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Microeconomics And Behavior 7th Edition Robert Frank - Solutions
5. The average number of yards gained by a college football team on a passing play is 8 12r, where r is the fraction of their total plays that are running plays. Their average gain per running play is 10 8r. What is their optimal fraction of running plays? At this value of r, what is the
4. Suppose that a firm with the production function Q min(2K, 3L)is currently using 6 units of capital and 5 units of labor. What are the marginal products of K and L in this case?
3. Can the Cobb-Douglas production function be used to portray a production process in which returns to scale are increasing at low output levels and are constant or decreasing at high output levels?
* 2. What is the marginal product of labor in the production function Q 2K13L13 if K is fixed at 27?
* 1. Do the following production functions have increasing, decreasing, or constant returns to scale? Which ones fail to satisfy the law of diminishing returns?a. Q 4K12L12b. Q aK2 bL2c. Q min(aK, bL)d. Q 4K 2Le. Q K0.5L0.6f. Q K1 0.3K2 0.3L0.3
12. In the fall, Crusoe puts 50 coconuts from his harvest into a cave just before a family of bears goes in to hibernate. As a result, he is unable to get the coconuts out before the bears emerge the following spring. Coconuts spoil at the same rate no matter where he stores them, and yet he
11. Hal is having difficulty choosing between two tennis rackets, A and B. As shown in the diagram, B has more power than A, but less control. According to the rational choice model, how will the availability of a third alternative—racket C—influence Hal’s final decision? If Hal behaves like
10. Mary will drive across town to take advantage of a 40 percent–off sale on a $40 blouse but will not do so to take advantage of a 10 percent–off sale on a $1000 stereo. Assuming that her alternative is to pay list price for both products at the department store next to her home, is her
9. In planning your next vacation, you have narrowed your choices down to two packages offered by your travel agent, a week in Hawaii for $1200 or a week in Cancun for $900.You are indifferent between these choices. You see an ad in the travel section of the newspaper for a week in Hawaii, with
8. Last week your travel agent called to tell you that she had found a great fare, $667, for your trip to the United Kingdom later this month. This fare was almost $400 below the APEX (advance purchase excursion) fare. You told her to book it immediately and went around the department telling
7. A witness testifies that the taxicab that struck and injured Smith in a dark alley was green. On investigation, the attorney for Green Taxi Company discovers that the witness identifies the correct color of a taxi in a dark alley 80 percent of the time. There are two taxi companies in town,
6. Dalgliesh the detective fancies himself a shrewd judge of human nature. In careful tests it has been discovered that he is right 80 percent of the time when he says that a randomly chosen suspect is lying. Dalgliesh says that Jones is lying. The polygraph expert, who is right 100 percent of the
5. Claiborne is a gourmet. He makes it a point never to visit a restaurant a second time unless he has been served a superb meal on his first visit. He is puzzled at how seldom the quality of his second meal is as high as the first. Should he be?
4. Studies have shown that in the New York City subway crime rates fall in the years following increased police patrols. Does this pattern suggest that the increased patrols are the cause of the crime reductions?
3. Give two examples of how the framing of alternatives tends to produce systematic effects on people’s choices.
2. Sears Roebuck has hired you as a consultant to give it marketing advice about how to sell its new all-terrain vehicle. On the basis of the material covered in this chapter, suggest two specific marketing strategies for Sears to consider.
1. Suppose your happiness is given by a Kahneman-Tversky value function like the one shown in the diagram.You have decided to put the most favorable spin on the various combinations of events that occur in your life. For each of the following pairs of events, will you be happier if you consider
5. The policy of one school was to punish students for being late, while the corresponding policy in an otherwise identical school was to reward students for being on time. If effectiveness is measured by behavior on the day following punishment or reward, which policy would seem to be more
4. Is there anything irrational about weighing gains less heavily than losses?
3. Distinguish between (1) the best decision and (2) the decision that leads to the best possible outcome.
2. Why is it rational to make decisions with less than complete information?
1. Suppose you were the owner of a small business and were asked the maximum you would be willing to pay in order to attend a course in the traditional theory of rational choice. In which case would your answer be larger: (1) if it were known that people always behave in strict accordance with the
7. Harold’s utility is given by U 3M 60V, where M is the dollar value of his annual consumption of the composite good and V takes the value 1 if he votes and 0 if he does not. Harold finances his consumption by working at a job that pays $30/hr for as many hours as he chooses to work. In
6. Describe the advantages and disadvantages of electing a political leader who is known to favor harsh military reprisals against foreign aggression, even when such reprisals are highly injurious to our own national interests.
5. Now, suppose Benjamin’s utility function is given by UB MB 2 in Problem 4. And suppose Abdul signs a contract saying that he will donate 20 to a cause he opposes in the event that he receives less than 90 percent of any money he earns jointly with Benjamin.Will Benjamin accept a
4. Abdul’s utility function is given by UA = M2 A MB where MA is Abdul's wealth level and MR is Benjamin's wealth level. Benjamin's utility function is given by M2 MA B UR = B Suppose M = M = 10 initially, and suppose there is a joint project that Abdul and Benjamin can undertake that will
3. Alphonse’s utility function is given by where MA and MG are the wealth levels of Alphonse and Gaston, respectively. If Alphonse’s initial wealth level is 100 while Gaston’s is only 20, how much of his wealth will Alphonse give to Gaston?
2. Consider a population with two types of people, C’s and D’s. Interactions among various combinations of the two types produce the following payoffs:C-C: 6 each C-D: 8 for D, 0 for C D-D: 4 each Invisible contact lenses are available at a cost of 1 unit that enable the wearer to identify each
1. A population consists of two types, “friendlies” and “aggressives.” Each individual interacts with a randomly chosen member of the population. When two friendlies interact, each earns 3 units. When two aggressives interact, each earns 0 units. When a friendly and an aggressive interact,
5. Explain how the military arms race between the United States and the former Soviet Union had the same formal structure as a prisoner’s dilemma.
4. In the commitment model, what role is played by the observability of preferences?
3. Try to think of at least two commitment problems you personally encountered during the last year.
2. Explain the role of rational analysis in the psychologist’s model of human motivation.
1. Summarize in your own words the major difficulties of the present-aim and self-interest standards of rationality.
*21. Given a choice between A (a sure win of 100) and B (an 80 percent chance to win 150 and a 20 percent chance to win 0), Smith picks A. But when he is given a choice between C (a 50 percent chance to win 100 and a 50 percent chance to win 0) and D (a 40 percent chance to win 150 and a 60 percent
*20. There are two groups, each with a utility function given by where M 144 is the initial wealth level for every individual. Each member of group 1 faces a loss of 44 with probability 0.5. Each member of group 2 faces the same loss with probability 0.1.a. What is the most a member of each group
*19. There are two groups of equal size, each with a utility function given by where M 100 is the initial wealth level for every individual. Each member of group 1 faces a loss of 36 with probability 0.5. Each member of group 2 faces the same loss with probability 0.1.a. What is the most a member
*18. In the preceding problem, assuming that the interview is costless for Smith to conduct, is he getting the highest possible expected income for himself by charging John the same fee regardless of the outcome of the interview?
17. John has a von Neumann–Morgenstern utility function given by where M is his income. If he becomes an economics professor, he will make M 81/yr with probability 1. If he becomes an attorney, he will make M 900/yr if he becomes a partner in a Wall Street firm, but only M 25/yr if he fails
16. Smith has an investment opportunity that pays 33 with probability 12 and loses 30 with probability 12.a. If his current wealth is M 111, and his utility function is will he make this investment?b. Will he make it if he has two equal partners? (Be sure to calculate the relevant expected
15. Your current wealth level is M 49 and you are forced to make the following wager: if a fair coin comes up heads, you get 15; you lose 13 if it comes up tails. Your utility function isa. What is the expected value of this gamble?b. What is its expected utility?c. How would your answers change
14. A farmer’s hens lay 1000 eggs/day, which he sells for 10 cents each, his sole source of income.His utility function is where M is his daily income. Each time a farmer carries eggs in from the hen house, there is a 50 percent chance he will fall and break all the eggs. Assuming he assigns no
13. Your utility function is Your current wealth is $400,000. There is a 0.00001 probability that your legal liability in an automobile accident will reduce your wealth to $0.What is the most you would pay for insurance to cover this risk?
12. Suppose your current wealth, M, is 100 and your utility function is U M2. You have a lottery ticket that pays $10 with a probability of 0.25 and $0 with a probability of 0.75. What is the minimum amount for which you would be willing to sell this ticket?
11. Suppose you have $10,000 to invest. A broker phones you with some information you requested on certain junk bonds. If the company issuing the bonds posts a profit this year, it will pay you a 40 percent interest rate on the bond. If the company files for bankruptcy, you will lose all you
10. Suppose your utility function is given by U = 2M,where M is your total wealth. If M has an initial value of 16, will you accept the gamble in the preceding problem?
9. A fair coin is flipped twice and the following payoffs are assigned to each of the four possible outcomes:H-H: win 20; H-T: win 9; T-H: lose 7; T-T: lose 16.What is the expected value of this gamble?
8. What is the expected value of a random toss of a die? (Fair and six-sided.)
7. At the turn of this century, most banks required tellers to have a high school diploma.Even though the tasks currently performed by tellers in most banks can still be performed by persons who have mastered the high school curriculum, many banks now require that their tellers have college
6. What grounds are there for assuming that a randomly chosen social worker is less likely to cheat you in cards than a randomly chosen person?
5. The exhaust system on your 1986 Escort needs to be replaced, and you suspect that the price of a new exhaust system is the same as what you would get if you tried to sell the car. If you know that the car is otherwise okay, what relevance does Akerlof’s model of lemons have to your decision
4. A new motorcycle sells for $9000, while a used motorcycle sells for $1000. If there is no depreciation and risk-neutral consumers know that 20 percent of all new motorcycles are defective, how much do consumers value a nondefective motorcycle?
3. It is known that some fraction d of all new cars is defective. Defective cars cannot be identified as such except by the people who own them. Each consumer is risk neutral and values a nondefective car at $6000. New cars sell for $4000 each, used ones for$1000. If cars do not depreciate
2. Explain in detail what will happen to an insurance company that charges teenage males the same rates for automobile insurance as it charges its other customers.
1. Suppose, finally, that all parents tried to teach their children never to let anyone in to see their apartments if they were over 80 on the messiness scale. If such a rule of thumb were widely observed, what would be your best estimate of the messiness index of someone who said, “You can’t
1. Suppose the messiness of apartments is measured on a scale from 0 to 100, with 0 the cleanest and 100 the messiest. Suppose also that the distribution of apartments by messiness is as shown in the diagram. That is, suppose 10 percent of the apartments lie between 0 and 20, 20 percent between 20
9. Give some examples in which people do not self-insure against minor losses.
8. Explain, in your own words, why it makes sense to selfinsure against minor losses.
7. Give some examples of behavior that seem inconsistent with the assumption of risk aversion.
6. Why is it intuitively plausible to assume that most people are risk averse?
5. How does statistical discrimination affect the average insurance premium paid by members of different groups?
4. How does statistical discrimination affect the distribution of insurance premiums within a group?
3. What practical difficulty confronts laws that try to regulate what questions can be asked of job applicants during employment interviews?
2. Explain why, despite the potential adversarial relationship between sellers and buyers, commercial advertising nonetheless transmits information about product quality.
1. Why must a signal between potential adversaries be costly to fake?
6. You are a buyer for a used-car dealer. You attend car auctions and bid on cars that will be sold at the dealer. The cars are sold “as is” and there is seldom an opportunity to make a thorough inspection. Under these conditions, the lower bound for the value of a car can be zero. A 1981 Dodge
5. The Earthly Bliss dating service charges $100 per date that it arranges. All of their dates will accept an offer of marriage. In your estimation the quality of the potential spouses offered by the dating service can be measured by an index that runs from 0 to 100. The potential spouses are
4. If the wages you are offered are uniformly distributed between $75 and $150, and if the cost of looking for another job is $2, what is the minimum wage you should accept?
3. Suppose you are the economic advisor for a firm that is trying to decide whether to acquire the Bumbler Oil Company, whose only asset is an oil field that has a net value X under its current management. The owners of Bumbler know the exact value of X but your company knows only that X is a
2. A class of 100 students is participating in an auction to see who gets a large jar of quarters.Each student has an unbiased estimate of the total value of the coins. If these estimates are drawn from the interval (0, C), where C is not known, and your own estimate is $50, how much should you bid?
1. You are searching for a high wage from a wage distribution that is uniform on the interval(5, 8). The cost of each search is 0.06. What is the smallest wage you should accept?
*21. Harry runs a small movie theater, whose customers all have identical tastes. Each customer’s reservation price for the movie is $5, and each customer’s demand curve for popcorn at his concession stand is given by Pc 4 Qc, where Pc is the price of popcorn in dollars and Qc is the amount
† 20. How will your answer to the preceding problem differ if the tuition charged by outside universities is $12000/yr? What is the economic interpretation of a value of k greater than 1?
† 19. Cornell is committed to its current policy of allowing the children of its faculty to attend the university without paying tuition. Suppose the demand curve of Cornell faculty children(CFCs) for slots in other universities is given by P 30 5Q0, where P is the tuition price charged by
*18. Herb wants to work exactly 12 hr/wk to supplement his graduate fellowship. He can either work as a clerk in the library at $6/hr or tutor first-year graduate students in economics.Pay differences aside, he is indifferent between these two jobs. Each of three first-year students has a demand
*17. All book buyers have the same preferences, and under current arrangements, those who buy used books at $22 receive the same utility as those who buy new books at$50. The annual interest rate is 10 percent, and there are no transaction costs involved in the buying and selling of used books.
*16. Tom and Karen are economists. In an attempt to limit their son Harry’s use of the family car, they charge him a user fee of 20 cents/mile. At that price he still uses the car more than they would like, but they are reluctant to antagonize him by simply raising the price further.So Tom and
15. At current prices, housing costs $50 per unit and the composite good has a price of 1 per unit. A wealthy benefactor has given Joe, a penniless person, 1 unit of housing and 50 units of the composite good. Now the price of housing falls by half. True or false: Joe is better off as a result of
14. Smith receives $100 of income this period and $100 next period. At an interest rate of 10 percent, he consumes all his current income in each period. He has a diminishing marginal rate of time preference between consumption next period and consumption this period. True or false: If the interest
13. Kathy earns $55,000 in the current period and will earn $60,000 in the future period.What is the maximum interest rate that would allow her to spend $105,000 in the current period? What is the minimum interest rate that would allow her to spend $120,500 in the future period?
12. Crusoe will live this period and the next period as the lone inhabitant of his island. His only income is a crop of 100 coconuts that he harvests at the beginning of each period.Coconuts not consumed in the current period spoil at the rate of 10 percent per period.a. Draw Crusoe’s
11. Find the present value of $50,000 to be received after 1 year if the annual rate of interest isa. 8 percentb. 10 percentc. 12 percent
9. Suppose Smith from Problem 7 views current and future consumption as one-to-one complements. Find his optimal consumption bundle.10. Karen earns $75,000 in the current period and will earn $75,000 in the futurea. Assuming that these are the only two periods, and that banks in her country borrow
8. Suppose Smith from Problem 7 views current and future consumption as perfect, onefor-one substitutes for one another. Find his optimal consumption bundle.
7. Smith lives in a world with two time periods. His income in each period, which he receives at the beginning of each period, is $210. If the interest rate, expressed as a fraction, is 0.05 per time period, what is the present value of his lifetime income? Draw his intertemporal budget constraint.
6. Jones spends all his income on two goods, X and Y. The prices he paid and the quantities he consumed last year are as follows: PX 15, X 20, PY 25, and Y 30. If the prices next year are PX 6 and PY 30, and Jones’s income is 1020, will he be better or worse off than he was in the
5. Jane spent all her income on hot dogs and caviar. Her demand curve for caviar was inelastic at all prices for caviar. Unfortunately, an accident at a nuclear power plant caused the supply of caviar to fall and the price to rise. What happened to Jane’s consumption of hot dogs? Explain. (Note:
4. The only DVD rental club available to you charges $4 per movie per day. If your demand curve for movie rentals is given by P 20 2Q, where P is the rental price($/day) and Q is the quantity demanded (movies per year), what is the maximum annual membership fee you would be willing to pay to
3. Larry demands strawberries according to the schedule P 4 (Q/2), where P is the price of strawberries ($/pint) and Q is the quantity (pint/wk). Assuming that the income effect is negligible, how much will he be hurt if the price of strawberries goes from$1/pint to $2/pint?
2. When the price of gasoline is $1gal, you consume 1000 gal/yr. Then two things happen:(1) The price of gasoline rises to $2/gal and (2) a distant uncle dies, with the instruction to his executor to send you a check for $1000/yr. If no other changes in prices or income occur, do these two changes
1. Using a diagram like Figure 5.2, explain why, under our current method of educational finance, a rich family is much more likely than a poor family to send its children to a private school.
7. Jennifer, who earns an annual salary of $20,000, wins$25,000 in the lottery. Explain why she most likely will not spend all her winnings during the next year.
6. Bus services are generally more energy efficient than cars yet the trend over the past 30 years has been a decline in the proportion of commuters taking buses despite an increase in real energy prices. Why?
5. Explain why 1 plus the interest rate in the intertemporal choice model is analogous to the relative price ratio in the consumer choice model discussed in Chapter 3.
4. Explain in your own words why even long-term heavy drinkers might be highly responsive to increases in the price of alcohol.
3. Do you think a college education has a high- or low-price(tuition) elasticity of demand?
2. Explain in your own words what a two-part pricing scheme is and why sellers might use one.
1. Explain in your own words why a gasoline tax whose proceeds are refunded to the consumer in a lump-sum amount will nonetheless reduce the consumption of gasoline.
*20. Suppose your local espresso bar makes the following offer: People who supply their own half-pint carton of milk get to buy a cup of cappuccino for only $1.50 instead of $2.50.Half-pint cartons of milk can be purchased in the adjacent convenience store for $0.50.In the wake of this offer, the
*19. Repeat the preceding problem on the assumption that rice and wheat are perfect, onefor-one complements.
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