Student Practice Manual

to Accompany

Microeconomics

B. Douglas Bernheim

Michael Whinston

Created by:

Jennifer Pate, Ph.D.

Loyola Marymount University

Table of Contents

Chapter 1

Page

3

Additional Exercises for Chapter 1

4

Chapter 2

5

Additional Exercises for Chapter 2

7

Chapter 3

11

Additional Exercises for Chapter 3

14

Chapter 4

18

Additional Exercises for Chapter 4

21

Chapter 5

27

Additional Exercises for Chapter 5

33

Chapter 6

44

Additional Exercises for Chapter 6

51

Chapter 7

57

Additional Exercises for Chapter 7

59

Chapter 8

65

Additional Exercises for Chapter 8

69

Chapter 9

73

Additional Exercises for Chapter 9

78

Chapter 10

82

Additional Exercises for Chapter 10

85

Chapter 11

89

Additional Exercises for Chapter 11

93

Chapter 12

99

Additional Exercises for Chapter 12

02

Chapter 13

09

Additional Exercises for Chapter 13

11

Chapter 14

15

Additional Exercises for Chapter 14

17

Chapter 15

22

Additional Exercises for Chapter 15

24

Chapter 16

28

Additional Exercises for Chapter 16

30

Chapter 17

34

Additional Exercises for Chapter 17

36

Chapter 18

41

Additional Exercises for Chapter 18

44

Chapter 19

50

Additional Exercises for Chapter 19

52

Chapter 20

55

Additional Exercises for Chapter 20

57

Chapter 1

Sample Problems

. Government intervention in markets is a politically divisive issue. What are some potential justifications of government intervention in markets?

Answer:

Government intervention in markets is potentially justifiable when market failures occur. In a case where there is little competition in a market, the government could step in and regulate prices so that consumers are not unjustly hurt by lack of competition in a market. The government could also intervene in markets to bridge the gap between buyers and sellers created by a lack of information. In such cases, the government could impose regulations and mandates on disclosure of information. Also, inequality across customers in a market could justify a government to implement policies to redistribute resources more equitably.

2. Simplifying assumptions are important when creating an economic model because it helps economists focus on the most important reasons for a phenomenon. How does assuming people are motivated by material self-interest simplify an economic model?

Answer:

Assuming material self-interest simplifies economic models because it means that everyone is motivated by the same principles. There are no altruistic individuals. In short it makes everyone similar and that allows models to be more broadly applicable.

3. Your roommate asks you for advice about what to do this Friday night. She has narrowed her options to two different choices. She could go to a party with her new friends, or she could attend an off-campus seminar on The Poetry of Robert Frost which her English professor recommended as an event she would truly enjoy. To ease her decision-making process, explain the trade-offs between her two choices.

Answer:

If she chooses to go to the party she will forgo the opportunity to experience the poetry of Robert Frost which was highly recommended to her. If she goes to the seminar instead of the party she will forgo a chance to bond with her new friends and the possibility of having a good time. Her decision will involve an opportunity cost equal to the forgone action.

Additional Exercises for Chapter 1

. Which type of economy, communist or capitalist, is more closely described as a free market system and why?

2. What are markets and why do they require property rights?

3. How does the principle of individual sovereignty allow economists to conduct normative analysis?

4. How does the field of economics go beyond the study of money?

5. Why is it important to identify additional implications after formulating a theory?

6. What is the benefit to economists of using simplifying assumptions when formulating a model?

7. List and briefly describe the three main categories of economic data.

8. Why might economists disagree about positive matters?

9. How does a natural experiment differ from a controlled experiment?

0. Given that people respond to incentives, how do changes in prices alter behavior?

1. How can trade benefit two people at the same time?

2. Why might it be useful to use economics to evaluate environmental policy?

Chapter 2

Sample Problems

. Assume the demand for ice cream takes the following form:

If the price of yogurt is $4.00, the price of a waffle cone is $3.00 and the average income is $32,000, what is the demand function for ice cream? Graph it below.

Answer:

To solve for the demand function, substitute in the prices for yogurt and waffle cones and the average income, then simplify as in the equations below:

To graph the equation, first find the endpoints. If, then and when, .

2. Using the information from the previous question, at what will the quantity demanded of ice cream equal 18 gallons? How will this change if the price of waffle cones decreases to $2.00?

Answer:

To find the price of ice cream where quantity demanded equals 18 gallons, set the equation for quantity demanded to 18 and solve for.

If the price of waffle cones falls to $2.00, the demand function changes to

To again find the price of ice cream where quantity demanded equals 18 gallons, set the equation for quantity demanded to 18 and solve for.

3. If this means that if, then and if, then. What is the elasticity of demand at a price of $3.00? What about at a price of $4.00?

Answer:

At $3.00:

At $4.00:

Additional Exercises for Chapter 2

. Assume the demand for French fries takes the following form:

If the price of onion rings is $5.00, the price of ketchup is $4.00, and the average income is $30,000, what is the demand function for French fries? Graph it below.

2. Following from the information in question (1), at whatwill the quantity demanded equal 15 million pounds? How will this change if the price of ketchup increases to $5.00?

3. What happens to the demand curve for French fries if the average income increases to $40,000, holding all else constant? Graph this new demand curve alongside your answer from (1).

4. Given the demand function in (1), how can you determine whether French fries and onion rings are substitutes or complements? Explain.

5.

Assume the supply of French fries (FF) takes the following form:

If the price of frying oil is $3.00 and the price of potato flakes is $5.00, what is the supply function for French fries? Graph it below.

6. Following from (5), at whatwill the quantity supplied equal 12.5 million pounds? How will this change if the price of potato flakes falls to $3.00?

7. How does your answer from (6) demonstrate that French fries and potato flakes are substitutes in production? Explain.

8. What happens to the supply curve for French fries if the price of frying oil increases to $4.50? Graph this new supply curve alongside your answer from (5).

9. Assume the demand function for French fries takes the form: and the supply function takes the form: . What is the equilibrium price in this market? What are the amounts bought and sold?

0. Following from (9), what happens to the equilibrium price and quantity if demand decreases to? Calculate the new equilibrium.

1. Starting again from (9), what happens to the equilibrium price and quantity if supply increases to? Calculate the new equilibrium.

2. Finally, what happens to the equilibrium price and quantity if demand decreases to and supply increases to? Calculate the new equilibrium. Does quantity increase, decrease, or stay the same and why?

3. Suppose the demand function for ice cream is: and the supply function is: Find the equilibrium price in the market for ice cream. What are the amounts that are bought and sold? Graph the supply and demand functions below.

4. If, this means that if, then and if, then. What is the elasticity of demand at a price of $3.50? What about at a price of $5.00?

5. If, this means that if, then and if, then. What is the elasticity of supply at a price of $3.50? What about at a price of $5.00?

6. Considering the demand function, at what price will total expenditure be the largest?

Chapter 3

Sample Problems

. In an effort to help him avoid the freshman 15, Jerry's parents bought him a gym membership. To keep himself motivated Jerry wants to arrange personal trainer sessions for the semester. Jerry can hire the trainer for up to 21 sessions in increments of 3 sessions. The total benefit (TB) and total cost (TC) of the training sessions are in the table below. Calculate the net benefit (NB) for each of Jerry's choices and use your answer to identify his best option.

Number of Sessions

Benefit

Cost

Net Benefit

0

0

0

3

15

90

6

245

74

9

396

252

2

525

324

5

563

390

8

608

450

21

649

504

Answer:

Number

of Sessions

Benefit

Cost

Net Benefit

0

0

0

0

3

15

90

25

6

245

74

71

9

396

252

44

2

525

324

201

5

563

390

73

8

608

450

58

21

649

504

45

The best choice for Jerry would be to hire the personal trainer for the number of sessions that yield the highest net benefit. According to the table Jerry's best choice is to hire the personal trainer for 12 sessions with a net benefit of 201.

2. Calculate the marginal benefit (MB) and marginal cost (MC) to fill in the table below. How can you use your answers to identify the best choice?

Number

of Sessions

Benefit

Marginal Benefit

Cost

Marginal Cost

0

0

0

3

15

90

6

245

74

9

396

252

2

525

324

5

563

390

8

608

450

21

649

504

Answer:

Number

of Sessions

Benefit

Marginal Benefit

Cost

Marginal Cost

0

0

X

0

X

3

15

15

90

90

6

245

30

74

84

9

396

51

252

78

2

525

29

324

72

5

563

38

390

66

8

608

45

450

60

21

649

41

504

54

The best choice for Jerry according to this schedule is to hire a personal trainer for twelve sessions. The twelve session mark is the last point at which the marginal benefit exceeds the marginal cost.

3. Suppose that Jerry can hire a personal trainer for up to twenty-one sessions. The total benefit of hiring the trainer is given by the functionand the total cost is given by The corresponding functions for MB and MC areandrespectively. What is Jerry's best choice?

Answer:

Using the Principle of No Marginal Improvement you can solve for Jerry's best choice by setting MB = MC and solving for S:

=

So, Jerry's best choice is to hire a personal trainer for 12.67 (twelve and two-thirds of a session) sessions.

4. Using the information from (3), what happens if the gym decides to charge Jerry a one-time non-refundable service fee of $25 for the use of a new member-trainer work-out area. How does this fee impact Jerry's choice of the best action in (3) and why?

Answer:

Introducing a one-time non-refundable consultation fee of $25 would have the effect of changing your total cost function from, to. On the graph from (8) the TC curve would be shifted up by 25 units. Despite this shift in the TC curve this does not change the marginal cost curve. Since the MC function and the MB function are the same you will find that your best choice from (8) is the same, even after adding a one-time service fee. The service fee is what is known as a sunk cost. Sunk costs have no effect on Jerry's best choice because regardless of how many sessions he employs his trainer, the service fee is constant.

5. What do you think might happen to Jerry's cost schedule if the gym charged a new fee of $5 per session for using the area? Do you think there might be a new best choice?

Answer:

If the gym introduced a new $5 per session fee for the new member-trainer area Jerry's cost schedule would be changed. The cost for each of Jerry's choices would increase by 5 times the number of total sessions. It is also likely that Jerry's benefit schedule could see and increase due to the new training area.

It is possible that if this new service fee was implemented that Jerry would be looking at a new best choice depending on how much the benefits outweigh the costs at each choice.

Additional Exercises for Chapter 3

. Assume you have a few hours free on a Saturday afternoon and you've ranked your options, starting with your most preferred, as (1) going to see a movie, (2) going to the gym, (3) reading a book or (4) watching grass grow. What is your opportunity cost of going to see a movie and why?

2. Why is it important to make a decision based on the net benefit of your options and not just the total benefit?

3. Suppose that you hire a mechanic to fix your motorcycle for up to six hours. The total benefit and total cost of the repair work are in the table below. Calculate the net benefit for each choice and use your answer to identify the best option.

Hours

Benefit

Cost

Net Benefit

0

0

0

460

80

2

840

220

3

140

420

4

360

680

5

500

000

6

560

380

4. Using the information from (3), what happens if the mechanic decides to impose an additional $50 hourly fee? What is the maximum net benefit now?

5. Calculate the marginal benefit and marginal cost to fill in the table below. How can you use your answers to identify the best choice?

Hours

Benefit

Marginal Benefit

Cost

Marginal Cost

0

0

0

460

80

2

840

220

3

140

420

4

360

680

5

500

000

6

560

380

6. Suppose that you hire a mechanic to fix your motorcycle for up to six hours. The total benefit of the repair work is and the total cost is. The corresponding functions for marginal benefit and marginal cost are and, respectively. What is your best choice?

7. The figure below displays the functions for total benefit and total cost for a decision. How can you use this information to determine the best choice? What is the maximum net benefit?

8. Suppose again that you hire a mechanic to fix your motorcycle for up to six hours. The total benefit of the repair work is and the total cost is. The corresponding functions for marginal benefit and marginal cost are and, respectively. What is your best choice?

9. Suppose that you hire a mechanic to fix your motorcycle for up to six hours. The total benefit and total cost of the repair work are in the table below. Calculate the net benefit for each choice and use your answer to identify the best option.

Hours

Benefit

Cost

Net Benefit

0

0

0

335

65

2

640

80

3

915

345

4

160

560

5

375

825

6

560

140

0. Using the information from (8), what happens if the mechanic decides to charge a one-time non-refundable consultation fee of $100? How does this fee impact your choice of the best option in question (8) and why?

1. Why should sunk costs be ignored when finding the best choice from a set of options?

2. How can the No Marginal Improvement Principle be used to find the best possible choice over a set of options?

3. Suppose once more that you hire a mechanic to fix your motorcycle for up to six hours. The total benefit of the repair work is and the total cost is. The corresponding functions for marginal benefit and marginal cost are and, respectively. What is your best choice? What if the mechanic requires a 1-hour minimum payment?

4. What is the difference between an interior action and a boundary action and why is it important to eliminate the boundary choices?

5. Suppose that you find the largest net benefit for repairs to be 4.3 hours but the mechanic requires that payments be made in one-hour increments, which forces you to choose either 4 hours or 5 hours. Which choice do you make and why?

Chapter 4

Sample Problems

. Jimmy is going to fraternity initiation dinner and has ranked his preference bundles for rolls of sushi and number of enchiladas according to the table below. Using the information on the table below, do Jimmy's rankings show support for the More-Is-Better Principle? Also, using the information on the table, can you tell whether Jimmy prefers sushi to enchiladas, or enchiladas to sushi?

Sushi

(rolls)

3

1

6

3

2

3

8

4

2

4

9

7

5

0

5

4

2

0

0

2

3

Enchiladas

(Number of enchiladas)

Answer:

To check whether Jimmy's preferences satisfy the more-is-better principle, notice that in any particular column the numbers at the top are smaller than the numbers at the bottom. Similarly, in any particular row, the numbers on the right-hand side are smaller than the numbers on the left-hand side. These two aspects of Jimmy's preferences imply that if either the number of rolls of sushi (number of enchiladas) is held constant Jimmy prefers more enchiladas (sushi).

2. Using the information from question (1) and starting with 2 rolls of sushi and 1 enchilada, will Jimmy

a) Swap 1 sushi roll for 1 more enchilada?

b) Swap 2 sushi rolls for 2 more enchiladas?

c) Swap 1 enchilada for 1 more sushi roll?

Answer:

a) Yes, he would swap

b) No, he will not swap

c) No, he will not swap

3. The figure below contains two indifference curves one for Jimmy and another curve for Ron, Jimmy's new fraternity brother. The points represent their current consumption bundles. Using the graphs, is trade favorable between the two? Explain your answer.

Answer:

Jimmy's current consumption bundle has him on the steep part of his indifference curve where he is willing to forgo more sushi in return for some more enchiladas. In contrast, Ron's current consumption bundle has him on the flat part of his indifference curve where he is willing to forgo more enchiladas in return for some more sushi. Therefore, a trade in which Jimmy gives Ron some of his sushi in return for a greater number of enchiladas than was previously possible would benefit both.

4. At their current consumption bundles, who has a greater marginal rate of substitution for enchiladas with sushi, Jimmy or Ron? Use the graph in (3). Explain your answer.

Answer:

According to their indifference curves, enchiladas are worth more to Jimmy than to Ron. This is evident from the slopes of both of their indifference curves. Jimmy is less willing to forgo enchiladas for more sushi than Ron. Thus, Jimmy's MRS for enchiladas with sushi is higher than Ron's.

5. Ron's preferences for sushi (S) and enchiladas (E) in a month correspond to the utility function How does Ron rank the following alternatives?

a) 1 roll of sushi and 4 enchiladas.

b) 4 rolls of sushi and 1 enchilada.

c) 2 rolls of sushi and 2 enchiladas.

d) 3 rolls of sushi and 2 enchiladas.

Answer:

Use Ron's utility function to find to help find the order of preference between the alternatives.

For example for (a): The rest are as follows: Therefore, Ron's preferences are as follows: 1st, 4 rolls of sushi and one enchilada; 2nd, 3 rolls of sushi and 2 enchiladas; and lastly, both (a) one roll of sushi and (c) 4 enchiladas, and 2 rolls of sushi and 2 enchiladas.

6. Given Ron's utility function in question (5), find a formula for his indifference curves. What is Ron's marginal utility of sushi? What is Ron's marginal utility of enchiladas? What is her marginal rate of substitution for sushi with enchiladas?

Answer:

Given Ron's utility function, the formula his indifference curves can be found by rearranging the equation and solving for E, as such:

(1)

Ron's marginal utility of sushi is (addingincreases the utility value by 3 so,)

The marginal utility of enchiladas is (adding ?E the utility value by so,

Now, to find Ron's marginal rate of substitution for sushi with enchiladas, use the equations for finding the MRS with the information about the marginal utilities of both sushi and enchiladas, as such:

Her MRS of sushi with enchiladas is enchiladas per roll of sushi.

Additional Exercises for Chapter 4

. Why is it important that consumers follow the Choice Principle? What would happen if they didn't?

2. Stephanie is going to a birthday party and has ranked her preference bundles of pieces of pie and scoops of ice cream according to the table below. Using the information in the table, how do Stephanie's rankings show support for the More-is-Better Principle?

Pie (pieces)

3

0

5

2

2

3

7

4

3

4

9

8

6

0

5

4

2

1

0

2

3

Ice Cream

(scoops)

3. Using the information in question (2) and starting with 1 piece of pie and 1 scoop of ice cream, will Stephanie

a) swap 1 scoop of ice cream for 1 piece of pie?

b) swap 1 scoop of ice cream for 2 pieces of pie?

c) swap 1 piece of pie for 2 scoops of ice cream?

4. Does the Ranking Principle allow for ties? What does this mean about Stephanie's preferences for pie and ice cream in question (2)?

5. The figure below contains two indifference curves and several options for consumption bundles for a consumer. Using this information, rank the bundles from most preferred to least preferred according to this consumer's preferences.

6. Suppose that Stephanie's preferences for pieces of pie (P) and scoops of ice cream (IC) follow the formula. Plot three indifference curves for Stephanie when , , and when on the graph.

7. Now suppose that Stephanie will only eat pie and ice cream in a 1-to-1 ratio and gains no additional benefit from any other combination. Draw a few examples of this indifference curve on the graph. What is this type of preference called?

8. Now suppose that Stephanie is asked about her preferences regarding pie and cake. She prefers pie and cake equally, but doesn't like to consumer them together. If pie and cake are perfect substitutes for Stephanie, draw her indifference curves if she has only 1 serving, 2 servings, or 3 servings of either pie or cake.

9. Stephanie has brought her daughters Ashleigh and Taylor to the birthday party. Ashleigh loves cake but hates pie, while Taylor loves pie but hates cake. Draw Ashleigh and Taylor's indifference curves on the graph if both girls each have 2 servings of their choice.

0. Stephanie's preferences for pie (P) and ice cream (IC) in a month correspond to the utility function. How does Stephanie rank the following alternatives:

a) 1 piece of pie and 4 scoops of ice cream

b) no pie and 5 scoops of ice cream

c) 4 pieces of pie and no ice cream

d) 2 pieces of pie and 3 scoops of ice cream

1. Given Stephanie's utility function in question (10), find a formula for her indifference curves. What is Stephanie's marginal utility of pie? What is Stephanie's marginal utility of ice cream? What is her marginal rate of substitution for pie with ice cream?

2. Given Stephanie's utility function in question (10), plot her indifference curves for, , and on the graph below.

3. Stephanie's husband Dave also likes pie and ice cream, but his utility function takes the form. Find a formula for Dave's indifference curves. What is Dave's marginal utility of pie? What is Dave's marginal utility of ice cream? What is his marginal rate of substitution for pie with ice cream?

4. If Dave's utility function is as in question (13) and he currently has 1 piece of pie and 2 scoops of ice cream, would he be willing to trade his current bundle for 2 pieces of pie and 1 scoop of ice cream? Why or why not?

5. Suppose Stephanie and Dave have preferences according to their utility functions in questions (10) and (13), respectively. If Stephanie has 4 scoops of ice cream and Dave has 3 pieces of pie, is there a trade they could make to improve both of their positions? Explain your answer.

Chapter 5

Sample Problems

. In the Chapter 4 exercises we examined Jimmy's preferences regarding rolls of sushi and numbers of enchiladas. If a roll of sushi is $2.50 and an enchilada is $1.50, which bundles can Jimmy afford if his income is $7.00? Fill in the table below with the total cost of each bundle and identify his affordable options. What happens to the number of affordable options if his income increases to $9.00?

Sushi

(rolls)

3

2

0

0

2

3

Enchiladas

(Number of enchiladas)

Answer:

Sushi

(rolls)

3

7.5

9

0.5

2

2

5

6.5

8

9.5

2.5

4

5.5

7

0

0

.5

3

4.5

0

2

3

Enchiladas

(Number of enchiladas)

If Jimmy's income is $7.00, his affordable options are lightly shaded.

If Jimmy's income is $9.00, his affordable options increase to include all of the lightly shaded options plus the new options which are more darkly shaded.

2. Suppose a sushi roll (S) costs $1.50 and an enchilada (E) costs $2.00, first plot Jimmy's initial budget line on the graph below when his income equals $6.00. Now suppose the price of sushi rolls doubles to $3.00. Plot Jimmy's new budget line and calculate the horizontal intercept, the vertical intercept, and the slope of his budget line. What happened to the number of affordable options and why?

Answer:

If the price of sushi doubles to $3.00 the new budget line is. His new budget line has a slope of, with a horizontal intercept at 3 enchiladas, and a vertical intercept at 2 rolls of sushi. The number of affordable options has decreased due to the increase in the price of rolls of sushi. This increase in the price of sushi has caused the original budget line to rotate inward from the origin (pivoting at the intercept for enchiladas).

3. Taking her friends advice before the start of the next semester, Amy decides to allocate $24 dollars per month of her income for the consumption of coffee and energy drinks instead of $40 per month. Coffee (C) costs $6 per pound and energy drinks (E) cost $12 per package. Fractions are allowed since the energy drink packages can be split and Amy can purchase coffee in uneven increments. If Amy'ss marginal rate of substitution is, how many pounds of coffee and energy drink packages will she buy?

Answer:

First, derive the equation for the budget line as follows:

.

(Budget line)

Now, use the tangency condition to help solve for C:

Next, use the previous result along with the equation for the budget line to solve for C and E:

&

Now use E to find C.

If Amy'ss marginal rate of substitutions for coffee with energy drinks is, then she should buy 3 pounds of coffee andpackage of energy drinks.

4. As in question (3), Amy spends money on coffee and energy drinks for the spring semester. Coffee (C) costs $6 per pound and energy drinks cost $12 per package. Suppose Amy's preferences correspond to the utility function. For that utility function, the marginal utility of coffee is 3E (the amount of coffee) and the marginal utility of energy drinks is (the number of energy drink packages). Fractions are still acceptable. Using,, and, draw Amy's income-consumption curve and her Engel curves for coffee and energy drinks.

Answer:

To plot the Income-consumption curves we first need to find the budget lines. Since the prices of coffee and energy drinks are constant and the only thing changing is income it is fairly simple to find the budget lines:

If:()

If:()

If:()

Next, we need to find the optimal bundles for each budget line. To do this we use the following equation:

Using the previous result you can solve for the optimal bundles at each budget line. The optimal bundles are as follows:

For:, For:, For:

Now we have all of the information needed to plot the income-consumption curves and the Engel curves.

Additional Exercises for Chapter 5

. In the Chapter 4 exercises we examined Stephanie's preferences regarding pieces of pie and scoops of ice cream. If a piece of pie is $2.00 and a scoop of ice cream is $1.00, which bundles can Stephanie afford if her income is $4.00? Fill in the table below with the total cost of each bundle and identify her affordable options. What happens to the number of affordable options if her income increases to $6.00?

Pie (pieces)

3

2

0

0

2

3

Ice Cream

(scoops)

2. Using the information in question (1), plot Stephanie's budget lines on the graph below when her income is $4.00. Calculate the horizontal intercept, the vertical intercept, and the slope of her budget line. What happens to her budget line if her income increases to $6.00? Again, calculate the horizontal intercept, the vertical intercept, and the slope of her budget line.

3. Using the information in question (1), first plot Stephanie's initial budget line on the graph below when her income equals $4.00. Now suppose the price of ice cream doubles to $2.00. Plot Stephanie's new budget line and calculate the horizontal intercept, the vertical intercept, and the slope of her budget line. What happened to the number of affordable options and why?

4. Using the information in question (1), first plot Stephanie's initial budget line on the graph below when her income equals $4.00. Now suppose that pie goes on sale for $1. Plot Stephanie's new budget line and calculate the horizontal intercept, the vertical intercept, and the slope of her budget line. What happened to the number of affordable options and why?

5. The table below reproduced from the Chapter 4 exercises shows Stephanie's preferences for pie and ice cream. First use your answer for question (1) when her income is $4.00 to shade in the unaffordable bundles. Next identify which bundle would maximize Stephanie's utility.

Pie (pieces)

3

0

5

2

2

2

7

4

3

4

9

8

6

0

5

4

3

1

0

2

3

Ice Cream

(scoops)

6. The table below reproduced from the Chapter 4 exercises shows Stephanie's preferences for pie and ice cream. First use your answer for question (1) when her income is $6.00 to shade in the unaffordable bundles. Next identify which bundle would maximize Stephanie's utility. How does this choice compare to your answer for question (5)?

Pie (pieces)

3

0

5

2

2

2

7

4

3

4

9

8

6

0

5

4

3

1

0

2

3

Ice Cream

(scoops)

7. Continuing with the example, what would happen if pie was rationed to a maximum of 2 pieces per person? Using the budget line below when the price of pie is $2.00, the price of ice cream is $1.00, and Stephanie's income is $8.00, demonstrate the impact of this rationing. Using her preferences given in question (5), how does pie rationing impact Stephanie's decision?

8. Now suppose that Stephanie's preferences are represented by three ranked indifference curves in the figure below. If pie and ice cream are $2.00 each and Stephanie's income is $8.00, which bundle will she choose? Plot her budget line and identify which indifference curve achieves this utility-maximizing bundle.

9. Why is it important that the budget line be tangent to the indifference curve at a utility-maximizing bundle for interior solutions? Why are boundary solutions excluded from the tangency condition?

0. Holly teaches second grade and has a budget of $50 per month to spend on candy and balloons for class parties. Candy (C) costs $5 per pound and balloons cost $10 per package. Fractions are allowed since the balloon packages can be split and Holly can purchase candy in uneven increments. If Holly's marginal rate of substitution is, how many pounds of candy and balloon packages will she buy?

1. Using the information in question (10), how many pounds of candy and balloon packages will Holly buy if her marginal rate of substitution is?

2. As before, Holly is buying candy and balloons for her class. Her preferences correspond to the utility function. For that utility function, the marginal benefit of candy is B (the number of balloon packages) and the marginal benefit of balloons is C (the amount of candy). Fractions are still acceptable. If candy (C) costs $5 per pound and balloons cost $10 per package and Holly's budget is $50, how many of each good will she buy for her classroom?

3. Using the information in question (12), calculate the utility-maximizing amounts of candy and balloons if Holly's utility function is . For that utility function, the marginal benefit of candy is and the marginal benefit of balloons is . If candy (C) costs $5 per pound and balloons cost $10 per package and Holly's budget is $50, how many of each good will she buy for her classroom?

4. As in question (10), Holly's marginal rate of substitution for candy and balloons is. Holly's budget is $50 and the price of candy is $5. Calculate her optimal amounts of candy and balloons when the price of balloons is $5 and when the price of balloons is $10. Draw her price-consumption curve and her demand curve for balloons on the graphs below.

5. Assume Holly's marginal rate of substitution for candy and balloons is . Holly's budget is $50 and the price of candy is $5. Calculate her optimal amounts of candy and balloons when the price of balloons is $5 and when the price of balloons is $10. Draw her price-consumption curve and her demand curve for balloons on the graphs below.

6. As in question (10), Holly spends money on candy and balloons for class parties. Candy (C) costs $5 per pound and balloons cost $10 per package. Suppose Holly's preferences correspond to the utility function. For that utility function, the marginal benefit of candy is B (the number of balloon packages) and the marginal benefit of balloons is C (the amount of candy). Fractions are still acceptable. Using , , and , draw Holly's income-consumption curve and her Engel curves for candy and balloons.

7. As in question (16), Holly spends money on candy and balloons for class parties. Candy (C) costs $5 per pound and balloons cost $10 per package. Suppose Holly's preferences correspond to the utility function. For that utility function, the marginal benefit of candy is and the marginal benefit of balloons is . Fractions are still acceptable. Using , , and , draw Holly's income-consumption curve and her Engel curves for candy and balloons.

8. How can the income-consumption curve be used to identify whether a good is normal or inferior?

Chapter 6

Sample Problems

. Starting a new semester, Amy has budgeted $24 per month to spend of coffee (C) and energy drinks (E). Coffee costs $6 per pound and energy drinks cost $12 per pack. Fractions are allowed as energy drink packs may be split and coffee may be purchased in uneven increments. Amy marginal rate of substitution isand the formula for her indifference curve is Suppose the price of energy drinks falls from $12 to $6. What is the uncompensated effect of her purchases of coffee and energy drinks? What is the compensated effect? How much compensation is involved? Decompose the uncompensated price change into the substitution and income effects.

Answer:

To find the uncompensated effect of Amy's purchases of coffee and energy drinks first use the tangency condition to solve for the E and C using a generic form of a budget constraint as follows:

(Budget line)

Tangency condition:

Now use the previous two results to solve for E and C:

&

So, withshe chooses. If the price of energy drinks falls to $6.00 she chooses.This uncompensated price reduction raises Amy's energy drink package purchases from to 1.5 and decreases the amount of coffee she buys from 8 to 5.

Next, to find the compensated effect we need to used the tangency condition and find the relationship between coffee and energy drinks at their new prices.

If, the relationship between candy and balloons is:

Amy's best choice with a compensated price change also lies on the indifference curve that passes through the bundle. Using the formula for her indifference curvethe value of U that runs through the bundleis 12.5, which implies that Holly's formula for this indifference curve is:

A bundle can satisfy both the tangency condition formula and the indifference curve formula only if: Solving for C using the quadratic equation. Using the tangency condition, we get that. So the compensated price effect shifts Holly from the bundleto the bundle.

At the new prices, Amy needs $30.42 to buy the bundle. Since her income is $24, we would have to give Amy $6.84 to compensate for the price cut.

To break up the uncompensated price change into substitution effects and income effects. Note that the substitution effect is the same as the effect of the compensated price change. The income effect is what is known as the residual; it shifts Amy from the bundleto the bundle.

2. Assume that Amy has a budget of $24 a month to spend on coffee (C) and energy drinks (E). Coffee cost $6 per pound and energy drinks cost $12 per package. Amy's marginal rate of substitution isand the formula for her indifference curve is After being recommended by her doctor to stop drinking coffee for one month, Amy was left with only energy drinks to keep her up during late night study sessions and early morning classes. Her friends know how much Amy likes coffee so they would like to help her through the month. Calculate her compensating variation.

Answer:

First we must use the budget line and the tangency condition to solve for optimal values of coffee and energy drinks.

(Budget line)

Tangency condition:

Solving for C and E we get&

Next, use the utility function in its functional form to solve for U with the optimal bundle:

Amy's indifference curve formula through this bundle is:

If the Amy is not allowed to have any coffee, thenTherefore, to place Amy on the same indifference curve, we must pick the value of E for whichSolving for E, we getTo buy 5 packages of energy drinks Amy would need $60.00, so her friends would have to lend her $36.00 to compensate for not having coffee for one month. This is Amy's compensation variation.

3. Suppose that Eric is buying coffee and energy drinks for the last month of the semester. His preferences correspond to the utility function.When coffee costs $6 per pound and energy drinks cost $12 per package and Eric's budget is $24, he buys 2 pounds of coffee and 1 package of energy drinks. Find the compensated demand curve for energy drinks that passes through this point and graph it.

Answer:

To find the equation of the compensated demand curve first take the formula for the tangency condition and set the price of coffee equal to 10:

Next, rewrite the utility function as follows using the bundle given:

Now set the tangency condition formula equal to the indifference curve formula equal to each other and solve for C:

This is the compensated demand curve.

4. Tom is a college senior that wants to analyze the change in cost of living over the four years he spent in college. He tracked his purchases and the change in prices of a bundle consisting of coffee, cereal, and pizza.

2004

2005

2006

2007

Coffee

97 cups at $1.65

20 cups at $1.70

55 cups at $1.70

90 cups at $1.75

Cereal

45 boxes at $2.45

35 boxes at $2.60

43 boxes at $2.70

50 boxes at $2.75

Pizza

50 pizzas at $7.00

40 pizzas at $7.50

35 pizzas at $7.80

25 pizzas at $8.00

a) Using 2004 as the base period, create a Laspeyres price index to determine how Tom's cost of living changed. How did his cost of living change according to this measure?

b) Repeat part (a) first using 2005 as the base period and then using 2006 as the base period.

c) Do the price indexes you found in parts (a) and (b) imply an increase in Tom's cost of living over time? If not, by how much do they differ?

Answer:

a) 2004 (base period)- use 2004 quantity and prices

2005- use 2004 quantity and 2005 prices

2006- use 2004 quantity and 2006 prices

2007- use 2004 quantity and 2007 prices

Lasperyres index using 2004 as base year

2004:

2005:

2006:

2007:

b) 2005 Base Period

2004- use 2005 quantity and 2004 prices

2005 (base period)- use 2005 quantity and 2005 prices

2006- use 2005 quantity and 2006 prices

2007- use 2005 quantity and 2007 prices

Lasperyres index using 2005 as base year

2004:

2005:

2006:

2007:

2006 Base Period

2004- use 2006 quantity and 2004 prices

2005- use 2006 quantity and 2005 prices

2006 (base period)- use 2006 quantity and 2006 prices

2007- use 2006 quantity and 2007 prices

Lasperyres index using 2006 as base year

2004:

2005:

2006:

2007:

c) No, the indexes found in (a) and (b) do not imply the same percentage increases in Tom's cost-of-living over time. If 2004 is treated as the base year, then the percentage change in the cost-of-living from 2004 to 2007 was 11.8%. If 2005 was treated as the base year, then the percentage change increase was 10.5%. Finally, for base year 2006, the percentage change increase was 9.72%. So between the different base years they differed by a matter of about 2.8%.

Additional Exercises for Chapter 6

. What is the difference between the substitution effect of a price change and the income effect of a price change? How do they relate to an uncompensated price change?

2. Holly teaches second grade and has a budget of $50 per month to spend on candy and balloons for class parties. Candy (C) costs $5 per pound and balloons cost $10 per package. Fractions are allowed since the balloon packages can be split and Holly can purchase candy in uneven increments. Holly's marginal rate of substitution is and the formula for her indifference curve is . Suppose the price of balloons falls from $10 to $5. What is the uncompensated effect of her purchases of candy and balloons? What is the compensated effect? How much compensation is involved? Decompose the uncompensated price change into the substitution and income effects.

3. Holly's options and budget are as in question (2), except her marginal rate of substitution is now and the formula for her indifference curve is . Suppose the price of balloons falls from $10 to $5. What is the uncompensated effect of her purchases of candy and balloons? What is the compensated effect? How much compensation is involved? Decompose the uncompensated price change into the substitution and income effects.

4. The graph below shows the impact of an increase in the price of good X. Demonstrate the income effect by drawing the compensated budget line. Identify the substitution effect by labeling the bundle chosen before the price change, the bundle chosen after the price change, and the bundle chosen on the compensated budget line.

5. The graph below shows the impact of a decrease in the price of good Y. Demonstrate the income effect by drawing the compensated budget line. Identify the substitution effect by labeling the bundle chosen before the price change, the bundle chosen after the price change, and the bundle chosen on the compensated budget line.

6. Explain why the income effect is negative for a price increase if a good is normal and positive for a price increase if a good is inferior.

7. What is a Giffen good and how could a good with these characteristics violate the Law of Demand?

8. Assume that everything is as in question (2) and Holly has a budget of $50 per month to spend on candy and balloons for class parties. Candy (C) costs $5 per pound and balloons cost $10 per package. Holly's marginal rate of substitution is and the formula for her indifference curve is . When Holly gets to the store she finds that they are out of balloons. Since Holly is a loyal customer, the store owner would like to know how much it would cost to make up for this issue. Calculate the compensating variation.

9. Assume that everything is as in question (2) and Holly has a budget of $50 per month to spend on candy and balloons for class parties. Candy (C) costs $5 per pound and balloons cost $10 per package. Holly's marginal rate of substitution isand the formula for her indifference curve is . When Holly gets to the store she finds that they are out of balloons. Since Holly is a loyal customer, the store owner would like to know how much it would cost to make up for this issue. Calculate the compensating variation.

0. The formula for Holly's monthly demand curve for pencils is . Suppose that pencils cost $1.00 each. First graph the demand curve and shade in the area representing Holly's consumer surplus. Calculate her consumer surplus. What if the price of pencils falls to $0.50? Calculate the change in consumer surplus and show this change in surplus on the graph.

1. The formula for Holly's monthly demand curve for bottles of paint is . Suppose that bottle of paint cost $6.00 each. First graph the demand curve and shade in the area representing Holly's consumer surplus. Calculate her consumer surplus. What if the price of paint increases to $7? Calculate the change in consumer surplus and show this change in surplus on the graph.

2. What is a cost-of-living index? How does the Laspeyres price index possibly overstate the increase in the cost of living?

3. Explain how an increase in the wage rate could either increase or decrease the quantity of labor supplied. When would each of these responses be likely to occur?

4. What is the difference between an uncompensated and a compensated demand curve? When would they be the same and when would they differ?

5. As before, Holly is buying candy and balloons for her class. Her preferences correspond to the utility function.When candy costs $5 per pound and balloons cost $10 per package and Holly's budget is $50, she buys 5 pounds of candy and 2.5 packages of balloons. Find the compensated demand curve for candy that passes through this point and graph it.

6. As before, Holly is buying candy and balloons for her class. Her preferences correspond to the utility function.When candy costs $5 per pound and balloons cost $10 per package and Holly's budget is $50, she buys 7 pounds of candy and 1.5 packages of balloons. Find the compensated demand curve for candy that passes through this point and graph it.

Chapter 7

Sample Problems

. The family of isoquants for a firm hiring interns with a bachelor's degree in Economics and interns with a bachelor's in Business Administration appears in the graph below. What does this graph demonstrate about the substitutability of the inputs for this firm? Explain.

Answer:

The graph above shows that for this firm Economics majors are perfect substitutes for Business majors. The firm is willing to substitute one Economics major for 3 business majors.

2. Alex and Jessica own a coffee shop close to the local college campus. Their long run production function is the marginal product of labor is and the marginal product of capital is . Calculate the marginal rate of technical substitution for labor with capital, . Does their technology have increasing, decreasing, or constants returns to scale?

Answer:

Since Alex and Jessica's production function is a Cobb-Douglas production function of the form finding whether their technology has increasing, decreasing, or constant returns to scale becomes a matter of checking the sum of the exponents and .

Therefore Alex and Jessica's technology exhibits increasing returns to scale.

3. Suppose Alex and Jessica close their coffee shop two hours early for one whole week to train their baristas to make better coffee at a faster rate, so their production of labor doubles relative to their production of capital. What happens to the shop's MRTS? Is this a factor-neutral technical change? Explain.

Answer:

The MRTS changes in its slope, because labor is more productive relative to capital. This cannot be a factor-neutral technical change because the MRTS changed due to the improvement of labor production.

4. Alex and Jessica own two coffee shops that supply coffee to the local university. Labor is their only variable input. Suppose the marginal product of labor in Shop A is , where is the number of workers allocated to Shop A. The marginal product of labor of Shop B is , where is the number of laborers assigned to Shop B. Suppose that Alex and Jessica employ a total of 10 workers. What is the best assignment of the 10 workers to the two shops?

Answer:

First, write the as a function of the number of laborers assigned to Shop A, LA:

Next, find the level of LA, that equates the MPL in the two shops. This can be done by setting

So Alex and Jessica should assign 6 workers to Shop A, and the other 4 workers to Shop B.

Additional Exercises for Chapter 7

. Giselle owns a specialty lemonade stand called Pucker Up. Her production options for several amounts of labor appear in the table below. First, identify which combinations are efficient and which are inefficient. What characteristic determines whether a production method is inefficient?
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Production

Method

Units of Labor

Output

Efficient?

A

48

B

2

24

C

2

12

D

3

205

E

3

216

F

4

312

G

4

295

2. How is a firm's efficient production frontier from its production possibilities set? Why should a firm aim to achieve a point on its efficient production frontier?

3. Giselle can produce her specialty lemonade at Pucker Up daily according to the production function . How ...

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