A monopolist faces a constant marginal cost of $1 per unit and has no fixed costs.If the price elasticity of demand for this product is constant and equal to -4, then
A)to maximize profits, he should charge a price of $4.
B)he is not maximizing profits.
C)to maximize profits, he should charge a price of $1.33.
D)to maximize profits, he should charge a price of $1.25.
E)None of the above.

Question

Quizplus · Accepted Answer

The profit-maximizing price for a monopolist is where marginal revenue (MR) equals marginal cost (MC). As the monopolist has no fixed cost, we can equate the total cost to the marginal cost, which is $1. 
As the price elasticity of demand is constant and equal to -4, we know that the monopolist faces a relatively elastic demand curve. This means that as the monopolist increases the price, the quantity demanded decreases proportionately more. 
Using the formula for the elasticity of demand, we can find that the monopolist's marginal revenue (MR) is equal to (price x (1 - elasticity)) or (P(1+4)) = 5P.
Setting 5P = MC = $1, we can find that profit-maximizing price is $0.2, or $1.33 rounded to the nearest cent. Thus, the correct answer is (C).

A Monopolist Faces a Constant Marginal Cost of $1 Per