Question

Competitive Market Equilibrium. Syracuse Paper supplies printer paper in upstate New York. Like the output of other wholesale distributors, Syracuse Paper must meet strict guidelines and the printer paper supply industry can be regarded as perfectly competitive. Total and marginal cost relations are:

TC = $3,600 + $5Q + $0.01Q2

MC = TC/Q = $5 + $0.02Q

where Q is cases of printer paper per day.

A.	Calculate the firm's optimal output and profits if prices are stable at $20 per case.
B.	Calculate optimal output and profits if prices rise to $25 per case.
C.	If Syracuse Paper is typical of firms in the industry, calculate the firm's equilibrium output, price, and profit levels.

Answer 1

(A) Firm maximizes profit by equating Price with its MC.

5 + 0.02Q = 20

0.02Q = 15

Q = 750

Total revenue (TR) = P x Q = $20 x 750 = $15,000

Total cost ($) = 3,600 + (5 x 750) + (0.01 x 750 x 750) = 3,600 + 3,750 + 5,625 = 12,975

Profit ($) = TR - TC = 15,000 - 12,975 = 2,025

(B) When P = $25,

5 + 0.02Q = 25

0.02Q = 20

Q = 1,000

Total revenue (TR) = P x Q = $25 x 1,000 = $25,000

Total cost ($) = 3,600 + (5 x 1,000) + (0.01 x 1,000 x 1,000) = 3,600 + 5,000 + 10,000 = 18,600

Profit ($) = TR - TC = 25,000 - 18,600 = 6,400

(C) In (long run) equilibrium, Price = MC = AC where AC = TC/Q = (3,600/Q) + 5 + 0.01Q

(3,600/Q) + 5 + 0.01Q = 5 + 0.02Q

3,600/Q = 0.01Q

Q² = 3,600/0.01 = 360,000

Q = 600

P = MC = 5 + (0.02 x 600) = 5 + 12 = 17

Since Price equals AC, TR equals TC and profit is zero.