Question

A natural monopolist faces the following demand: P = 11.2 - 0.039Q The natural monopolist has the following cost function: C = 0.032Q + 711 What price will this firm produce to maximize profit? Round your answer to one decimal.

Answer 1

In order to maximize profit a natural monopolist should produce that quantity at which MR = MC

where MC = marginal cost = dC/dQ = 0.032

MR = Marginal revenue = d(TR)/dQ = d(PQ)/dQ = d((11.2 - 0.039Q)Q)/dQ = 11.2 - 2*0.039Q = 11.2 - 0.078Q

Note TR = Total Revenue = Price* Quantity

So, MC = MR
=> 0.032 = 11.2 - 0.078Q

=> Q = 143.2

From demand equation we get P = 11.2 - 0.039Q = 11.2 - 0.039*143.2 = 5.6

Hence In order to maximize profit this firm should produce Quantity = 143.2 units and charge Price = 5.6