Take Out Your Pencils

For those blog readers who fondly recall exams in introductory economics (I am sure there are many), here is a fun problem based on a question from a recent ec 10 test. Enjoy!

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.