Detailed Profit Maximization Calculation With Variations
Not what you're looking for?
A firm uses a single plant with cost 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 cost identical to the first) to product the output in part (a)? Explain.
Purchase this Solution
Solution Summary
A calculation of a firm's profit-maximizing price and output, followed by mathematical analysis of other possible production strategies.
Solution Preview
A)
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 + ...
Purchase this Solution
Free BrainMass Quizzes
Basics of Economics
Quiz will help you to review some basics of microeconomics and macroeconomics which are often not understood.
Pricing Strategies
Discussion about various pricing techniques of profit-seeking firms.
Elementary Microeconomics
This quiz reviews the basic concept of supply and demand analysis.
Economics, Basic Concepts, Demand-Supply-Equilibrium
The quiz tests the basic concepts of demand, supply, and equilibrium in a free market.
Economic Issues and Concepts
This quiz provides a review of the basic microeconomic concepts. Students can test their understanding of major economic issues.