Question

Suppose that a firm operating in a perfectly competitive market can produce at a constant marginal cost of $15 per unit. Suppose also that if the same firm operated as a monopoly it would produce at a constant marginal cost of $20 per unit. If the market demand the firm faces is given by Qd=1260-4P and the marginal revenue is given by MR= 315-0.5Q. Determine the following: i) The perfectly competitive and monopoly outputs and prices ii) The amount of dead weight loss under monopoly production.

Answer 1

i) The perfectly competitive and monopoly outputs and prices

In perfect competition, P=MC. The demand equation is:

$Q=1260-4Q$

The inverse demand equation is:

$P=315-0.25Q$

The marginal cost under perfect competition is MC=$15. Therefore:

$15=315-0.25Q\\[0.3cm] 0.25Q=300\\[0.3cm] Q^*=\boxed{1200}\; \rm units$.

The price charged in perfect competition is:

$P=MC=\boxed{\$15}$

ii) The amount of deadweight loss under monopoly production.

Under monopoly, MR=MC.

The marginal revenue is MR=315-0.5Q and the marginal cost is20. Therefore:

$315-0.5Q=20\\[0.3cm] 0.5Q=295\\[0.3cm] Q_m=\boxed{590}\; \rm units$

The monopoly price is equal to:

$P=315-0.25(590)\\[0.3cm] P_m=\boxed{\$167.5}$

The monopoly deadweight loss will be equal to:

$DWL=\dfrac{1}{2}(P_m-P^*)(Q^*-Q_m)\\[0.3cm] DWL=\dfrac{1}{2}(167.5-15)(1200-590)\\[0.3cm] DWL=\boxed{\$46,512.5}$