Question

Suppose that the monopolist’s demand is: P = 10 – Q, so that marginal revenue is: MR = 10 – 2Q.
The marginal cost is: MC = 2, and total fixed cost = 0.
a. Determine the profit maximizing price and output.
b. Calculate the amount of economic profit or loss at the profit maximizing output.
c. Calculate the price elasticity of demand at the profit maximizing point and explain it.

use relevant diagram to answer the question

Answer 1

(a) Monopolist maximizes profit by equating MR & MC.

10 - 2Q = 2

2Q = 8

Q = 4

P = 10 - 4 = 6

In following graph, profit is maximized at point A with price P0 (= 6) and quantity Q0 (= 4).

(b) Profit = Q x (P - MC) = 4 x (6 - 2) = 4 x 4 = 16

In above graph, profit is shown by area P0BAC.

(c) Since P = 10 - Q, we have Q = 10 - P

Elasticity of demand = (dQ/dP) x (P/Q) = - 1 x (6 / 4) = - 1.5

It means that as price rises (falls) by 1%, quantity demanded falls (rises) by 1.5% and demand is elastic (since absolute value of elasticity is higher than 1). So, a rise (fall) in price will decrease (increase) total revenue.