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_04___Tastes_and_Indifference_Curves

 

True / False

 

1. Complete tastes are tastes that make people desire at least some of every good.

  a. True
  b. False

 

ANSWER:   False
RATIONALE:   Complete tastes are tastes that allow a consumer to always rank any two bundles of goods.
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. If you observe me choosing bundle A over bundle B on Monday, bundle B over bundle C on Tuesday and bundle C over bundle A on Wednesday, it must be that my tastes violate transitivity.

  a. True
  b. False

 

ANSWER:   False
RATIONALE:   Not necessarily — it might be that I am indifferent between the three bundles. (It might also be that my tastes include a taste for variety over the course of the week.)
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. You like bundle A better than bundle B, and bundle C is an average between A and B. If your tastes satisfy convexity, then C is at least as good as A and as B.

  a. True
  b. False

 

ANSWER:   False
RATIONALE:   Convexity implies that you will prefer average bundles to extremes that you are indifferent between.
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. Bundle A is worse than bundle B, and bundle C is an average of bundles A and B. Then our usual assumptions about tastes imply that bundle B is at least as good as bundle C.

  a. True
  b. False

 

ANSWER:   False
RATIONALE:   The graph below illustrates a case that contradicts the statement.
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. The number of units of the good on the horizontal axis that we are willing to give up to get one more unit of the good on the vertical axis is equal to the absolute value of the slope of the indifference curve.

  a. True
  b. False

 

ANSWER:   False
RATIONALE:   The slope of the indifference curve gives us the number of units of the good on the vertical axis that we are willing to give up to get one more unit of the good on the horizontal 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

 

6. If the marginal rate of substitution is not diminishing, it must mean that tastes violate convexity (assuming that our other assumptions about tastes hold).

  a. True
  b. False

 

ANSWER:   True
RATIONALE:   The diminishing MRS feature of indifference maps is identical to the convexity assumption when our other assumptions about tastes hold.
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. Suppose tastes are NOT monotonic anywhere. Then diminishing MRS is not consistent with convexity of tastes.

  a. True
  b. False

 

ANSWER:   True
RATIONALE:   The indifference curve below has diminishing MRS, with bundles A and B both lying on the indifference curve. Bundle C is the average of A and B — but it lies in the less preferred region given that less is better when monotonicity is violated everywhere.Thus, averages are worse than extremes (i.e. convexity is violated) when we have diminishing MRS.
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. When the price of beer goes up, our model of tastes would typically require tastes to change.

  a. True
  b. False

 

ANSWER:   False
RATIONALE:   Prices change budgets — not tastes. Beer still tastes the same.
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. Two rationality assumptions economists make about tastes are first, that some individuals are not able to compare any two bundles of goods to one another, and second, that there is an internal consistency to tastes that makes it possible to choose a “best” bundle.

  a. True
  b. False

 

ANSWER:   False
RATIONALE:   It is true that one fundamental assumption economists make about tastes is that there is an internal consistency to tastes that makes it possible for one to choose a “best” bundle (transitivity), but it is not correct that the other fundamental assumption is that some people cannot compare bundles. On the contrary, the assumption is that everyone CAN compare two bundles (completeness).
POINTS:   1
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   10/7/2015 12:26 PM
DATE MODIFIED:   10/7/2015 12:36 PM

 

10. Economists define “rational” tastes as those which are objective and transitive.

  a. True
  b. False

 

ANSWER:   False
RATIONALE:   Economists define “rational” tastes as those which satisfy both completeness and transitivity.
POINTS:   1
DIFFICULTY:   A section material
QUESTION TYPE:   True / False
HAS VARIABLES:   False
DATE CREATED:   10/7/2015 12:26 PM
DATE MODIFIED:   10/7/2015 12:40 PM

 

Multiple Choice

 

11. You like bundle A better than bundle B, and bundle C is an average of bundles A and B. Which of the following is correct if your tastes satisfy our usual assumptions?

  a. Bundle C is at least as good as bundle B.
  b. Bundle A is at least as good as bundle C.
  c. Both (a) and (b).
  d. None of the above.
  e. There is not enough information to tell.

 

ANSWER:   a
RATIONALE:   If we removed some of each good from bundle A, continuity implies we’ll eventually get to a bundle A’ that is indifferent to B. The average of A’ and B — denoted C’ — is at least as good as B (due to convexity). But C has more of everything than C’ — which must mean that C is preferred to B. Thus, answer (a) is correct. Bundle A, however, might be worse than C, as illustrated in the graph below. Thus, (b) is not correct.
POINTS:   1
DIFFICULTY:   A-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

 

12. Consider a worker who dislikes working end enjoys consuming a composite good. With labor hours on the horizontal and the composite consumption good on the vertical axis, which of the following statements are true.

  a. If the worker’s tastes are convex, the slope of indifference curves increases as we move to the right in the graph.
  b. The worker becomes better off as we move to the northwest in the graph.
  c. A tax on wage income does not change this worker’s indifference map.
  d. All of the above.
  e. None of the above.

 

ANSWER:   d
RATIONALE:   The graph below shows an indifference curve that satisfies convexity here — A and B are indifferent, and C is the average of the two. C has more consumption (that the worker likes) and less labor (which the worker does not like) then D — and thus C is preferred to D. Since D is indifferent to A and B, we therefore have the average C being preferred to the extremes A and B. We also see that the more preferred bundles lie to the northwest — with more consumption and less labor. Finally, a tax on wages has nothing to do with how a worker feels about consumption and working — a tax on wages affects the worker’s budget, not his tastes.
POINTS:   1
DIFFICULTY:   A-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

 

Subjective Short Answer

 

13. Explain the following statement: For the same individual, tastes over goods may vary at the margin as we move from one bundle to another.

ANSWER:   At the margin, tastes are characterized by the marginal rate of substitution — which typically varies across an individual’s indifference map. Thus, as the bundle changes, an individual feels differently about the way in which he would like to trade the goods off against one another. But the entire indifference map characterizes the individual’s overall tastes — so the same overall tastes allow for different tastes at the margin as we move across the indifference map.
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

 

14. Explain the following statement: Individuals with different tastes might have the same tastes at the margin at their current consumption bundles.

ANSWER:   By different tastes, we mean different maps of indifference curves. So, to say that individuals have different tastes is the same as saying that different individuals have different indifference maps. But it may well be the case that individuals have chosen bundles at which their marginal rates of substitution are the same — which implies that their tastes are the same at the margin even though they differ overall.
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. Prove formally that the rationality axioms alone rule out the possibility of indifference curves crossing.

ANSWER:   Suppose A is strictly preferred to B and thus lies on a different indifference curve. Suppose further that the two indifference curves cross at some point C, a point that therefore lies on both indifference curves. This implies that and . But we know that . Transitivity implies that and implies — which contradicts A and C lying on the same indifference curve. Thus, it can’t be that indifference curves cross and the indifference map satisfies transitivity.
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

 

16. Suppose bundle A is better than bundle B for a consumer, and bundle C is an average of bundles A and B.

a. Use the continuity, convexity and monotonicity assumptions to formally prove that this implies that bundle C is better than bundle B.

b.Did you also — implicitly or explicitly — use the rationality axioms?

ANSWER:   a. Start with bundle A and imagine slowly removing some of each good from the bundle. Continuity and monotonicity then implies that eventually we will get to a bundle that is just as good (but no better) than B, i.e. . .

Next, take the average bundle between and B — and call it . Convexity implies that . is at least as good as B.

Finally, note that C contains more of every good than . Thus, monotonicity implies that C — and, since is at least as good as B, this implies that C B.

b. Yes, both the completeness and the transitivity assumptions were used. Completeness was used implicitly because we created bundles and just assumed that the consumer is able to compare them to other bundles. Transitivity was used in the last step where we concluded that we know C is better than B because we C is better than and is at least as good as B.

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. Consider the utility function . (Explain all your answers.)

a. Derive the function for the marginal rate of substitution.
b. Do the tastes represented by this utility function satisfy diminishing MRS?
c. The marginal utility of a good is defined as the change in utility from additional consumption of that good (holding all else constant). Derive the marginal utility of and .
d. Why does an ordinal approach to utility theory not any attention to what you derived in (c)?
e. Why does an ordinal approach to utility not treat the marginal rate of substitution the way it treats the marginal utility concept?

ANSWER:   a.
b. Holding fixed, our MRS function decreases (in absolute value) as increases — i.e. the slope of the indifference curves becomes shallower as we move to the right. Thus, the tastes indeed satisfy diminishing MRS.

c. and
d. The marginal utility of a good is in “utility units” — it gives us the additional utility the individual gets from more consumption of one of the goods. An ordinal approach to utility assumes utility cannot be measured objectively — and therefore utility-denominated concepts lack solid interpretation.

e. The marginal rate of substitution is not in utility units — but rather in units of that are objectively measurable. The reason for that is that the MRS is composed of one MU divided by another — which cancels the utility units; i.e.

.

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

 

 

 

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