A firm uses a single plant with Costs C=160+16Q+0.1Q^2 and faces the price equation P=96-0.4Q
(a). Find the firm`s profit-maximizing price and quantity. What is its profit?
(b). The firm`s production manager claims that the firm`s average cost of production is minimized at an output of 40 units. Furthermore, she claims that 40 units is the firm`s profit-maximizing level of output. Explain whether these claims are correct.
(c). Could the firm increase its profit by using a second plant (with costs identical to the first) to produce the output in part (a)? Explain.© BrainMass Inc. brainmass.com October 10, 2019, 3:45 am ad1c9bdddf
The firm's profit-maximizing output (Q) is where Marginal Revenue (MR) = Marginal Cost (MC)
Total Revenue (TR) = PQ
TR = (96 - 0.4Q)Q
TR = 96Q - 0.4Q^2
MR is the derivative of TR
MR = 96 - 2(0.4Q)
MR = 96 - 0.8Q
Total Cost (TC) = 160 + 16Q + 0.1Q^2
MC is the derivative of TC
MC = 16 + 2(0.1Q)
MC = 16 + 0.2Q
To maximize profit, let MR = MC
96 - 0.8Q = 16 + 0.2Q ...
This solution shows detailed calculations to answer a question in three parts:
a) Given a firm's cost and price equations, find its profit-maximizing price and quantity.
b) Does the profit-maximizing quantity correspond to the cost-minimizing quantity?
c) Could the firm increase its profits by using a second plant to also produce the profit-maximizing quantity?