Consider a monopolist facing an inverse demand function of p(q) = 15 - 3q, where 'q' denotes units of output

A) We have given:

• P = 15-3q is the demand function for a monopolist.
• TC = 5+4q is the cost function for a monopolist.

Total Revenue(TR) = P x q

=> (15-3q) x q

Differentiating it w.r.t Q, we get

Marginal Revenue(MR) = 15-6q.

TC = 5+4q.

Differentiating it w.r.t q, we get

Marginal Cost(MC) = 4.

B) MC = MR

=> 15-6q = 4

=> q = 19/6.

C) P = 15 - 3 x 19/6.

=> P = 5.5.

Profit = TR - TC

=> Profit = P x q - 5 - 4q

=> 5.5 x 19/6 - 5 - 4 x 19/6.

Profit = -0.25.

Consumer Surplus = 1/2 x (15-5.5) x (19/6)

=> 15.042.

Producer Surplus = (5.5-4) x (19/6)

=> 4.44.

Total welfare = 15.042+4.44 = $19.482.

D) Under perfect competition

P = MC

=> P = 4

then q = 11/3.

E) Profit = P x q - 5 - 4q

=> 4 x 11/3 - 5 - 4 x 11/3 = -5

Consumer Surplus = 1/2 x (15-4) x (11/3)

=> 20.17

Producer Surplus = 0

Total welfare = 20.17.

F) Under monopoly market the loss is to the firm is less than the loss in the perfectly competitive market. Secondly, under the monopoly market, the producer had some surplus whereas under perfect competition the producer surplus is zero.