Question

You are a manager of a monopolistically competitive firm, and your demand and cost functions are given by q=20-p and c(q)=20+q+q2.

Determine optimum price and optimum output?

Is this firm making the positive profit?

What will happen in the long run?

Answer 1

1) Optimum price: 15.25 ; Optimum output 4.75 units

2) No; firm is making loss

3) In the long run the exiting firm will exit the market and thus firm's product demand will increase until it earns zero economic profits. Otherwise the firm have tp leave the market in the long run. But it should continue operating because it is covering variable costs. In the long run exit will happen and the demand for this product's demand will increase until it earns zero economic profits. Otherwise, in the long run the firm should exit the business

Working:

q=20-p or p = 20-q

c(q)=20+q+q^2.

R = p*q

= (20-q)) * q

= 20q-q^2

MR = 20-2q

MC = q+2q

MR = MC

20-2q = q+2q

4q= 19

q= 4.75

p= 20-4.75 = 15.25

R =p*q = 15.25* 4.75 = 72.4375

Thus loss = 15.25 - 72.4375 = -57.1875