Question

Fuji is the sole manufacturer of racing bikes, and the cost of manufacturing is TC(Q) = 40 + 20Q + 2Q^2 , so that the marginal cost is MC(q) = 20 + 4Q. Demand for racing bikes is characterized by P = 50 - 4Q.

A) What is the optimal level of production and price for Fuji? Show math for full credit.

B) What is the average and variable cost associated with this level of production? Show your work.

C) Will Fuji remain in this industry in the short run? What about the long run?

Answer 1

Given that TC(Q) = 40 + 20Q + 2Q^2 , so that the marginal cost is MC(q) = 20 + 4Q. Demand for racing bikes is characterized by P = 50 - 4Q. This gives MR = 50 - 8Q

A) What is the optimal level of production and price for Fuji?  

For a monopolist, production rule is MR = MC

50 - 8Q = 20 + 4Q

30 = 12Q

Q = 2.5 units and price P = 50 - 4*2.5 = $40.

B) What is the average and variable cost associated with this level of production?  

Average cost = TC/Q = 40/Q + 20 + 2Q = 40/2.5 + 20 + 2*2.5 = $41

Variable cost = 20*2.5 + 2*(2.5^2) = 62.50

C) Will Fuji remain in this industry in the short run? What about the long run?

Find profits. Profit = Revenue - cost = 2.5*40 - 102.50 = 100 - 102.50 = -2.50.

It will stay in the short run but not in the long run as it is facing economic losses.