Question

< Back to Assignment Attempts: In Progress Average: / 4 9. Problems and Applications Q9 Only one firm produces and sells soccer balls in the country of Wiknam, and as our 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=13−Q Marginal Revenue: MR=13−2Q Total Cost: TC=3+Q+0.5Q2 Marginal Cost: MC=1+Q where Q is quantity and P is the price measured in Wiknamian dollars. The monopolist produces soccer balls and sells them at a price of $ each. The monopolist’s profit is $ in this case. 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 $8. The firm is now a price taker in a competitive market. The domestic production of soccer balls will to soccer balls, and domestic consumption will to soccer balls. Therefore, Wiknam will soccer balls in this case. 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. In this case, the price without trade is than the world price, and the country is an . This is because the claim made in Chapter 9 assumed the domestic market was . Suppose that the world price was not $8 but, instead, happened to be exactly the same as the domestic, monopolistic price without trade. Allowing trade in this case would result in the country soccer balls. Grade It Now Save & Continue Continue without saving

Answer 1

When the firm acts as a monopolist,

its demand is P=13-Q

Then, TR =P*Q = 13Q-Q²

and MR=dTR/dQ = 13-2Q

Its TC=3+Q+0.5Q²

and MC=dTC/dQ = 1+Q

For equilibrium of the monopolist,

MR=MC

or, 13-2Q=1+Q

or, 3Q=12

or, Q=4

and P=13-Q = 13-4 = $9

Then monopolist's profit = TR-TC =P*Q - (3+Q+0.5Q²) = 36-(3+4+8) = $21

When world price is $8, the non trade price is greater than trade price, and thus, the country becomes an importer.

Now, domestic consumption increases to P=13-Q

or, Q= 13-P = 13-8 =5 units.

When the free trade price is equal to monopolist's price, P = $9

then, Q = 13-9 = 4 units.