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. |
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B. |
Calculate optimal output and profits if prices rise to $25 per case. |
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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
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.
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