Question

Suppose a single firm produces all of the output in a contestable market. The market inverse demand function is P = 350 -5Q, and the firm’s cost function is C(Q) = 8Q. Determine the firm’s equilibrium price and corresponding profits.

Price: $ ?

Profits: $ ?

Answer 1

This is a monopoly market, since the market has only one firm to produce and supply. Equilibrium in this market is (MR = MC).

Given,

P = 350 – 5Q …… (Price function)

TR = P × Q = 350Q – 5Q^2

MR = Derivative of TR with respect to Q

            = 350 – (5 × 2) Q

            = 350 – 10Q

Again given,

TC = 8Q

MC = Derivative of TC with respect to Q

            = 8

Now at equilibrium,

MR = MC

350 – 10Q = 8

350 – 8 = 10Q

342 = 10Q

342/10 = Q

Q = 34.2

Now this is to be placed in the price function to get price (P).

P = 350 – 5Q …… (Price function)

   = 350 – 5 × 34.2

   = 350 – 171

   = 179

Answer: price is $179.

Profit = TR – TC

            = (P × Q) – 8Q

            = (179 × 34.2) – 8 × 34.2

            = 6,121.80 – 273.6

            = $5,848.20 (Answer)