Question

Suppose a firm's inverse demand curve is given by P = 120 - 0.5Q and its cost equation is

C = 420 + 60Q + Q².

1. Find the firm's optimal Q, P, and π two ways…first, by using the profit and marginal profit equations and then by setting MR = MC. Also, provide an Excel-created graph of the demand curve, MR curve, and MC curve (please do the excel graphs).

2. Suppose instead that the firm can sell any and all of its output at the fixed market price     P = $120. Find the firm's optimal output.

Answer 1

A) Profit = PQ - C

= 120Q - 0.5Q^2 - 420 - 60Q - Q^2

= 60Q - 1.5Q^2 - 420

Marginal profit = 60 - 3Q and it should be 0

This gives Q = 60/3 = 20 units and P = 120 - 20*0.50 = $110

Now use MR = MC

120 - Q = 60 + 2Q

60 = 3Q

Q = 20

P = 120 - 0.5*20 = $110

Hence both P and Q are same from both methods

Profit = 110*20 - 420 - 60*20 - 20^2 = $180

Graph is provided below

b) When P is 120, MC is 60 + 2Q which gives P = MC or Q = 60/2 = 30 units