Question

Suppose that the demand for a special kind of silica is given by Q = 55 – 0.5P, where Q is in tons of silica per day and P is the price per ton. This special kind of silica is produced by Thorpe Industries (a monopolist) that has a constant marginal and average total cost of $10 per ton. [up to 6 points] a. Derive the inverse demand and marginal revenue curves faced by Thorpe Industries. b. Equate marginal cost and marginal revenue to determine the profit-maximizing level of output. c. Find the profit maximizing price for Thorpe Industries. d. How would your answer change if marginal cost were instead given by MC = 10+Q?

Answer 1

A) Inverse demand curve will be : P= (55/2) - (Q/2)

Total Revenue = PQ = {(55/2) - (Q/2)} Q = (55/2) Q - (Q^{​​​​​​2}/2)

Marginal Revenue = d(TR)/dQ = (55/2) - 2Q/2 = (55/2) - Q

B) MC = 10

MC= MR ==> 55/2 - Q = 10 ==> Q = 35/2 = 17.5

C) Putting value of Q in the Inverse Demand :

P= (55/2) - (35/2)/2 = (55/2) - (35/4) = 75/4 = 18.75

D) If MC were 10 + Q , then equating MC to MR gives :

10 + Q = (55/2) - Q

2Q = (55/2) -10 = (35/2) = 17.5

Q= 17.5/2 = 8.75

Hence when Marginal Cost increases, the Profit maximizing Quantity decreases and the price now will be = (55/2) -8.75/2 = 23.125 ( increases) .