Answer to Question #210950 in Microeconomics for Momin ali

Question

Only one firm produces and sells soccer balls in a country namely XYZ, 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 – 2 Q

Total Cost: TC = 3 + Q + 0.5 

 

Marginal Cost: MC = 1 + Q

Where Q and P represent the quantity and prices respectively;

a. How many soccer balls does the monopolist produce? What will be the price and profit?

b. One day country decides free trade in the market that opens the doors for exporters and 

importers. The world price for soccer balls is now $6. The market is now perfectly 

competitive market. What will happen to the domestic production of the soccer balls?

Answer 1

Solution:

a.). A monopoly market produces profit maximizing quantity at which MR = MC:

MR = MC

10 – 2Q = 1 + Q

10 – 1 = Q + 2Q

9 = 3Q

Q = 3

The monopolist will produce 3 soccer balls.

Substitute in the demand function to derive price:

P = 10 – Q

P = 10 – 3

P = 7

The monopolist price will be $\$7$

Profit = TR – TC

 = (P $\times$ Q) – (3 + Q + 0.5Q²)

= (7 $\times$ 3) – (3 + 3 + 0.5(3²))

= 21 – 10.5

Profit = 10.5

The monopolist will earn a profit of $\$10.5$.

 

b.). The domestic production of soccer balls will drop or be less. This is because the monopolistic soccer producer would have to reduce their price of $7 to match the market price of $6. Therefore, domestic consumption would increase and domestic production will decrease since XYZ will be forced to import soccer balls to keep up with the increased demand.