Unformatted text preview: Elements of Microeconomics
Final Exam Spring 2000 1. a. [6 pts] You are promised $100 one year from today. What is the present value of that
b. [6 pts]Draw the budget constraint for a consumer who has income Y0 this year, Y1 next year, and faces an interest rate r. Explain.
c, [6 pts] How does the budget constraint in Part b change if the consumer must pay a higher interest rate when borrowing than he receives on his savings?
d. [7 pts] In the market economy that we discussed in class (before monopoly, taxes an the like)
is the allocation of resources between producing current and future consumption economically efﬁcient? Explain.
e. [8 pts] You own a large amount of genHlik (a potion that keeps you young). You can sell it this year at a given price P0 or next year at a given price PL The cost of marketing and producing genHlik is
zero. The interest rate is r. Under what condition(s) would you sell some of your genHlik this year and
some next year (as opposed to selling all of it this year or all of it next year)? [6 pts] Deﬁne the Law of Diminishing Returns and state why it makes sense.
[6 pts] Does the Law of Diminishing Returns hold when there are increasing returns to scale?
[8 pts] Draw a competitive ﬁrm’s short-run average and marginal cost curves, and explain
i. The general shape of the average cost curve
ii. the relationship between the average and marginal cost curves.
[6 pts] For a given price of the good, show the ﬁrm’s proﬁt-maximizing level of output.
Explain why this level of output maximizes proﬁt and show how much proﬁt the ﬁrm makes.
[7 pts] Describe the long-run equilibrium for an industry made up of many ﬁrms like the one
you described in parts c and d. 3. There are two goods, x1 and x2. They are produced by competitive industries. a. [7 pts] Show that the equilibrium allocation of goods is economically efﬁcient. b. [10 pts] Now the government levies a tax, t1 on x1. Is the new equilibrium efﬁcient? If so,
show that it is. If not, show a mutually beneﬁcial transaction that does not occur. 0. [9 pts]Now suppose that X1 is produced by a monopolist (and X2 is produced by a competitive
industry). The government needs to tax one of the goods, to raise revenue for national
defense. On the criterion of economic efﬁciency, should it tax X1 (the monopoly good) or X2?
Explain. d. [7 pts] Now return to the assumption at the beginning of the problem: both goods are
produced by competitive industries. Is economic efﬁciency restored by levying equal taxes on both goods? Explain. 4. a. [10 pts] Derive one point on a supply curve for labor. Develop whatever analytical tools you need. b. [12 pts] An employer has hired a group of workers, at wage w, and has observed that they all
work 7 hours per day. The employer would like each of his workers to work at least 8 hours
per day, but cannot just order them to work at least 8 hours. He considers two options. 1. ii. Raise the wage rate by 50%
Offer a special overtime wage rate, equal to 1.5 times the going wage W. Which plan is more likely to induce workers to work at least 8 hours? Explain. c. [11 pts] In Baltimore, housing costs $20,000 per year. In New York housing costs $3 0,000
per year. Except for the housing-cost difference workers are indifferent between living in
Baltimore and New York. Furthermore, all workers have identical preferences. 1. ii. Depict the equilibrium wage difference between Baltimore and New York. Explain
Can you predict whether people will work more hours in one city or the other? Explain. [6 pts] Deﬁne an externality. Explain why externalities give rise to economic
[6 pts] Two factories, F1 and F2, each pollute the air. The government wishes to reduce
pollution and understands that the factory owners have no incentive to do it on their own. For
each factory, draw a marginal-cost—of—pollution—abatement schedule and show what it depicts.
[7 pts] Given the schedules you drew in part b, indicate the rule that should be obeyed if the
objective is to ﬁnd the cheapest possible way to reduce pollution by any given amount.
[7 pts] State whether this cheapest—possible—way objective will be achieved under each of the
following three pollution-abatement programs: [NOTEz you are not asked to comment on the
amount of pollution abatement under the three schemes, just whether that amount of
pollution abatement rs achieved 1n the cheapest possible way. ] ‘ i. The government allows each factory to do a certain amount of pollution. Any
pollution above this amount, by either factory, results 1n prison time for the
factory owner. [No side deals allowed] ii. The government allows each factory a certain level of pollution as in above.
But now factory owners are free to buy or sell the pollution permits that the
government issued. iii. The government charges a fee for each ton of pollution. c" 1” Use the graphs from parts b and c to show that your answers are right. [7 pts] If the government uses plan “ii” ﬁom part d above, it has one more decision to make:
It can allow factory owners to buy and sell pollution rights to any other polluter in the
country, or it can restrict them to buying and selling only to other polluters in a small
geographic area. Which do you recommend and why? [The next problem is quite hard. Do not do it until you have gotten all the points you can from the
ﬁrst five problems.] 6. Ford Motor Company is the only manufacturer of cars (this is a long time ago). The ﬁgure below
shows the demand curve in the Baltimore market and Ford’s marginal cost curve. Ford realizes that,
whereas it knows a lot about making cars it knows nothing about marketing cars in Baltimore. Therefore it
decides to franchise an Exclusive Ford Dealership in Baltimore. It takes no special skills to be a Ford
dealer; anybody who lives in Baltimore knows how to be a Baltimore Ford dealer. The terms of the dealership are as
iv. follows: Ford charges an annual franchise fee F. Ford charges the dealer a price Pd for each car. The dealer is then free to set its own price Pc to customers. The dealership is exclusive; Ford agrees not to license any other dealers in the Baltimore
Metro area. a. [11 pts] Suppose Ford sets Pd = MC; it sells cars to the dealer at cost. i.
iv. What price Pc will the dealer charge to his customers when selling Fords in Baltimore?
What is the maximum franchise fee F that you would be willing to pay in order to acquire
a dealership? Explain. How much proﬁt will the dealer earn (be sure to net out the franchise fee)? How much proﬁt will Ford earn? [Remember, Ford has two sources of proﬁt — selling
cars and the franchise fee.] b. [11 pts] Now suppose that Ford sets Pd = Pm where Pm is the standard monopoly price (i.e., it is the price that Ford would charge to consumers if it were to simply set a monopoly price and sell cars
direct to customers).
i. What price Pc will the dealer charge his customers now?
ii. What is the maximum he is willing to pay as a franchise fee F?
iii. How much proﬁt does Ford earn?
c. [11 pts] If Ford wishes to maximize proﬁt [from selling cars plus the ﬁanchise fee] what price Pd should it charge its dealer for cars? [Bear in mind that the franchise fee Ford can collect depends
upon the price it charges for cars] ...
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- Summer '11