Question

A firm is considering entering a market where demand for its product is Q = 100 - P. This demand function implies that the firm’s marginal revenue function is MR = 100 - 2Q. The firm’s total cost of producing the product for that market is TC = 860 + 20Q + Q2 which indicates that its marginal cost function is MC = 20 + 2Q. Calculate the firm’s profit and hence indicate whether or not the firm should enter the market. Also represent your findings on an appropriate graph.

Answer 1

Answer : Here firm's equilibrium condition is MR = MC.

=> 100 - 2Q = 20 + 2Q

=> 100 - 20 = 2Q + 2Q

=> 80 = 4Q

=> Q = 80 / 4

=> Q = 20

Now, from demand function we get,

Q = 100 - P

=> 20 = 100 - P

=> P = 100 - 20

=> P = 80

TR (Total Revenue) = P * Q = 80 * 20

=> TR = 1600

TC = 860 + (20 * 20) + (20)^2

=> TC = 1660

Profit = TR - TC = 1600 - 1660 = - 60

Here the firm faces loss of $60. As here the firm face loss, hence the firm should not enter into the market.  

The above findings are shown by the following picture's diagram.