# 1:
Only one firm produces and sells soccer balls in the country of Wiknam, and as the story begins, international trade in soccer balls is prohibited. The following equations describe the monopolist’s demand, marginal revenue, total cost, and marginal cost:
Demand: P = 10 – Q
Marginal Revenue: MR = 10 – 2Q
Total Cost: TC = 3 + Q + 0.5 Q^2
Marginal Cost: MC = 1 + Q
where Q is quantity and P is the price measured in Wiknamian dollars.
a. How many soccer balls does the monopolist produce? At what price are they sold? What is the monopolist’s profit?
b. One day, the King of Wiknam decrees that henceforth there will be free trade—either imports or exports— of soccer balls at the world price of $6. The firm is now a price taker. What happens to domestic production of soccer balls? To domestic consumption? Does Wiknam export or import soccer balls?
c. In our analysis of international trade in Chapter 9, a country becomes an exporter when the price without trade is below the world price and an importer when the price without trade is above the world price. Does that conclusion hold in your answers to parts (a) and (b)? Explain.
d. Suppose that the world price was not $6 but, instead, happened to be exactly the same as the domestic price without trade as determined in part (a). Would anything have changed when trade was permitted? Explain.
#2.
The town of Wiknam has 5 residents whose only activity is producing and consuming fish. They produce fish in two ways. Each person who works on a fish farm raises 2 fish per day. Each person who goes fishing in the town lake catches X fish per day. X depends on N, the number of residents fishing in the lake. In particular,
X = 6 – N.
Each resident is attracted to the job that pays more fish.
a. Why do you suppose that X, the productivity of each fisherman, falls as N, the number of fishermen, rises? What economic term would you use to describe the fish in the town lake? Would the same description apply to the fish from the farms? Explain.
b. The town’s Freedom Party thinks every individual should have the right to choose between fishing in the lake and farming without government interference. Under its policy, how many of the residents would fish in the lake and how many would work on fish farms? How many fish are produced?
c. The town’s Efficiency Party thinks Wiknam should produce as many fish as it can. To achieve this goal, how many of the residents should fish in the lake and how many should work on the farms? (Hint: Create a table that shows the number of fish produced—on farms, from the lake, and in total—for each N from 0 to 5.)
d. The Efficiency Party proposes achieving its goal by taxing each person fishing in the lake by an amount equal to T fish per day and distributing the proceeds equally among all Wiknam residents. Calculate the value of T that would yield the outcome you derived in part (c).
e. Compared with the Freedom Party’s hands-off policy, who benefits and who loses from the imposition of the Efficiency Party’s fishing tax?
#3.
A group of athletes are competing in a multi-day triathlon. They have a running race on day one, a swimming race on day two, and a biking race on day three. You know the order in which the eligible contestants finish each of the three components. From this information, you are asked to rank them in the overall competition. You are given the following conditions:
- The ordering of athletes should be transitive: If athlete A is ranked above athlete B, and athlete B is ranked above athlete C, then athlete A must rank above athlete C.
- If athlete A beats athlete B in all three races, athlete A should rank higher than athlete B.
- The rank ordering of any two athletes should not depend on whether a third athlete drops out of the competition just before the final ranking.
No comments:
Post a Comment