Microeconomics An Intuitive Approach With Calculus 2nd Edition by Thomas Nechyba – Test Bank

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Microeconomics An Intuitive Approach With Calculus 2nd Edition by Thomas Nechyba – Test Bank

Chapter_02___A_Consumer_s_Economic_Circumstances

 

True / False

 

1. If all consumers are price-takers facing the same prices, then their budget lines will all have the same slope.

  a. True
  b. False

 

ANSWER:   True
RATIONALE:   The slope of the budget constraint is -p1/p2 — i.e. it is made up solely of prices. If those are the same for all consumers, then the slope is the same for all consumers.
POINTS:   1
DIFFICULTY:   A section material
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   9/1/2015 1:26 PM

 

2. If all consumers are price-takers facing the same prices, then all choice sets are the same.

  a. True
  b. False

 

ANSWER:   False
RATIONALE:   While the slopes of the budget constraints will be the same for all consumers, the choice sets will differ depending on each consumer’s income.
POINTS:   1
DIFFICULTY:   A section material
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   9/1/2015 1:26 PM

 

3. Regardless of which consumption bundle in her choice set a consumer chooses, she will spend all of her available income.

  a. True
  b. False

 

ANSWER:   False
RATIONALE:   All available income is spent only on the portion of the choice set that is equal to the budget line (or budget constraint).
POINTS:   1
DIFFICULTY:   A section material
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   9/1/2015 1:26 PM

 

4. In a graph of choice sets, a price change causes the slope of budget lines to change.

  a. True
  b. False

 

ANSWER:   True
RATIONALE:   As the price of a good is reduced, the budget line swings outward.
POINTS:   1
DIFFICULTY:   A section material
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   10/7/2015 11:46 AM

 

5. If a consumer’s fixed income increases, his opportunity cost also increases.

  a. True
  b. False

 

ANSWER:   False
RATIONALE:   Although a consumer’s choices may change, his opportunity cost does not, since the opportunity cost is determined by the price of the good, not by his increased income.
POINTS:   1
DIFFICULTY:   A section material
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   10/7/2015 11:33 AM

 

6. When the good on the vertical axis is a composite good, the slope of the budget line is equal to minus the price of the good on the horizontal axis.

  a. True
  b. False

 

ANSWER:   True
RATIONALE:   The price of composite goods is 1 — which means that the usual slope -p1/p2 becomes -p1.
POINTS:   1
DIFFICULTY:   A section material
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   9/1/2015 1:26 PM

 

7. When the good on the horizontal axis is a composite good, the slope of the budget constraint is minus the price of the good on the vertical axis.

  a. True
  b. False

 

ANSWER:   False
RATIONALE:   The slope is usually -p1/p2 — and when p1=1 (as it is when good 1 is a composite good), then the slope of the budget line is -1/p2; i.e. minus the inverse of p2.
POINTS:   1
DIFFICULTY:   A section material
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   9/1/2015 1:26 PM

 

8. While the endowment bundle must lie on the original budget line, it need not lie on the budget line when prices change.

  a. True
  b. False

 

ANSWER:   False
RATIONALE:   Consumers always have the option of consuming their endowment bundle — which means the endowment bundle always lies on the budget line regardless of what happens to prices.
POINTS:   1
DIFFICULTY:   A section material
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   9/1/2015 1:26 PM

 

9. For choice sets emerging from “exogenous” income, the budget line will shift parallel whenever both prices change by the same percentage.

  a. True
  b. False

 

ANSWER:   False
RATIONALE:   Since the slope of the budget constraint is the negative price ratio, the slope will remain the same if both prices increase by the same factor — which means the new budget line will be parallel to the original.
POINTS:   1
DIFFICULTY:   A section material
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   9/1/2015 1:26 PM

 

10. For choice sets generated from endowment bundles, the budget line will shift parallel if both prices change by the same proportion.

  a. True
  b. False

 

ANSWER:   False
RATIONALE:   The slope of the budget remains unchanged — as does the endowment bundle. Since the budget line always has to pass through the endowment bundle, an simultaneous and proportionate increase in both prices will cause no change in the budget constraint.
POINTS:   1
DIFFICULTY:   A section material
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   9/1/2015 1:26 PM

 

11. ​The budget line on a graph represents choices which exhaust all resources.

  a. True
  b. False

 

ANSWER:   True
RATIONALE:   The budget line represents all combinations of goods that, if chosen by a particular consumer would leave no money in his or her budget.
POINTS:   1
DIFFICULTY:   A Section material
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   10/7/2015 11:29 AM
DATE MODIFIED:   10/7/2015 11:34 AM

 

12. In a graph of choice sets, a price change affects the ratio but does not affect the budget line.

  a. True
  b. False

 

ANSWER:   False
RATIONALE:   A price change will cause the slope of a budget line to change.
POINTS:   1
DIFFICULTY:   A section material
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   10/7/2015 11:39 AM
DATE MODIFIED:   10/7/2015 11:44 AM

 

Multiple Choice

 

13. The following changes in a consumer’s economic circumstances result in a steeper budget line with the vertical intercept unchanged. (Denote the good on the horizontal as good 1 and the good on the vertical as good 2.)

  a. A k percent decrease in the price of good 2 combined with a k percent decrease in income
  b. A k percent increase in the price of good 2 combined with a k percent decrease in income
  c. A k percent decrease in the price of good 2 combined with a k percent increase in income
  d. A k percent increase in the price of good 2 combined with a k percent increase in income.
  e. None of the above

 

ANSWER:   a
RATIONALE:   A decrease in the price of good 2 causes the slope to become steeper, and a decrease in income shifts the budget line inward. Together, these imply that the budget line rotates inward with the vertical intercept fixed — just as it would if the price of good 1 increases by itself.
POINTS:   1
DIFFICULTY:   A section material
QUESTION TYPE:   Multiple Choice
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   9/1/2015 1:26 PM

 

14. Suppose inflation comes in the form of an across-the board increase in all prices by some percentage k. For a consumer with exogenous income operating in a 2-good world, this will cause the budget constraint to

  a. rotate inward b. rotate outward
  c. shift out in a parallel way d. shift inward in a parallel way
  e. none of the above    

 

ANSWER:   d
RATIONALE:   Since the slope of the budget is the price ratio, and since both prices increased by the same proportion, the slope is unchanged — but the same level of exogenous income now buys less.
POINTS:   1
DIFFICULTY:   A section material
QUESTION TYPE:   Multiple Choice
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   9/1/2015 1:26 PM

 

15. Suppose you are given a coupon for pizza. This coupon lowers the price for each additional pizza you buy by 5% for each addition pizza you buy. What happens to your budget constraint, with pizza on the horizontal axis and a composite good on the vertical?

  a. The vertical intercept remains the same but the slope becomes steeper as more pizzas are bought.
  b. The vertical intercept increases and the slope becomes steeper as more pizzas are bought.
  c. The vertical intercept remains the same but the slope becomes shallower as more pizzas are bought.
  d. The vertical intercept increases but the slope becomes shallower as more pizzas are bought.
  e. None of the above.

 

ANSWER:   c
RATIONALE:   If no pizzas are bought, then nothing changes — implying that the vertical intercept remains the same. But as more pizzas are bought, the price falls, implying an increasingly shallower budget line.
POINTS:   1
DIFFICULTY:   A-Section material
QUESTION TYPE:   Multiple Choice
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   9/1/2015 1:26 PM

 

16. Suppose the government wants to discourage excessive consumption of alcohol. It therefore imposes a per-unit tax on alcohol that increases as more alcohol is bought by a consumer at a store. What happens to a consumer’s budget at a liquor store (with liters of alcohol on the horizontal axis and a composite good on the vertical) — assuming the consumer takes only one trip to the store.

  a. The vertical intercept decreases and the slope becomes shallower as more alcohol is bought.
  b. The vertical intercept remains constant but the slope becomes shallower as more alcohol is bought.
  c. The vertical intercept decreases and the slope becomes steeper as more alcohol is bought.
  d. The vertical intercept remains constant but the slope becomes steeper as more alcohol is bought.
  e. None of the above.

 

ANSWER:   d
RATIONALE:   If no alcohol is bought, nothing changes as a result of the tax — implying the vertical intercept remains unchanged. But the price of alcohol increases as more is bought — implying a steepening of the slope.
POINTS:   1
DIFFICULTY:   A-Section material
QUESTION TYPE:   Multiple Choice
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   9/1/2015 1:26 PM

 

Subjective Short Answer

 

17. Consider a consumer with a choice set that emerges from an exogenous income I. Suppose that, as a result of changes in a consumer’s economic circumstances, the budget line rotates outward, with the vertical intercept remaining unchanged but the horizontal intercept shifting to the right. How could this have happened if the price of the good on the horizontal axis did not change?

ANSWER:   If the price of the good on the vertical axis increases by the same proportion as income does. (The increase in income along causes a parallel shift outward, and the increase in the price of good 2 causes the slope to become shallower. If the two increase by the same percentage, the amount of good 2 that is affordable remains unchanged while the amount of good 1 that is affordable increases.)
POINTS:   1
DIFFICULTY:   A section material
QUESTION TYPE:   Subjective Short Answer
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   9/1/2015 1:26 PM

 

18. Consider a consumer with a choice set that emerges from an exogenous income I. Suppose that, as a result of changes in a consumer’s economic circumstances, the budget line rotates outward, with the vertical intercept remaining unchanged but the horizontal intercept shifting to the right. Demonstrate, using the budget line equation, how this could have happened if the price of the good on the horizontal axis did not change?

ANSWER:   The budget equation is x2=I/p2 – (p1/p2)x12, with the first term representing the intercept and the term in parenthesis representing the slope. The rotation of the budget that is described implies the intercept remains constant and the slope falls in absolute value. If p1 does not change, this can happen only if I and p2 change by the same factor k — which then cancels in the first term (leaving the intercept unchanged) and causes the second term to fall in absolute value.
POINTS:   1
DIFFICULTY:   B-Section material
QUESTION TYPE:   Subjective Short Answer
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   9/1/2015 1:26 PM

 

19. Suppose that the price of a TV is $200 and he price of an MP3 player is $50. What is the opportunity cost of a TV (in terms of MP3 players), and what is the opportunity cost of an MP3 player (in terms of TVs)?

ANSWER:   The opportunity cost of a TV is 4 MP3 players, and the opportunity cost of an MP3 player is one fourth of a TV.
POINTS:   1
DIFFICULTY:   Section A material
QUESTION TYPE:   Subjective Short Answer
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   9/1/2015 1:26 PM

 

20. Derive the budget line equation for the case where good 2 is a composite good. What is the vertical intercept and what is the slope?

ANSWER:   Since p2 = 1, the usual budget line equation x2=I/p2 – (p1/p2)x1 becomes x2=Ip1x1, an equation with a vertical intercept of I and a slope of – p1.
POINTS:   1
DIFFICULTY:   B section material
QUESTION TYPE:   Subjective Short Answer
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   9/1/2015 1:26 PM

 

21. Derive the budget line equation for the case where good 1 is a composite good. What is the vertical intercept and what is the slope?

ANSWER:   Since p1 = 1, the usual budget line equation x2=I/p2 – (p1/p2)x1 becomes
x2=I/p2 – (1/p2)x1, an equation with a vertical intercept of I/p2 and a slope of – (1/p2).
POINTS:   1
DIFFICULTY:   B section material
QUESTION TYPE:   Subjective Short Answer
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   9/1/2015 1:26 PM

 

22. A consumer has $1,000 a week to spend on renting square feet of housing (at a price of $5 per square foot) and eating out (at a price of $20 per meal). With square feet of housing on the horizontal and meals on the vertical axis, what is the vertical intercept and what is the slope of this consumer’s budget constraint?

ANSWER:   The most meals that can be consumed with $1,000 is 50 per week — implying a vertical intercept of 50. The most square feet that can be rented with $1,000 per week is 200, implying a horizontal intercept of 200. The slope is then -50/200=-1/4.
POINTS:   1
DIFFICULTY:   A-Section material
QUESTION TYPE:   Subjective Short Answer
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   9/1/2015 1:26 PM

 

23. A consumer has $1,000 a week to spend on renting square feet of housing x1 (at a price of $5 per square foot) and eating out meals x2 (at a price of $20 per meal). Derive the budget line equation and find the opportunity cost of housing in terms of meals in your equation.

ANSWER:   The budget equation x2=I/p2 – (p1/p2)x1 becomes x2=1000/20 – (5/20)x1 or x2=50 – (1/4)x1. The slope of the budget line is equal to the opportunity cost of housing in terms of meals — and this slope is -1/4 in the equation.
POINTS:   1
DIFFICULTY:   B-Section material
QUESTION TYPE:   Subjective Short Answer
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   9/1/2015 1:26 PM

 

24. Suppose the government levies a per-unit tax on TVs, and this tax increases the price of TVs by $10.

a. On a graph with TVs on the horizontal axis and “$’s of other consumption” on the vertical, illustrate how the budget constraint for a consumer with exogenous income changes as a result of the tax.

b. Suppose you know the bundle on the after-tax budget that is chosen by the consumer. Illustrate on your graph how much in tax revenue the government is raising from this consumer.

c. If the government replaced the tax on TVs with a lump sum tax that does not alter any prices but raises the same amount of revenue from the consumer, how would this consumer’s budget constraint change?

ANSWER:   a. The graph should have two budget constraints with the same vertical intercept but different slopes — with the steeper budget line representing the after tax case.

b. The tax revenue the government collects is the vertical distance between the after-tax bundle that is bought and the before-tax budget line.

c. The consumer’s after-tax budget constraint would rotate through the previous after-tax bundle — becoming shallower as the price distortion from the TV tax is lifted and ending up parallel to the before-tax budget.

POINTS:   1
DIFFICULTY:   A-Section material
QUESTION TYPE:   Subjective Short Answer
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   9/1/2015 1:26 PM

 

25. Suppose the government levies a per-unit tax on TVs, and this tax increases the price of TVs by $100. Model TVs as x1 and all other goods as a composite good x2.

a. For a consumer with income I, write down an equation for the before-tax budget line.

b. Write down the after-tax budget line equation.

c. Suppose you know the bundle on the after-tax budget that is chosen by the consumer contains 3 TVs. How much in tax revenue is the government raising from this consumer?

d. If the government replaced the tax on TVs with a lump sum tax that does not alter any prices but raises the same amount of revenue from the consumer, how would this change the consumer’s budget line equation?

ANSWER:   a. x2=Ip1x1 or I= p1x1+ x2

b. x2=I – (p1+100)x1 or I= (p1+100)x1+ x2

c. $300

d. x2=(I – 300)/p2 – (p1/p2)x1 or I= p1x1+ x2 + 300

POINTS:   1
DIFFICULTY:   B-Section material
QUESTION TYPE:   Subjective Short Answer
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   9/1/2015 1:26 PM

 

26. Suppose a business offers a 10% discount on the good x1 that it sells.

a. Illustrate a consumer’s before and after-discount budget constraint by modeling x2 as a composite good.

b. Suppose you observe only the after-discount consumption decision of the consumer. Can you tell from this information how much revenue the firm is giving up (from this consumer) by offering the discount? If so, illustrate this in your graph.

c. Suppose that, instead of the firm offering the 10% discount, the government subsidized consumption of x1 sufficiently to reduce p1 by 10%. Suppose again that you only observe the after-subsidy decision of the consumer. Can you tell how much of a subsidy payment is made to this consumer by the government? If so, illustrate it in your graph.

d. Why are your answers to (b) and (c) different?

ANSWER:   a. The graph should contain two budget lines with the same vertical intercept but different slopes — with the shallower constraint representing the after-discount budget constraint.

b. No, you cannot. The reason for this is that we do not know what decision the consumer would have made in the absence of the discount — and so we can’t tell whether (or how much) revenue was lost.

c. Yes, you can. The subsidy payment by the government is the vertical difference between the before and after-subsidy constraints measured at the after-subsidy consumption bundle.

d. If you are a firm and you want to assess the impact on revenues of a discount policy, you need to know what consumers do both before and after the discount — because you need to calculate the difference in revenues. If you are a government subsidizing a good, you don’t have to know what consumers do before the subsidy in order to calculate how much the subsidy will cost — because all that matters is how much consumers will buy under the subsidy.

POINTS:   1
DIFFICULTY:   A-Section material
QUESTION TYPE:   Subjective Short Answer
HAS VARIABLES:   False
DATE CREATED:   9/1/2015 1:26 PM
DATE MODIFIED:   9/1/2015 1:26 PM

 

Chapter_06___Doing_the__Best__We_Can

True / False

 

1. When the price of peaches went up, people bought fewer peaches and more strawberries. This is an indication that tastes have changed as a result of the price increase.

  a. True
  b. False

 

ANSWER:   False
RATIONALE:   This is an indication the optimal quantity demanded has changed as a result of the increase in price — and the optimal quantity demanded results from tastes confronting economic circumstances. The change in the price of peaches is a change in circumstances — which in turn affects demand, not a change in tastes.
POINTS:   1
DIFFICULTY:   A-Section Material
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   2/11/2015 10:52 PM
DATE MODIFIED:   2/11/2015 10:52 PM

 

2. The only way a consumer can optimize at a corner of her budget is if at least one of the goods is not essential.

  a. True
  b. False

 

ANSWER:   True
RATIONALE:   A corner solution where a consumer does not consume some of one good can arise only if indifference curves cross at least some of the axes — which implies that at least some goods are not essential.
POINTS:   1
DIFFICULTY:   A-Section Material
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   2/11/2015 10:52 PM
DATE MODIFIED:   2/11/2015 10:52 PM

 

3. If not all goods are essential, a consumer will end up optimizing at a corner solution.

  a. True
  b. False

 

ANSWER:   False
RATIONALE:   If not all goods are essential, a consumer might end up optimizing at a corner solution — but she might also optimize at an interior solution, as illustrated in this graph.
POINTS:   1
DIFFICULTY:   A-Section Material
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   2/11/2015 10:52 PM
DATE MODIFIED:   2/11/2015 10:52 PM

 

4. If all goods are essential, a consumer will optimize at an interior solution.

  a. True
  b. False

 

ANSWER:   True
RATIONALE:   When all goods are essential, no indifference curve crosses any axis — which means no optimum can ever occur on an axis.
POINTS:   1
DIFFICULTY:   A-Section Material
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   2/11/2015 10:52 PM
DATE MODIFIED:   2/11/2015 10:52 PM

 

5. Suppose tastes satisfy our usual assumptions. Kinks in budget constraints do not give rise to the possibility of multiple solutions unless the kinds produce a non-convexity in the choice set.

  a. True
  b. False

 

ANSWER:   True
RATIONALE:   Multiple solutions can only arise from non-convexities — and if tastes are convex, it must be that the non-convexity is in the choice set. But not all kinks produce non-convexities — only inward pointing kinks.
POINTS:   1
DIFFICULTY:   A-Section Material
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   2/11/2015 10:52 PM
DATE MODIFIED:   2/11/2015 10:52 PM

 

6. Ellie and Jenny both brought grapes and crackers in their school lunches. If they have different marginal rates of substitution of grapes for crackers, their parents have not allocated lunch resources efficiently.

  a. True
  b. False

 

ANSWER:   True
RATIONALE:   If they both have some of each, then efficiency requires their MRS to be the same — otherwise they can trade and make each other better off.
POINTS:   1
DIFFICULTY:   A-Section Material
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   2/11/2015 10:52 PM
DATE MODIFIED:   2/11/2015 10:52 PM

 

7. If we were the only two people in the world and I like bananas while you hate them, efficiency demands that I get all bananas.

  a. True
  b. False

 

ANSWER:   True
RATIONALE:   If you get any bananas, we can make both of us better off by taking some of your bananas and giving them to me.
POINTS:   1
DIFFICULTY:   A-Section Material
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   2/11/2015 10:52 PM
DATE MODIFIED:   2/11/2015 10:52 PM

 

8. You have observed a consumer who purchases only goods and and have concluded that the consumer’s tastes are quasilinear in . Whether the consumer purchases more or less of when the price of falls then depends on the size of the substitution effect.

  a. True
  b. False

 

ANSWER:   False
RATIONALE:  
POINTS:   1
DIFFICULTY:   A-Section Material
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   2/11/2015 10:52 PM
DATE MODIFIED:   2/11/2015 10:52 PM

 

9. Kinks in budget constraints always produce non-convexities in choice sets.

  a. True
  b. False

 

ANSWER:   False
RATIONALE:   Only inward kinks produce such non-convexities; outward kinks do not.
POINTS:   1
DIFFICULTY:   A section material
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   10/7/2015 2:13 PM
DATE MODIFIED:   10/7/2015 2:19 PM

 

10. Essential goods give rise to corner solutions.

  a. True
  b. False

 

ANSWER:   False
RATIONALE:   On the contrary, essential goods cannot give rise to corner solutions. It can never be optimal to choose a bundle with zero quantity of one of the goods, since that would be the same as choosing zero quantity of all the goods.
POINTS:   1
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   10/7/2015 2:14 PM
DATE MODIFIED:   10/7/2015 2:25 PM

 

Multiple Choice

 

11. Suppose you solve a consumer’s constrained 2-good optimization problem for a given economic environment — and your answer contains a negative consumption level of good 2. Which of the following is a valid conclusion on your part:

  a. The true optimum has the consumer consume none of good 1.
  b. The true optimum has the consumer consume none of good 2.
  c. There are multiple “true” optimal consumption bundles.
  d. The consumer will sell good 2.
  e. None of the above.

 

ANSWER:   b
RATIONALE:   The first order conditions identify tangencies of indifference curves with budget constraints — no matter where they occur. If the consumption level is negative for one good, it means that the true optimum has the consumer consume none of that good, with all income spent on the other good. The math method does not pick up this true optimum because the indifference curve that passes through this corner solution is not tangent to the budget constraint.
POINTS:   1
DIFFICULTY:   B-Section Material
QUESTION TYPE:   Multiple Choice
HAS VARIABLES:   False
DATE CREATED:   2/11/2015 10:52 PM
DATE MODIFIED:   2/11/2015 10:52 PM

 

Multiple Response

 

12. Which of the following is correct about a consumer’s optimization problem:

  a. In order for a consumer to not be optimizing at a corner solution, it is necessary  for us to assume that all goods are essential.
  b. In order for a consumer to not be optimizing at a corner solution, it is sufficient for us to assume that all goods are essential.
  c. In order for a consumer to not be optimizing at a corner solution, it is necessary and sufficient for us to assume that all goods are essential.
  d. None of the above.

 

ANSWER:   b
RATIONALE:   It is not necessary for us to assume that all goods are essential, because it is possible for some goods not to be essential and for consumers to still be optimizing at an interior solution. It is, however, sufficient, for us to make this assumption — because if we assume all goods are essential, then we know for sure that a corner solution is not possible.
POINTS:   1
DIFFICULTY:   A-Section Material
QUESTION TYPE:   Multiple Response
HAS VARIABLES:   False
DATE CREATED:   2/11/2015 10:52 PM
DATE MODIFIED:   2/11/2015 10:52 PM

 

13. Suppose that choice sets are convex but we tastes may or may not be convex. (Assume all our other usual assumptions about tastes hold.) The first order conditions of the constrained utility maximization problem are then

  a. necessary conditions for a true optimum.
  b. sufficient conditions for a true optimum.
  c. necessary and sufficient conditions for a true optimum.
  d. none of the above.

 

ANSWER:   d
RATIONALE:   The first order conditions do not hold at a corner solution — and thus the first order conditions are not necessary. When tastes are non-convex, there will furthermore be points at which the first order conditions hold but that are not a true optimum. Thus, if tastes are permitted to be non-convex, the first order conditions are not sufficient either.
POINTS:   1
DIFFICULTY:   B-Section Material
QUESTION TYPE:   Multiple Response
HAS VARIABLES:   False
DATE CREATED:   2/11/2015 10:52 PM
DATE MODIFIED:   2/11/2015 10:52 PM

 

Subjective Short Answer

 

14. Which of the following statements is correct and which is not? Explain why.

a. When we all face the same prices, our tastes become the same.
b. When we all face the same prices, our tastes become the same at the margin.

ANSWER:   The correct statement is statement (b). When we all face the same prices, we all optimize where our MRS is equal to the same value, the negative price ratio. Thus, our MRS — our “tastes at the margin” — is the same as a result of the decisions we make when we face the same prices. But there is nothing about the fact that we all face the same prices that changes our indifference maps — or our tastes. Thus, we are as different in our tastes before we face the same prices as we are afterwards.
POINTS:   1
DIFFICULTY:   A-Section Material
QUESTION TYPE:   Subjective Short Answer
HAS VARIABLES:   False
DATE CREATED:   2/11/2015 10:52 PM
DATE MODIFIED:   2/11/2015 10:52 PM

 

15. Suppose that choice sets are convex. State assumptions about tastes that are necessary and sufficient to guarantee that the solution to the consumer optimization problem is a unique interior solution. (Explain)

ANSWER:   To rule out corner solutions, it is necessary and sufficient to assume that all goods are essential. To rule out multiple interior solutions, it is necessary and sufficient to assume that tastes are (strictly) convex. While these assumptions are not necessary for the solution to be a unique interior solution, they are necessary to guarantee that the solution to be unique and in the interior.
POINTS:   1
DIFFICULTY:   A-Section Material
QUESTION TYPE:   Subjective Short Answer
HAS VARIABLES:   False
DATE CREATED:   2/11/2015 10:52 PM
DATE MODIFIED:   2/11/2015 10:52 PM

 

16. Suppose that choice sets are convex. State assumptions about tastes that are necessary and sufficient to guarantee that the first order conditions are necessary and sufficient for identifying a true optimum.

ANSWER:   First order conditions are necessary and sufficient for an optimum if there are no corner solutions and no multiple “solutions” (where some of them are local minima). Ruling out corners solutions is accomplished by assuming that all goods are essential. Ruling out multiple “solutions” is done by assuming convex tastes. Thus, assuming convex tastes and all goods being essential makes first order conditions necessary and sufficient.
POINTS:   1
DIFFICULTY:   B-Section Material
QUESTION TYPE:   Subjective Short Answer
HAS VARIABLES:   False
DATE CREATED:   2/11/2015 10:52 PM
DATE MODIFIED:   2/11/2015 10:52 PM

 

17. Explain how we can estimate the shape of a person’s indifference map by observing choices under different economic circumstances. Explain also why we will not be able to identify any non-convexities in tastes from our observations.

ANSWER:   The reason we can identify the shape of indifference maps from choices is that we know that, at any interior solution, the MRS is equal to the negative price ration. So, if we observe an interior choice at a given set of prices, we know what the MRS is at that bundle. If we observe enough of these bundles with associated MRS, we can estimate the shape of indifference curves. But no choice is ever made along non-convex portions of indifference curves — which means we can never identify the shape of non-convexities if they are there.
POINTS:   1
DIFFICULTY:   A-Section Material
QUESTION TYPE:   Subjective Short Answer
HAS VARIABLES:   False
DATE CREATED:   2/11/2015 10:52 PM
DATE MODIFIED:   2/11/2015 10:52 PM

 

18. Currently, the price of consuming housing is lowered by the fact that home mortgage interest is tax deductible. Suppose the government proposed to eliminate this implicit subsidy of your housing consumption and at the same time lowers taxes on all other goods.

a. With housing consumption on the horizontal axis and all other consumption on the vertical, illustrate you current optimal consumption bundle.

b. After looking over the government’s proposal, you decide that you don’t care one way or another whether the government implements this proposal. On your graph, indicate your new budget constraint and new optimal bundle under the proposal.

c. I also look over the proposal and find that my current consumption bundle also lies on the budget constraint I would face under the proposal. Am I also indifferent between the two proposals?

ANSWER:  

a. The current optimal bundle is A in the graph below.

b. The price of housing increases while the price of other consumption falls. Thus, the budget becomes steeper, as indicated by the steeper constraint in the graph. The new optimal bundle is B.

c. My new budget constraint passes through A, with a portion above A then lying above my original indifference curve. I will therefore choose some point on that portion of the new budget (like bundle B) — and this will place me on a higher indifference curve. So I will prefer the proposal over the current tax law.

POINTS:   1
DIFFICULTY:   A-Section Material
QUESTION TYPE:   Subjective Short Answer
HAS VARIABLES:   False
DATE CREATED:   2/11/2015 10:52 PM
DATE MODIFIED:   2/11/2015 10:52 PM

 

19. Currently. the price of consuming housing is lowered by the fact that home mortgage interest is tax deductible. Suppose the government proposed to eliminate this implicit subsidy of your housing consumption, raising the price from to . At the same time, the government lowers the tax on other consumption, lowering the price from to .

a. Write down your original budget constraint assuming the consumer has income I.
b. Suppose the utility function captures your tastes, and suppose ,  , , and . Write out the utility maximization problem for this consumer prior to any policy change.
c. How much housing and other goods will this consumer consume prior to any policy change?
d. When the policy change goes into effect, will this consumer still be able to afford the bundle you derived in (c)?
e. When the policy change goes into effect, what bundle will the consumer consume?

ANSWER:   a.
b.
c.
d. Yes, because .
e. Solving , we get .
POINTS:   1
DIFFICULTY:   B-Section Material
QUESTION TYPE:   Subjective Short Answer
HAS VARIABLES:   False
DATE CREATED:   2/11/2015 10:52 PM
DATE MODIFIED:   2/11/2015 10:52 PM

 

20. In the movie “Baby Boom”, Dianne Keaton finds out that a relative tragically died in an accident and bequeathed her an infant. The movie then explores how Dianne Keaton makes fundamentally different choices as a result of this unexpected change in her life. It makes the point that new parents often emphasize — our “tastes change” when children enter the household.
a. Consider Dianne Keaton’s budget constraint over leisure (on the horizontal axis) and consumption (on the vertical). What is the slope of the budget constraint? Indicate her optimal choice A prior to finding out she suddenly has an infant child.
b. Suppose that the child came with a trust fund that permits Dianne Keaton to charge any child-related expenses to that fund. Thus, the child does not come with any additional expenses – and the budget constraint you derived in part (a) does not change. Still, we observe that Dianne Keaton now chooses more leisure and less consumption. What must have happened to the marginal rate of substitution at the bundle A in order for us to make sense of Dianne Keaton’s change in behavior?
c. Draw the indifference curve through A before and after Dianne Keaton finds out she suddenly has a child. If you ordinarily saw two such indifference curves (outside the context of this example), could you think that these could emerge from the same map of indifference curves or would you think they represent indifference curves from two different people whose tastes differ? Explain.
d. Economists tend to resist the temptation of explaining changes in behavior as resulting from changes in tastes. Rather, we tend to think of changes in behavior as arising from changes in circumstances. Suppose that Dianne Keaton’s tastes are actually over three “goods” – consumption of goods and leisure — and “consumption” of children. Dianne Keaton’s true indifference curves would thus be three dimensional – with your graphs so far representing two dimensional “slices”. When viewed in this light, could the 2-dimensional indifference curves you graphed in (c) arise from a single set of 3-dimensional indifference surfaces? Explain (without attempting to graph anything in 3 dimensions).
e. Suppose that it had always been an option for Dianne Keaton to adopt a child, and suppose that the cost of doing so is negligible. If Dianne Keaton reports being happier after she inherits her relative’s child, was she fully optimizing before (assuming that she attaches no particular value to the fact that the child she inherited was her relative’s)?
f. In principle, could Dianne Keaton’s tastes be such that she works more when she gets the child and is still happier than before? Under the usual assumption about tastes – and treating children the way we treat goods – could Dianne Keaton be less happy as a result of getting the child?

ANSWER:   a.

b. The indifference curve through A must be getting steeper — which means the MRS is getting larger in absolute value.

c. These could ordinarily not come from the same tastes because indifference curves from the same tastes cannot cross.

d. Yes. If there is a third good, then the before and after indifference curves in the graph are “slices” projected onto 2 dimensions — but they lie at different levels of the third good and therefore do not actually cross in 3 dimensions.

e. No, in this case she was not originally optimizing since her after bundle was also available before.

f. If children are really “good”, then “more is better” all else equal. So, under the usual assumptions, Dianne Keaton should be happier after inheriting the child. But it also could be the case that her after slice is shallower at A when she gets the child — in which case she would consume less leisure and work more.

POINTS:   1
DIFFICULTY:   A-Section Material
QUESTION TYPE:   Subjective Short Answer
HAS VARIABLES:   False
DATE CREATED:   2/11/2015 10:52 PM
DATE MODIFIED:   2/11/2015 10:52 PM

 

 

 

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