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

Answer : a) At monopoly equilibrium, MR = MC

TR (Total Revenue) = P*Q = ( 50 - 4Q )*Q = 50Q - 4Q²

MR (Marginal Revenue) = TR / Q = 50 - 8Q

According to the given information, by putting the values of MR and MC, we have,

50 - 8Q = 20 + 4Q

=> 50 - 20 = 4Q + 8Q

=> 30 = 12Q

=> Q = 30/12

=> Q = 2.5

Therefore, the optimal output level is Q= 2.5 ;

price(P) = 50 - 4×2.5 = 40

b) Given, TC = 40 + 20Q + 2Q^2

Here Total variable cost = 20Q + 2Q^2 [ As this part of TC varies by the output level ]

Average variable cost (AVC)=Total variable cost / Q

AVC = (20Q + 2Q^2) / Q = 20 + 2Q

ATC ( Average Total Cost ) = TC/Q = (40+20Q+2Q^2)/Q

ATC = 40 + 20 + 2Q = 60 + 2Q

As Q = 2.5,

ATC = 60 + 2×2.5 = 65

AVC = 20 + 2*2.5 = 25

c) As price (P= 40) is lower than the ATC= 65, the manufacturer faces loss in short run. But the manufacturer will stay in the industry and will continue it's production in short run as price level is higher than the AVC=25.

As in monopoly entry barrier exists in the market, the new firms can not enter into the market in long run and hence in long run the monopolist earns maximum profit level . But in the given situation the price is lower than ATC but higher than AVC , so, the firm may continue it's production or may stop it's production in long run .