Question

A firm has the following demand function 𝑷 = 𝟔𝟎 − 𝟎. 𝟓𝑸 and its total cost are defined by 𝑻𝑪 = 𝟏𝟑 + 𝑸.

a. Find the maximum revenue.

b. Find the production to optimize the profit.

c. Verify if the marginal revenue and marginal cost are the same at the profit-maximizing production level. 

Answer 1

a) Maximum revenue is determined from the equation TR'=0. TR=PQ=(60-0.5Q)Q=60Q-0.5Q²

TR'=60-Q=0; Q=60

b) Optimal profit is determined from the equation MR=MC. MR=TR'=60-Q; MC=TC'=(13+Q)'=1; 60-Q=1; Q=59

c) At Q=59 MR=60-59=1=MC