Question

A firm operates in a perfectly competitive market with a price of P = 50 for the product. TVC = 0.5Q3 − 18Q2 + 170Q Q (output) TFC = 300.

Write an equation expressing the firm’s total revenue (TR) as function of Q.

Write an equation expressing the firm’s total cost (TC), as a function of Q.

Write an equation expressing the firm’s profit (π), as a function of Q.Find the first-order condition for the firm’s profit-maximization decision.

Find the optimal output (Q*) that will maximize profits for the firm.

Find the firm’s marginal revenue, as evaluated at the optimal quantity (Q*).

Find the firm’s marginal cost, as evaluated at the optimal quantity (Q*). (This is all one question.)

Answer 1

P = 50 Tea TFC + TVC=/300+ 0.5Q3-1807 profit condition At manimum MC - MR - d (TC) = q (TR) do ОУ » d (300+0.593_18 Q ) = I do f (500) - 11.5Q²-360 - 50 on solving we get /Q* - 25.3] THO. 50; MC= 1.5Q²-369 = 1.5(25.3)? - 36(25.3) 7 507