The Bell Automotive is one of several makers of electric motors. Accordingly, it is believed that the firm operates in a monopolistically competitive market. The demand function for its product is estimated as:

Q=8,300−2.1P,Q=8,300−2.1P,

and its total cost function is:

C(Q)=2,200+480Q+20Q2.C(Q)=2,200+480Q+20Q2.

a. What price and quantity will the company choose to maximize profit? What is the company's total profit?

b. Is this likely to be a long-run equilibrium for the firm? Why? Why not? If not, what kind of adjustment will occur in the market and how will it affect the company?

The total revenue (TR), marginal revenue (MR), and marginal cost (MC) functions are:

TR=PQ=8,300Q2.1−Q22.1MR=8,3002.1−2Q2.1MC=∂C(Q)∂Q=480+40QTR=PQ=8,300Q2.1−Q22.1MR=8,3002.1−2Q2.1MC=∂C(Q)∂Q=480+40Q

a) To obtain the price and quantity that maximize profits, equate the MC and MR:

MR=MC8,3002.1−2Q2.1=480+40Q8,300−2Q=10,008+84Q7,292=86QQ=84.79P=8,3002.1−84.792.1=$3,912.004MR=MC8,3002.1−2Q2.1=480+40Q8,300−2Q=10,008+84Q7,292=86QQ=84.79P=8,3002.1−84.792.1=$3,912.004

The total profit earned by the company is:

π=TR−TC=(3,912.004×84.79)−(2,200+480(84.79)+20(84.79)2)=343,434.83−186,686.08=$156,748.75π=TR−TC=(3,912.004×84.79)−(2,200+480(84.79)+20(84.79)2)=343,434.83−186,686.08=$156,748.75

b) This is not going to be the long-run equilibrium for the firm because the profits, in the long run, are zero. Many new firms will enter the market as the market has positive profits which will decrease the market price. Thus, the profits will decrease for the company.