   Chapter 15, Problem 9PA

Chapter
Section
Textbook Problem

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 – QMarginal Revenue: MR = 10 - 2Q  Total Cost TC = 3 + Q +0.5 Q2  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 in a competitive market 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 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. Docs that conclusion hold in you 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 allowing trade have changed any thing in the Wiknamian economy? Explain. How does the result here compare with the analysis in Chapter 9?

Subpart (a):

To determine
Profit maximization.

Explanation

The monopolist maximizes profit, profit is maximized at point where MR=MC and then substitute the profit-maximizing quantity into the demand curve to find the price. This is done as follows:

The profit maximizing quantity can be calculated as follows.

MC = MR102Q = 1 + Q3Q = 9Q = 3

The profit maximizing quantity is 3 units.

The profit maximizing price can be calculated by substituting the profit maximizing quantity in to demand equation. This is done as follows.

P=10Q=103=7

The profit maximizing price is \$7

Subpart (b):

To determine
The monopolist’s demand, marginal revenue and marginal cost curves.

Subpart (c):

To determine
Reason for decreasing price.

Subpart (d):

To determine
Reason for increase the export.

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