Answer to Question #41650 in Microeconomics for Manisha

Question

Bringing Up Baby has a monopoly in the production of step-by-step manuals for child rearing. Its total cost of producing manuals is given by TC = 12.5Q, and the demand for manuals is given by the non-linear demand, Q = 25,000P –2.
Calculate the profit maximizing price and quantity of manuals

Answer 1

TC = 12.5Q, Q = 25,000/P^2, P = (25,000/Q)^0.5
Profit maximizing quantity of manuals can be found in the point, where marginal revenue equals marginal cost (MR = MC) and the price can be found from the demand curve at this quantity.
MC = TC' = 12.5
MR = TR' = (P*Q)' = ((25,000/Q)^0.5*Q)' = (158.11Q^0.5)' = 79.06/Q^0.5
MR = MC, so:
79.06/Q^0.5 = 12.5
Q = (79.06/12.5)^2 = 40 units - profit-maximizing quantity
P = (25,000/40)^0.5 = $25 - profit-maximizing price.