- If two goods are perfect substitutes, what is the demand function for good 2?
- Which of the following utility functions have the expected utility property(a) u(c1, c2, π1, π2) = a(π1c1 + π2c2), (b) u(c1,c2, π1,π2) = π1c1 + π2c2,(c)u(c1, c2, π1,π2) =
- How would your answer to the last problem change if the worker’s alter-native employment gave him u̅ = 1?
- Given the setup of the previous problem, what would the worker be willing to pay to rent the production technology?
- A worker can produce x units of output at a cost of c(x) = x2/2. He can achieve a utility level of u̅ = 0 working elsewhere. What is the optimal wage-labor incentive schemes(x) for this worker?
- In the same model, how much consumers’ surplus would be created by randomly assigning buyers to sellers? Which method gives the larger surplus?
- Consider the model of the used-car market presented in this chapter. What is the maximum amount of consumers’ surplus that is created by trade in the market equilibrium?
- Cowflop, Wisconsin, has 1,000 people. Every year they have a fireworks show on the Fourth of July. The citizens are interested in only two things—drinking milk and watching fireworks. Fireworks
- Ten people have dinner together at an expensive restaurant and agree that the total bill will be divided equally among them.(a) What is the additional cost to any one of them of ordering an appetizer
- Suppose that 10 people live on a street and that each of them is willing to pay $2 for each extra streetlight, regardless of the number of streetlights provided. If the cost of providing x
- Suppose that demand for DoorKnobs is as given in the previous problem, and assume that the perceived market share in any period is equal to the actual market share in the previous period. Then where
- Suppose that the marginal cost of producing an extra video is zero and the transactions cost of renting a video is zero. Does a producer make more money by selling the video or by renting it?
- Describe how the demand for a word processing package might exhibit network externalities.
- If the cost to a customer from switching long-distance carriers is on the order of $50, how much should a long-distance carrier be willing to pay to acquire a new customer?
- Suppose that the government wants to control the use of the commons, what methods exist for achieving the efficient level of use?
- List some other examples of positive and negative consumption and production externalities.
- True or false? The distributional consequences of the delineation of property rights are eliminated when preferences are quasilinear.
- True or false? An explicit delineation of property rights usually eliminates the problem of externalities.
- Romeo loves Juliet and Juliet loves Romeo. Besides love, they consume only one good, spaghetti. Romeo likes spaghetti, but he also likes Juliet to be happy and he knows that spaghetti makes her
- The ability to set the voting agenda can often be a powerful asset. Assuming that social preferences are decided by pair-wise majority voting and that the preferences given in Table 30.1 hold,
- Suppose that an allocation is Pareto efficient, and that each individual only cares about his own consumption. Prove that there must be some individual that envies no one, in the sense described in
- Suppose that the utility possibilities set is a convex set and that consumers care only about their own consumption. What kind of allocations represent welfare maxima of the Nietzschean welfare
- A Rawlsian welfare function counts only the welfare of the worst off agent. The opposite of the Rawlsian welfare function might be called the “Nietzschean” welfare function—a welfare function
- Suppose that we say that an allocation x is socially preferred to an allocation y only if every one prefers x toy. (This is sometimes called the Pareto ordering, since it is closely related to the
- Suppose that Robinson and Friday both want 60 pounds of fish and 60 pounds of coconuts per day. Using the production rates given in the chapter, how many hours must Robinson and Friday work per day
- If Robinson’s marginal rate of substitution between coconuts and fish is −2 and the marginal rate of transformation between the two goods is−1, what should he do if he wants to increase his
- In what sense is a competitive equilibrium a good or bad thing for a given economy?
- What would happen if the firm depicted in Figure 32.2 decided to pay a higher wage?Figure 32.2: COCONUTS Isoprofit line Production function C* Profit = * L* LABOR
- The competitive price of coconuts is $6 per pound and the price of fish is $3 per pound. If society were to give up 1 pound of coconuts, how many more pounds of fish could be produced?
- Can some individual be made better off if we are at a Pareto efficient allocation?
- If the value of excess demand in 8 out of 10 markets is equal to zero, what must be true about the remaining two markets?
- True or false? If we know the contract curve, then we know the outcome of any trading.
- Is it possible to have a Pareto efficient allocation where everyone is worse off than they are at an allocation that is not Pareto efficient?
- Is it possible to have a Pareto efficient allocation where someone is worse off than he is at an allocation that is not Pareto efficient?
- Charley Citrus has to leave town quickly and cannot take his car with him. Since he does not have time to seek another buyer, he must either sell it to his neighbor Harriet Hardnose or simply destroy
- John decides that he will save $5 this week and $10 next week. But when next week arrives, he decides to save only $8. What is the term used to describe this sort of inconsistent behavior?
- What is the probability that a fair coin will come up heads three times in a row when tossed?
- In the above example, if the price changes from 4 to 6, what is the change in consumer’s surplus?
- You are the human resources director for a medium-size company and are trying to decide how many mutual funds to offer in your employees’ pension plan. Would it be better to offer 10 choices or 50
- Mary plans the entire week’s meals for her family, while Fred shops each day. Which is likely to produce more varied meals? What is this effect called?
- Subjects are allowed to buy tickets in a lottery. One group is told that they have a 55 percent chance of winning, the other group is told that they have a 45 percent chance of not winning. Which
- Can you explain why taking a monotonic transformation of a utility function doesn’t change the marginal rate of substitution?
- The Iron Chicken restaurant is located on a busy interstate highway. Most of its customers are just passing through and will never return to the Iron Chicken. But some are truck drivers whose routes
- The prices are (p1, p2) = (2, 3), and the consumer is currently consuming (x1, x2) = (4, 4). There is a perfect market for the two goods in which they can be bought and sold costlessly. Will the
- A contractor says that he intends to “low-ball the bid and make up for it on change orders.” What does he mean?
- If a consumer’s net demands are (5,−3) and her endowment is (4,4), what are her gross demands?
- The text claims that row scores 62 percent of the time in equilibrium. Where does this number come from?
- Suppose that two goods are perfect complements. If the price of one good changes, what part of the change in demand is due to the substitution effect, and what part is due to the income effect?
- If both players make the same choice in a coordination game, all will be well.
- Look at the best responses for row and column in the section on mixed strategies. Do these give rise to best response functions?
- In this case would the consumers be better off or worse off if the tax with rebate based on original consumption were in effect?
- In a two-person Nash equilibrium, each player is making a best response to what? In a dominant strategy equilibrium, each player is making a best response to what?
- In the case described in the preceding question, would the government be paying out more or less than it received in tax revenues?
- In the case of the gasoline tax, what would happen if the rebate to the consumers were based on their original consumption of gasoline,x,rather than on their final consumption of gasoline, x'?
- Suppose that preferences are concave. Is it still the case that the substitution effect is negative?
- Suppose a consumer has preferences between two goods that are perfect substitutes. Can you change prices in such a way that the entire demand response is due to the income effect?
- In the same framework as the above question, what kind of preferences would leave the consumer just as well-off as he was in the base year, for all price changes?
- We saw that the Social Security adjustment for changing prices would typically make recipients at least as well off as they were at the base year. What kind of price changes would leave them just as
- Suppose that player B rather than player A gets to move first in the sequential game described in this chapter. Draw the extensive form of the new game. What is the equilibrium for this game? Does
- The prices are (p1, p2) = (2, 3), and the consumer is currently consuming (x1, x2) (4, 4). Now the prices change to (q1, q2) = (2,4). Could the consumer be better off under these new prices?
- What is the dominant Nash equilibrium strategy for the repeated prisoner’s dilemma game when both players know that the game will end after one million repetitions? If you were going to run an
- The U.S. currently imports about half of the petroleum that it uses. The rest of its needs are met by domestic production. Could the price of oil rise so much that the U.S. would be made better off?
- We know that the single-shot prisoner’s dilemma game results in a dominant Nash equilibrium strategy that is Pareto inefficient. Suppose we allow the two prisoners to retaliate after their
- Suppose that by some miracle the number of hours in the day increased from 24 to 30 hours (with luck this would happen shortly before exam week). How would this affect the budget constraint?
- Suppose your opponent is not playing her Nash equilibrium strategy. Should you play your Nash equilibrium strategy?
- If leisure is an inferior good, what can you say about the slope of the labor supply curve?
- In the United States, real wage rates in manufacturing have risen steadily from 1890 to the present. In the period from 1890 to 1930, the length of the workweek was reduced dramatically. But after
- Are dominant strategy equilibria always Nash equilibria? Are Nash equilibria always dominant strategy equilibria?
- Consider the tit-for-tat strategy in the repeated prisoner’s dilemma. Suppose that one player makes a mistake and defects when he meant to cooperate. If both players continue to play tit for tat
- How much is $1 million to be delivered 20 years in the future worth today if the interest rate is 20 percent?
- As the interest rate rises, does the intertemporal budget constraint become steeper or flatter?
- Would the assumption that goods are perfect substitutes be valid in a study of intertemporal food purchases?
- Nickleby has an income of $2,000 this year, and he expects an income of $1,100 next year. He can borrow and lend money at an interest rate of 10%. Consumption goods cost $1 per unit this year and
- In many communities, a restaurant that sells alcoholic beverages is required to have a license. Suppose that the number of licenses is limited and that they may be easily transferred to other
- What is the present value of $100 one year from now if the interest rate is 10%? What is the present value if the interest rate is 5%?
- A consumer, who is initially a lender, remains a lender even after a decline in interest rates. Is this consumer better off or worse off after the change in interest rates? If the consumer becomes a
- Suppose asset A can be sold for $11 next period. If assets similar to A are paying a rate of return of 10%, what must be asset A’s current price?
- Here are a few problems on present values. In all of the following examples, assume that you can both borrow and lend at annual interest rate of r and that the interest rate will remain the same
- Suppose that Carl and Simon sign a marketing agreement. They decide to determine their total output jointly and to each produce the same number of pumpkins. To maximize their joint profits, how many
- A house, which you could rent for $10,000 a year and sell for $110,000 a year from now, can be purchased for $100,000. What is the rate of return on this house?
- The payments of certain types of bonds (e.g., municipal bonds) are not taxable. If similar taxable bonds are paying 10% and everyone faces a marginal tax rate of 40%, what rate of return must the
- Do oligopolies produce an efficient level of output?
- Draw a set of reaction curves that result in an unstable equilibrium.
- Suppose there are n identical firms in a Cournot equilibrium. Show that the absolute value of the elasticity of the market demand curve must be greater than 1/n.
- Can the leader ever get a lower profit in a Stackelberg equilibrium than he would get in the Cournot equilibrium?
- Suppose that a scarce resource, facing a constant demand, will be exhausted in 10 years. If an alternative resource will be available at a price of $40 and if the interest rate is 10%, what must the
- How can one reach the consumption points to the left of the endowment in Figure 12.1? Endowment $35,000 Slope = Choice $35,000 – yK $25,000 $25,000 + K- yK Съ
- Consider a cartel in which each firm has identical and constant marginal costs. If the cartel maximizes total industry profits, what does this imply about the division of output between the firms?
- Suppose that we have two firms that face a linear demand curve p(Y) = a − bY and have constant marginal costs, c, for each firm. Solve for the Cournot equilibrium output
- A risk-averse individual is offered a choice between a gamble that pays $1000 with a probability of 25% and $100 with a probability of 75%, or a payment of $325. Which would he choose?
- What if the payment was $320?
- It is a slow day at Bunsen Motors, so since he has his calculator warmed up, Clarence Bunsen (whose preferences toward risk were described in the last problem) decides to study his expected utility
- Draw a utility function that exhibits risk-loving behavior for small gambles and risk-averse behavior for larger gambles.
- Why might a neighborhood group have a harder time self insuring for flood damage versus fire damage?
- If the risk-free rate of return is 6%, and if a risky asset is available with a return of 9% and a standard deviation of 3%, what is the maximum rate of return you can achieve if you are willing to
- In our example of the minimum wage, what would happen if the labor market was dominated by a monopsonist and the government set a wage that was above the competitive wage?
- We saw that a monopolist never produced where the demand for output was inelastic. Will a monopsonist produce where a factor is inelastically supplied?
- What is the price of risk in the above exercise?
- In our examination of the upstream and downstream monopolists we derived expressions for the total output produced. What are the appropriate expressions for the equilibrium prices, p and k?
- If a stock has a β of 1.5, the return on the market is 10%, and the risk-free rate of return is 5%, what expected rate of return should this stock offer according to the Capital Asset Pricing Model?

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