Question

A monopolist firm faces a demand with constant elasticity of negative 2.6−2.6. It has a constant marginal cost of ​$2020 per unit and sets a price to maximize profit. If marginal cost should increase by 1515 ​percent, would the price charged also rise by 1515 ​percent?

Answer 1

YES

Step-by-step explanation:

The percentage markup of price over marginal cost for a profit maximizing monopolist is (Price -Marginal cost) / Price = -1 / elasticity of demand

(price - 20) / price = -1 / -2.6

(price - 20) / price = 0.3846

price - 20 = 0.3846 price

0.6154 x price = 20

price = $32.50 or price = 1.625 x Marginal cost

The relationship between price and marginal cost is constant, since the monopolist will want to keep maximizing its profit. So if marginal costs increase by 15%, then the price will increase by 15%:

price x 1.15 = 1.625 x Marginal cost x 1.15