Use the following information for a monopoly firm. Assume that QQ equals the level of output and all costs are economic costs.

TR=250Q−0.5Q2MR=250−QTC=2,000+50Q+0.5Q2MC=50+QTR=250Q−0.5Q2MR=250−QTC=2,000+50Q+0.5Q2MC=50+Q

A. At the profit-maximizing or loss-minimizing output level, what is the economic profit?

B. Under these conditions, how much output should the firm produce?

C. At the output of 200 units, what will be the total costs?

A. At the profit-maximizing or loss-minimizing output level, what is the economic profit?

The profit-maximizing output is where MR =MC:

• 250−Q=50+Q200=2QQ=100P=250−0.5Q=200250−Q=50+Q200=2QQ=100P=250−0.5Q=200

We calculate the maximizing profit:

• Profit=TR−TCProfit=250Q−0.5Q2−2,000−50Q−0.5Q2Profit=200Q−Q2−2,000Profit=200(100)−1002−2,000Profit=20,000−10,000−2,000=8,000Profit=TR−TCProfit=250Q−0.5Q2−2,000−50Q−0.5Q2Profit=200Q−Q2−2,000Profit=200(100)−1002−2,000Profit=20,000−10,000−2,000=8,000

B. Under these conditions, how much output should the firm produce?

A monopoly produces at the quantity where MR=MC, at which it maximizes its profit. As calculated in the part A, the quantity output that the firm should produce is 100 units with the respective profit of 8,000.

C. At the output of 200 units, what will be the total costs?

• TC(200)=2,000+50(200)+0.5(2002)TC(200)=32,000