Answer to Question #270246 in Economics of Enterprise for deboraj

Question

A. Assume that in a product market, the demand function for the product is Q^d = 500-0.5P and the cost function of a company operating in this market is TC = 50 + 3Q². The company selects the amount of Q produced to maximize its profits.

(a) Solve for the equilibrium price and quantity when the business operates in conditions of full competition.

(b) Solve for the equilibrium price and quantity when the business is a monopoly.

(c) Compare and evaluate your solutions in (a) and (b).

Answer 1

(a) The equilibrium price and quantity when the business operates in conditions of full competition are:

P = MC,

$MC = TC'(Q) = 6Q,$

P = 1,000 - 2Q,

$1,000 - 2Q = 6Q,$

Q = 125 units,

$P = 1,000 - 2×125 = 750.$

(b) The equilibrium price and quantity when the business is a monopoly are:

MR = MC,

$MR = TR'(Q) = 1,000 - 4Q,$

$1,000 - 4Q = 6Q,$

Q = 100 units,

$P = 1,000 - 2×100 = 800.$

(c) Under full competition the equilibrium price is lower and the equilibrium quantity is higher.

Under monopoly the equilibrium price is higher and the equilibrium quantity is lower.