/3)734.8 = 489.9.

In 1995, the bundle of 734.8 food and 489.9 clothing would cost $2939.60 and Meredith would still get 360,000 in utility.

We can now calculate the ideal index:

I = 100($2939.60/$1200) = 244.9.

平狄克微观经济学课后习题答案-第7-8章

第七章 复习题 1.显性成本 2.她自己做其他事时会得到的最高收入 3.多用资本,少用工人 4.完全竞争价格给定,即斜率不变 5.不意味 6.意味着递增 7.AVC

第七章附录 练习题 1、我们考查规模报酬时可由F（aK，aL）与aF（K，L）之间的关系判断 当F（aK，aL）>aF（K，L）,表明是规模报酬递增； 当F（aK，aL）=aF（K，L）,表明是规模报酬不变； 当F（aK，aL）

微观经济学课后习题答案

第二章计算题 1．假定某商品的需求函数为P＝100—5Q，供给函数为P=40+10Q。(1)求该商品的均衡价格和均衡产量；(2)由于消费者收入上升导致对该商品的需求增加15，则求新的需求函数；(3)由于技术进步导致对商品的供给增加15，则求新的供给函数；(4)求供求变化后新的均衡价格与均衡数量；(5)将(4)与(1)比较，并说明结果。 2.某市的房租控制机构发现，住房的总需求是Qd=100—5P，其中数量Qd以万间套房为单位，而价格P（即平均月租金率）则以数百美元为单位。该机构还注意到，P较低时，Qd的增加是因为有更多的三口之家迁入该市，且需要住房。该市房地产经纪人委员会估算住房的供给函数为Qs=50+5P。(1)如果该机构与委员会在需求和供给上的观点是正确的，那么自由市场的价格是多少(2)如果该机构设定一个100美元的最高平均月租金，且所有未找到住房的人都离开该市，那么城市人口将怎样变动(3)假定该机构迎合委员会的愿望，对所有住房都设定900 美元的月租金。如果套房上市方面的任何长期性增长，其中的50%来自新建筑，那么需要新造多少住房 3．在某商品市场中，有10000个相同的消费者，每个消费者的需求函数均为Qd=12-2P；同时又有1000个相同的生产者，每个生产者的供给函数均为Qs=20P。(1)推导该商品的市场需求函数和市场供给函数；(2)求该商品市场的均衡价格和均衡数量；(3)假设政府对售出的每单位商品征收2美元的销售税，而且1000名销售者一视同仁，这个决定对均衡价格和均衡数量有什么影响实际上是谁支付了税款政府征收的税额为多少(4)假设政府对产出的每单位商品给予1美元的补贴，而且1000名生产者一视同仁，这个决定对均衡价格和均衡数量又有什么影响该商品的消费者能从中获益吗 4．某君对商品x的需求函数为P＝100-，求P＝60和P=40时的需求价格弹性系数。 5．假定需求函数Qd＝500一lOOP，试求：(1)价格2元和4元之间的弧弹性；(2)分别求出价格为2元和4元时的点弹性。 6．假定某商品的需求函数为Qd=100-2P，供给函数为Qs=10+4P，试求：(1)均衡价格和均衡数量；(2)均衡点的需求弹性与供给弹性。 7．甲地到乙地的汽车票价为10元，火车的乘客为12万人，如果火车乘客与汽车票价的交叉弹性为，试问当汽车票价从10元下降至元时，乘座火车的人数将会有什么变化 8．假定猪肉市场存在着蛛网周期，供给和需求函数分别是：Qst=-10+3Pt-1，Qdt=30-2Pt，并且在初始状态时产量为20，问第二年的市场价格是多少均衡价格是多少这个均衡能达到吗

微观经济学试题及答案

一、填空题（每空 1 分，共20 分） 1．“生产什么”、“如何生产”和“为谁生产”是人类社会所必须解决的基本问题，这三个问题被称为_______问题。 2．需求曲线向左移动是需求_________，向右移动是需求____________。 3．边际效用是指某种物品的消费量每增加一单位所增加的_____________。 4．生产要素是指生产中所使用的各种资源，这些资源可以分为________、________、土地和企业家才能。 5．在完全竞争市场上，平均收益__________边际收益；而在其他市场上，一般是平均收益________边际收益。 6．分配理论是__________理论在分配问题上的应用。 7．公共物品是由集体消费的物品，它的特征是消费的__________和_________。 8．国内生产净值－间接税＝_____________。 9．M2＝______________＋___________。 10．消费函数图中的45°线表示在这条线上任何一点都是____________。 11．货币供给是指_______________。 12．周期性失业又称为___________的失业，是由于_________而引起的短期失业。13．在开放经济中，出口的增加会使均衡的国内生产总值________，贸易收支状况_______。 二、单项选择题：从下列每小题的四个选项中，选出一项正确的，将其标号填在题后的括号内。（每小题 2 分，共20 分） 1．一种商品的需求曲线向右下方倾斜，如果其供给曲线向左移动则会引起：（） A。均衡数量增加，均衡价格上升B。均衡数量增加，均衡价格下降 C。均衡数量减少，均衡价格上升D。均衡数量减少，均衡价格下降 2．已知X商品的价格为5元，Y商品的价格为2元。如果消费者从这两种商品的消费中得到最大效用时，商品Y的边际效用为30，那么，此时X商品的边际效用为：（） A。60 B。45 C。150 D。75 3．内在经济是指：（） A。一个企业在生产规模扩大时由自身内部所引起的产量增加 B。一个企业在生产规模扩大时由自身内部所引起的产量或收益减少 C。一个行业的扩大对其中每个企业带来的产量或收益的增加 D。整个社会经济的发展给一个企业所带来的产量或收益的增加 4．垄断竞争市场上长期均衡的条件是：（） A。MR=MC B。MR=MC，AR=AC C。AR=AC D。MR=AC 5．当劳伦斯曲线和绝对平均线所夹面积为零时，基尼系数：（） A。等于零B。等于一C。等于无穷大D。无法确定 6．最全面反映经济中物价水平变动的物价指数：（） A。消费物价指数B。生产物价指数 C。GDP平减指数D。遗憾指数 7．假如要使经济增长率从5%提高到8%，在储蓄率为20%的条件下，根据哈罗德模型，资本—产量比率应该是：（） A。4 B。2。5 C。6 D。5 8．在总需求的构成中，哪一项与物价水平无关：（） A。消费需求B。投资需求C。政府需求D。国外的需求 9．在IS曲线不变的情况下，货币量增加会引起：（） A。国内生产总值增加，利率下降B。国内生产总值增加，利率上升

微观经济学第3章部分练习题答案

《微观经济学》第三章练习题参考答案 1、已知一件衬衫的价格为80元，一份肯德鸡快餐的价格为20 元，在某消费者关于这两种商品的效用最大化的均衡点上，一份肯德鸡快餐对衬衫的边际替代率MRS是多少？ 解：按照两商品的边际替代率MRS的定义公式,可以将一份肯德 鸡快餐对衬衫的边际替代率写成: MRS XY Y X 其中:X表示肯德鸡快餐的份数;Y表示衬衫的件数;MRS表示 在维持效用水平不变的前提下,消费者增加一份肯德鸡快餐时所需 要放弃的衬衫消费数量。 在该消费者实现关于这两件商品的效用最大化时，在均衡点上有 MRS xy=P x/P y 即有MRS xy=20/80=0.25 它表明：在效用最大化的均衡点上，消费者关于一份肯德鸡快餐对衬衫的边际替代率MRS为0.25。 2假设某消费者的均衡如图1-9所示。其中，横轴OX1和纵轴 OX，分别表示商品1和商品2的数量，线段AB为消费者的预算线，2 曲线U为消费者的无差异曲线，E点为效用最大化的均衡点。已知商品1的价格P1=2元。

X2 （1）求消费者的收入； (2)求上品的价格P； 2 20 A U B E(3)写出预算线的方程； 10 (4)求预算线的斜率； O 1020 30 X1 (5)求E点的MRS的值。 12 解：（1）图中的横截距表示消费者的收入全部购买商品1的数量 为30单位，且已知P1=2元，所以，消费者的收入M=2元×30=60。 （2）图中的纵截距表示消费者的收入全部购买商品2的数量为 20单位，且由（1）已知收入M=60元，所以，商品2的价格P2斜率= －P1/P2=－2/3，得P2=M／20=3元 （3）由于预算线的一般形式为： P1X1+P2X2=M 所以，由（1）、（2）可将预算线方程具体写为2X1+3X2=60。 （4）将（3）中的预算线方程进一步整理为X2=-2/3X1+20。很 清楚，预算线的斜率为－2/3。 （5）在消费者效用最大化的均衡点E上，有MRS12==MRS12=P1/P 2， 即无差异曲线的斜率的绝对值即MRS等于预算线的斜率绝对值P1/P 2。 因此，在MRS12=P1/P2=2/3。 3请画出以下各位消费者对两种商品（咖啡和热茶）的无差异曲

(完整版)微观经济学课后习题答案

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《微观经济学》（高鸿业第四版）第三章练 习题参考答案 1、已知一件衬衫的价格为80元，一份肯德鸡快餐的价格为20元，在某消费者关于这两种商品的效用最大化的均衡点上，一份肯德鸡快餐对衬衫的边际替代率MRS 是多少？ 解：按照两商品的边际替代率MRS 的定义公式,可以将一份肯德鸡快餐对衬衫的边际替代率写成: X Y MRS XY ??- = 其中:X 表示肯德鸡快餐的份数;Y 表示衬衫的件数; MRS 表示在维持效用水平不变的前提下, 消费者增加一份肯德鸡快餐时所需要放弃的衬衫消费数量。 在该消费者实现关于这两件商品的效用最大化时，在均衡点上有 MRS xy =P x /P y 即有MRS xy =20/80=0.25 它表明：在效用最大化的均衡点上，消费者关于一份肯德鸡快餐对衬衫的边际替代率MRS 为0.25。 2 假设某消费者的均衡如图1-9所示。其中，横轴1OX 和纵轴 2OX ，分别表示商品1和商品2的数量，线段AB 为消费者的预算线， 曲线U 为消费者的无差异曲线，E 点为效用最大化的均衡点。已知商

品1的价格P1=2元。 (2)求上品的价格 P； 2 (3)写出预算线的方程； (4)求预算线的斜率； (5)求E点的 MRS的值。 12 解：（1）图中的横截距表示消费者的收入全部购买商品1的数量为30单位，且已知P1=2元，所以，消费者的收入M=2元×30=60。 （2）图中的纵截距表示消费者的收入全部购买商品2的数量为20单位，且由（1）已知收入M=60元，所以，商品2的价格P2斜率=－P1/P2=－2/3，得P2=M／20=3元 （3）由于预算线的一般形式为： P1X1+P2X2=M 所以，由（1）、（2）可将预算线方程具体写为2X1+3X2=60。 （4）将（3）中的预算线方程进一步整理为X2=-2/3 X1+20。很清楚，预算线的斜率为－2/3。 （5）在消费者效用最大化的均衡点E上，有MRS12= = MRS12=P1/P2，即无差异曲线的斜率的绝对值即MRS等于预算线的斜率绝对值P1/P2。 因此，在MRS12=P1/P2 =2/3。

平狄克《微观经济学》(第9版)章节题库-第5章 不确定性与消费者行为【圣才出品】

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为无风险条件下持有固定财富的效用大于项目A的期望效用，因此是风险厌恶者。 3．假设你去买一张彩票，而且你知道将以0.1的概率得到2500元，0.9的概率得到100元。假设你的效用函数为U（w）＝w1/2，那么你从所购买的彩票中得到的期望效用为（ ）。 A．360 B．14 C．46 D．1300 【答案】B 【解析】期望效用的计算公式为 U（g）＝π1U（w1）＋π2U（w2） 其中，π1，π2为两种自然状态w1，w2发生的概率。将U（w）＝w1/2以及 π1＝0.1，w1＝2500，π2＝0.9，w2＝100代入期望效用计算公式，可得期望效用为14。 4．假设一个消费者的效用函数为U（w）＝w2，那么该消费者是（ ）。 A．风险规避的 B．风险中性的 C．风险偏好的 D．都不是 【答案】C 【解析】消费者的效用函数为U（w）＝w2，边际效用为MU（w）＝2w，边际效用

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