Computation of Profit-Maximizing Price Level and Output

A firm uses a single plant with costs C = 160 + 16Q + .1Q2 and faces the price equation P = 96 - .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.

Solution Preview

a. Find the firm's profit-maximizing price and quantity. What is its profit?

For profit maximization, the condition is MR=MC
C = 160 + 16Q + .1Q2
MC=dC/dQ = 16+0.2Q

Now P = 96 - .4Q
Total Revenue TR=P*Q=(96-0.4Q)*Q
MR=dTR/dQ = 96-0.8Q

Equating MR and MC, we get ...

Solution Summary

This solution provides formulas, calculations and answers for computing the profit-maximizing level of output.

1. A profit-maximizing firm operating in a perfectly competitive market can sell products for $100 per unit. The firm has a cost function represented by:
C(Q) = 1000- 160Q + 10QSqr(10 q squared) . The market demand function for this product is Qd = 500 - 3P.
a.What is the profit maximizing output for this company?
b.Wh

Please refer attached file for diagram.
The follwing diagram shows the cost structure of a mononpoly firm as well as market demand. Identify on the graph and calculate the following:
a. Profit-maximizingoutputlevel
b. Profit-maximizingprice
c. Total Revenue
d. Total Cost
e. Total profit or loss.
State the correct

P = $130 - $0.000125Q
MR - $130 - 0.00025
Fixed development cost = $600,000
Marginal costs are $63 per unit.
Calculate output, price, total revenue and total profit at the revenue maximizing activity leveland then at the profit maximizing level (present each with relevant diagrams).

Define Q to be the level of output produced and sold, and assume that the firm's cost function is given by the relationship:
TC = 20 + 5Q + Q^2 (Q is squared)
Furthermore, assume that the demand for the output of the firm is a function of price P given by the relationship:
Q = 25 - P
1. Define total profit as the

2) A monopolist faces the following demand function for its product:
Q = 45 - 5P
The fixed costs of the monopolist are $12 and the monopolist incurs variable costs of $5.00 per unit.
a) What is the profit-maximizinglevel of priceand quantity for this monopolist? What will profits be at this priceandoutputlevel?
b)

Suppose that the total cost function for a single firm in a purely competitive industry is given by the following equation:
TC = $5,625 + $5Q + $0.01Q2
Because this industry is purely competitive in nature, each firm behaves as a price taker and market price is given at $20 per unit (so that P = MR = $20). Finally, assume

John is considering opening a shop to make desks. He estimates the cost information for the first-through-the-ninth desk (nine is his estimated maximum monthly output).
The first desk costs $520 to produce, including $380 in overhead expenses.
The price of the desk has been set at $199.
The additional desk have the fol

A firm produces output at a cost of: C = 50 + 20 X and sells it at a price of P = 220 - 4 X
1. Determine the profit maximizing equilibrium output, priceand the total profit under two conditions:
1.1 A firm is a monopolist (15)
1.2 A firm under perfect competition (15)
See attached file for full problem description.

Suppose the demand curve faced by a monopolist is:
q=p^-a where a>0
The total cost for the monopolist are C=sq
a) Find the profit maximizing level of output.
b) Specify the first and second order condition for profit maximization.
c) What is the price elasticity of demand faced by this monopolist
d) What hap