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. 
(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
Q^{2} = 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.
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