Suppose that a typical firm in a monopolistically competitive industry faces a demand curve given by:

Question

q = 60 - (1/2)p, where q is quantity sold per week.
The firm's marginal cost curve is given by: MC = 60.

1. How much will the firm produce in the short run?
2. What price will it charge?

Answer 1

Since it is a monopolistic product, it will be assumed everything made will be sold, and at the predicted price.
p = selling price
Quantity sold=quantity manufactured = q(p) =60-p/2
Cost, C = 60 at all sales volumes
Profit in terms of price, p
P(p)= (selling price - cost)*quantity sold
=(p-C)q(p)
=(p-C)(60-p/2)
=(p-60)(60-p/2)
Maximize profit by setting P'(p)=0 to solve for p
dP(p)/dp
= d(-p^2/2+90p-3600)/dp
= -p+90
Setting derivative to zero,
-p+90=0
solve for (most profitable p)
p=90 => product will be sold at unit price of 90.

Production quantity
q(p) = 60-p/2 = 60-45 = 15 units.