Question

Suppose that the single-priced monopolist’s demand is: P = 12 – 2Q, and marginal revenue is: MR = 12 – 4Q. Assume that marginal cost is: MC = 4, and fixed cost is 0.

a. Determine the profit maximizing price and output.
b. Calculate the amount of economic profit or loss at the profit maximizing output.
c. Using a diagram to explain your answers in (a) and (b).
d. Calculate the price elasticity of demand at the profit maximizing point and explain it.

Answer 1

a) At the profit maximizing price and output, MR=MC (Since if they were not equal, the monopolist will keep increasing production until they become equal)

12-4Q=4

Q=2

Therefore at the profit maximizing output=2 and the profit maximizing price= 12-2Q=8

b) Total revenue at the profit maximizing output and price= PQ=2*8= 16

Total costs at the profit maximizing output and price= Fixed costs+4*Quantity= 0+4*2=8

Therefore the total economic profit= 16-8=8

c) In the graph with Quantity on x axis and price on y axis

The demand curve(blue)

The marginal revenue curve(green)

The marginal cost curve(purple) are plotted

The profit maximizing output is decided by where the Marginal revenue and the marginal cost curve intersect i.e at (2,4) shows the profit maximizing output is 2 and the price is decided by the corresponding Y-value of that quantity on the demand curve i.e. 8 (The monopolist can charge 8 at a quantity of 2 as seen on the demand curve)

d) Rewriting the Demand curve P=12-2Q as Q=6-P/2

Now dQ/dP=-1/2=-0.5 (i.e. The quantity decreases by a factor of half as price increases)

The price elasticity of demand is determined as the percentage change in Quantity(Change in quantity/Total quantity) per percentage change of price

i.e. dQ/Q / dP/P= (P/Q) * (dQ/dP)= (8/2) (-0.5)= -2

Hope it's clear. Do ask for any clarifications required.