Thursday, November 12, 2009

A Mankiw Quiz

The following question was posed by Harvard economist Greg Mankiw on his well-read blog. See if you can provide an answer.

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.

3 comments:

Xiaotian said...

a) since MR=MC, then 10-2Q=1+Q. So, the monopolist produce Q=3
price P=10-Q=10-3=7
profit=7*3-TC=21-(3+3+0.5*3^2)=10.5

b)since the P=7>6, domestic production will decrease for importing soccer balls. The domestic consumption will increase for relative less price of importing. For Wilknam, it will import soccer balls.

c)yes, it holds that Wiknam will be an importer. Because the price for domestic production is 7 which is less than the world price 6.

d)Since the price within country is the same with price out of country, and also, MC=1+Q=4<6, Wiknam will not import soccer balls; even the trade was permited.

Yang Yang said...

a:the monopolist produce 3balls at price7,profit is 10.5.
I use MR=MC to get the monopolist's profit-manimizing quantity of output.10 – 2Q=1 + Q ,Q=3
Then put it in the (Demand: P = 10 – Q)to get price=7.the monopolist’s profit = TR - TC=7*3-(3 + 3 + 0.5 3^2)=10.5.
b Because the world price of $6 is less than the domestic price. The domestic price will be $6. Wiknam will import soccer balls.So the domestic production of soccer balls will be less. the domestic consumption will be more. The consumer and society benefit will gain from trade.
c: yes, the Wiknam price without trade is above the world price.when the King of Wiknam decrees that henceforth there will be free trade,The wiknam become an importer.
d: there is a big change. the monopolist market will become a competitive market.Even though the price won't change,the product will be of high quality and so on. The market will become more equilibrium.

Molly said...

Hello,Dr. Greg Delemeester,
This is Qi Wu.
a)Since Marginal Cost = Total Cost / Q
1 + Q = 3 + Q + 0.5 Q^2 / Q
P = 10 – Q
So: Q = √6
P = 10 - √6
Profit = MC – MR = 3Q – 9 = 3√6 - 9

b) The domestic production of soccer balls will decrease, and the domestic consumption will increase. Wilknam will import soccer balls.
c) Yes, at the first time, it is a monopolist market. Market price is higher than world price. Nobody can import at that time. Then, it is allowed to trade with other countries. The demand of soccer balls will increase and surplus of demand will occur. More and more will choose to import.

d) The supply will increase and demand is constantly. So, the price of soccer balls will decrease.