Assume a perfectly competitive market is represented by the functions Qd = -4p + 400 and Qs = p

Economics Dec 17, 2020

Assume a perfectly competitive market is represented by the functions Qd = -4p + 400 and Qs = p. If a firm produces in this market subject to a total cost function of TC = 2Q2 + 25Q + 100 determine the amount of profit this firm will make

Expert Solution

Find the inverse demand

Qd = -4P + 400

4P = 400 - Qd

P = 100 - 0.25Qd

Find the Marginal Cost

TC = 2Q^2 + 25Q + 100

MC = 4Q + 25

in perfect competition P+MC

100 - 0.25Q = 4Q + 25

4.25Q = 75

Q = 75/4.25

P = 100 - 0.25(75/4.25)

P = 95.5882

Total Revenue (TR) = P*Q

TR = 95.5882 * 75/4.25

TR = 1686.85

TC = 2((75/4.25)^2) + 25(75/4.25) + 100

TC = 622.837 + 100 + 441.176

TC = 1164.01

Profit = 1686.85 - 1164.01 = 522.84

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