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microeconomics

Questions and Answers of Microeconomics

e. Calculate the ratio of his period 1 to period 2 consumption plans in the two scenarios. Why are they the same?
d. Suppose that b 5 0.5. How much credit card debt does the student plan to have when he graduates?
c. Suppose I 5 $100,000, r 5 0.2, and d 5 0.95. If the student does not have present-bias, what consumption levels will the student plan to have in each period, and how much credit card debt does the
b. ** Derive his optimal consumption plan c0, c1, and c2 as a function of I, r,b, and d.
a. The student is unable to consume in periods 0 and 1 unless he borrows on his income from period 2. A credit card company offers him a credit card that charges no interest while he is in school and
B. Consider a three-period model of a college student in his junior year. Suppose this student has no income in periods 0 and 1 while he is in school but then expects an income I in period 2 after he
f. Prior to 2007, mortgage companies offered low teaser interest rates to new home buyers.Home values increased dramatically from 2001 through 2005, allowing homeowners to refinance at new teaser
e. Explain how students might end up with considerably more debt than they had planned to, and how limits on credit card borrowing might improve the welfare of some students.
d. Now consider our student in his sophomore year. Will the present-biased student now take on more debt than he planned as he was contemplating his sophomore year during his time as a freshman?
c. As our student consumes in his freshman year, he plans for consumption in his remaining three years in college. Will the present-biased student’s plans for consuming over the coming years now
b. Next, consider the student in his freshman year. How will students deviate in their actual consumption from their previous plans if they are present-biased?
a. Consider first a college student who receives credit card offers with teaser rates that charge low interest until the student graduates. As a high school senior, our student decides on how much
29.7 Everyday and Business Application: Teaser Rates on Credit Cards and Mortgages: Credit card companies often offer “teaser rates” to new customers; that is, interest rates that are initially
d. Can you use prospect theory to explain the fact that people prefer A to B and D to C? Draw a graph to explain your answer.
c. Would someone have to be risk seeking or risk averse when choosing D over C?
b. There is a different way to frame the same two programs: Under plan C, 400 people will die, and under plan D, there is a one-third chance that no one will die and a two-thirds chance that 600
B. Suppose that a local outbreak of a rare disease will, unless something is done, result in 600 deaths.There are two mutually exclusive emergency plans that can be put into place. Under plan A, 200
b. How can reference-based preferences on the part of the bishop explain the different responses to what amounts to the same question as to whether or not one can smoke during prayer?
29.6 Everyday Application: Framing the Options: Praying while Smoking, and Fighting Pandemics: By framing options for people in particular ways, we can sometimes get them to choose what we’d like
29.5 Everyday Application: Extreme Altruism and Normative Economics: In exercise 29.4, we considered the case of two individuals where one had the usual preferences that depend only on his own
g. Does your conclusion from A(g) hold?
f. Repeat (for the case of a 5 0.5 and b 5 0) using the Cobb–Douglas social welfare function W 5 u1 du2 112d2 and then using the Rawlsian social welfare function W 5 min5u1, u2 6.
e. What allocation of utilities and resources will be chosen if the ethical standard determining the distribution of resources is encompassed in the Benthamite social welfare function W 5 u1 1 u2?
d. Consider the special case in which a 5 0.5 and b 5 0. Which of the two individuals now has reference-based preferences, and in what way can you characterize these as being driven by some degree of
b. Solve for the allocation 1x, y2 as a function of u1; that is, solve for the optimal allocation of I between the two individuals given that individual 1 gets utility u1. (Hint: You do not need to
B. Let x indicate individual 1’s consumption (in dollars) and let y indicate individual 2’s consumption (in dollars). Suppose that individual 1’s utility is given by u1 1x, y2 5 x 2 ay and
h. Can you explain how many might feel discomfort in incorporating such reference-based preferences as a foundation for normative analysis of redistribution?
g. True or False: Envy is rewarded by each of our social indifference maps, but it is increasingly more rewarded as we move from the Rawlsian to the Benthamite extreme.
f. For an equal allocation of utilities when a . 0, will resources also be equally allocated?
e. Now consider the utility possibility frontier when a . 0. How will the Rawlsian and Benthamite social indifference maps now give different optimal divisions of resources? What about in-between
d. True or False: When a 5 0, equal division of resources between the two individuals is socially optimal for any social indifference map that is symmetric across the 45-degree line, including the
c. Suppose utility for individual 2 is simply equal to dollars of consumption and utility for individual 1 is dollars of own consumption minus some fraction a of dollars of individual 2’s
29.4 * Everyday Application: Reference Points, Happiness, and Envy: The stylized results from the happiness literature suggest that happiness, at least as reported on surveys, is
e. My friend used the evidence that four boys in a row was an unlikely event and five boys in a row would be an even more unlikely event as her reason for why she thought she had a good chance of her
d. What is the probability that my friend’s next (and fifth) child will be a boy? How does it compare to the probability that a woman who has had the boy-girl-boy-girl sequence will have a girl as
c. What is the probability that the sequence of a woman’s first four children is boy-girl-boy-girl?What about any other gender sequence?
b. What is the probability that her first five births are all boys?
B. One of my friends had four children, each a boy. She had really been hoping for a girl for some time and reasoned that she should try again. After all, having four boys in a row was an unlikely
f. In lotteries where people guess what number will be chosen, the total money pot gets split between the winners. In light of the fact that the gambler’s fallacy appears to be strong among lottery
e. The empirical evidence suggests that investors generally are less likely to dispose of losing stocks than they are to dispose of winning stocks. Is there another aspect of behavioral economics,
d. In the period leading up to the housing market crash in 2007, housing values were increasing at dramatic rates—by as much as 20% to 25% annually in some markets. Lots of people invested with
A. Both types of fallacies arise, for instance, for naive investors in stocks.a. When a stock falls in value, people often hold on to it based on the argument that “what goes down must come up.”
29.3 One topic investigated by behavioral economists but not covered in the text relates to how individuals assess probabilities of random events occurring repeatedly. The hot-hand fallacy is the
d. We mentioned in the text that prospect theory also allows for the possibility of probability weighting. If people overestimate what low probabilities mean, could this also help explain the Allais
c. Show that the Allais paradox would arise if the reference point were always $0 rather than what you assumed in your resolution to the Allais paradox.
b. Which gamble would be chosen by someone with such preferences in each of the two choices?How does this compare to the choices people actually make?
a. Consider the case where the reference points are as described in A(b). What are the utility values associated with the three outcomes when the choice is between G1 and G2? What are they when the
B. Suppose that individuals’ reference-based tastes can be described by u1x, r2 5 1x 2 r2 0.5 when x $ r and by v1x, r2 5 21r 2 x2 0.75 when x , r (where x is the dollar value of the outcome and r
b. Suppose that people use reference-based preferences to evaluate outcomes when making their choice between gambles. Why might the most reasonable reference point in the choice between G1 and G2 be
a. Why is this set of choices inconsistent with standard expected utility theory?
29.2 In the Appendix to Chapter 17, we introduced the Allais Paradox. It went as follows: Suppose there are three closed doors with $5 million, $1 million, and $0 behind them. You are first offered a
f. How could you keep the same (ordinal) preferences but transform the utility function in such a way as to cause the utility possibility set to be non-convex? Explain.
e. Do the two different utility functions represent the same underlying (ordinal) preferences? If so, explain the difference in the two utility possibility frontiers.
d. How would your answers change if we had specified the utility function as u1x1, x2 2 5 x1 bx2 10.52b2 with 0 , b , 0.5.
c. Use this to derive the utility possibility frontier. What shape does it have?
b. Derive the contract curve for this economy.
B. Suppose we have an Edgeworth economy in which both individuals have the utility function u1x1, x2 2 5 x1 ax2 112a2 and where the economy’s endowment of each of the two goods is e.a. Set up a
g. If markets were not allowed to operate in the case described in (f), where would the secondbest utility possibility frontier now lie relative to the first best?
f. Suppose instead that the current endowment bundle lies off the contract curve on the diagonal that runs from the upper left to the lower right corner of the Edgeworth Box. If competitive markets
e. Suppose that the government does not have access to efficient taxes for the purpose of redistributing resources. Rather, the government uses distortionary taxes, with the marginal cost of
d. Consider the original utility possibility frontier from part (b). Suppose the two individuals are currently endowed with the midpoint of the Edgeworth Box. Locate the point on the utility
c. How would the utility possibility frontier be different if the utility of consumer 2 were given by half the sum of the quantities of x1 and x2 in his basket?
b. What does the utility possibility frontier that derives from this contract curve look like? Carefully label intercepts and slopes.
a. Illustrate the contract curve for these two consumers in the Edgeworth Box assuming the overall endowment of each of the two goods in the economy is e.
29.1 For students who have read Chapter 16, we have indicated that, for exchange economies, the utility possibility frontier corresponds to utility levels on the contract curve that is contained in
Can you graph these two utility possibility frontiers and explain their relationship intuitively?
Verify the derivation of the second-best utility possibility frontier.
In Sectiona, we suggested that the shape of the utility possibility frontier has something to do with our assumptions about the marginal utility of income. Can you apply this insight here to explain
Verify the derivation of this first-best utility possibility frontier.
Explain how probability weighting can make sense of the fact that risk-averse individuals play in state lotteries. How can it explain purchases of insurance against small, low-probability risks when
Using the points analogous to A and B from panel (a) in Graph 29.5, show how panels (b) and(c) represent an increasingly equal income distribution.
Can the relationship in these graphs ever cross the 45-degree line?
Now suppose that government redistribution programs cause changes in behavior (such as those predicted by the Laffer Curve from Chapter 8). Can you argue that Rawlsian social indifference curves
Suppose that government income redistribution programs cause no change in behavior. True or False: Then the Rawlsian social indifference curves would imply full redistribution of income; that is,
In light of reference-based preferences with loss aversion, can you think of why credit card companies might have lobbied so hard for this?
Some years ago, Congress passed a law permitting stores to charge different amounts to cash customers than they do to credit card customers. When it became clear that the law would pass, the credit
Explain how the two sets of options are equivalent.
In his book Predictably Irrational, my psychologist colleague Dan ariely suggests (incorrectly, it turns out) that taxing gasoline may not have much impact on long-run gasoline consumption because,
On several occasions, I have observed one of my colleagues insist on taking a special trip to the movie rental place in order to return a movie that would otherwise be overdue when he could have just
In end-of-chapter exercise 10.7, we considered a very similar situation in which two individuals are identical except that one has a pizza coupon. We concluded that the two individuals will be able
True or False: If individual tastes are quasilinear in basketball tickets, the prices people were willing to accept should be identical to the prices they were willing to pay. (Hint: You may have
In the period prior to the 2007 housing crisis, it was easy for people to refinance their homes. If people choose 15-year (rather than 30-year) mortgages as a savings commitment device (as suggested
mortgages are the same and even if the 30-year mortgages allow people to pre-pay (and thus pay them off in 15 years) if they want to. How does this make sense from a behavioral economist’s
Many people buy health club memberships only never to use them. Yet they hold on to them and continue paying their monthly fees for long periods of time. How can the purchase of such memberships be
Consider again the example in within-chapter-exercise 29a.2. Suppose d 5 1/ 1.05 < 0.952. What is the highest level of b that could lead to the choices in the example? What would d have to be now if
What does it mean for b to be greater than 1 in the beta-delta model?
When psychologists offer people the choice of $50 today or $100 next year, they tend to pick the $50 immediately. But when the same people are offered the choice of $50 five years from now or $100
Suppose c 5 100, b 5 125, d 5 0.95, and b 5 0.8. What is the expected value of undertaking the investment c in period 1 when viewed from t 5 0? What is it when viewed from t 5 1?
28.11 Policy Application: The Pork Barrel Commons and the “Law of 1/N”: If you did not do these in Chapter 27, you can now do end-of-chapter exercises 27.11 and 27.12 to explore the problem of
f. What does your answer to (e) imply about the spending levels by benevolent local governments as competitive pressures increase in environments such as those described in (e)?
e. Suppose next that local property taxes are paid by both households and firms, but only households benefit from local public goods (like schools). If firms are mobile, in what sense does community
d. Consider an equilibrium with benevolent local governments providing efficient levels of local public goods. Can any government raise property values by raising or lowering taxes?True or False:
c. Suppose governments are charging low tax rates that result in inefficiently low levels of public goods. If community i raises its tax rate and provides more public goods, will population increase
b. Next, consider the competitive case. If the projects funded by local governments are truly local public goods, in what sense are taxes imposed by benevolent governments offset by benefits received?
B. Next, consider the opposite type of government, that is, one that is benevolent and raises taxes only to the extent to which it can find worthwhile public goods to finance. Suppose again that
h. True or False: To the extent to which government behavior is characterized by rent seeking, greater competition between governments enhances efficiency.
g. Evaluate the following statement: “Unless housing supply is perfectly elastic, government competition between Leviathan governments is not sufficient to eliminate political rents, but it
f. Use your answer to (e) to argue that there must exist some level of Leviathan taxation across competing communities that will be a Nash equilibrium.
e. Now consider all local governments setting some tax rate t and using revenues for political rents. If t is very low, can a single community’s Leviathan’s mayor benefit from raising his tax
d. True or False: So long as housing supply is not perfectly elastic, the Leviathan mayor in part(c) will be able to raise property taxes to fund political rents.

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