Question

1. Suppose faces an inverse demand curve ? = 25 − 2.5?, with total costs, ?? = 2.5?2. Therefore its profit function is ? = (25 − 2.5?)? − 2.5?2. It’s marginal revenue function then is ?? = 25 − 5? and its marginal cost curve is ?? = 5?. Solve for the the profit-maximizing level of output, Q*, the price at the profit maximizing level of output, P*, and the firm’s profits.

Answer 1

Answer : At equilibrium MR = MC. By using given equations,

25 - 5Q = 5Q

=> 25 = 5Q + 5Q

=> 25 = 10Q

=> Q = 25 / 10

=> Q = 2.5

Now from demand function we get,

P = 25 - (2.5 * 2.5)

=> P = 25 - 6.25

=> P = 18.75

Therefore, the profit maximizing output level is, Q = 2.5 and price is, P = $18.75.

Now,  

Profit = (25 - 2.5 * 2.5) * 2.5 - 2.5 * (2.5)^2

=> Profit = 18.75 * 2.5 - 2.5 * 6.25

=> Profit = 46.875 - 15.625

=> Profit = 31.25

Therefore, profit is $31.25 .