Question

A monopolist firm faces a demand with constant elasticity of -1.8. It has a constant marginal cost of $22 per unit and sets a price to maximize profit. If marginal cost should increase by 18 percent, would the price charged also rise by 18 percent?

1) Yes. Since the price elasticity of demand is constant, P = 2.25 MC. Thus, if MC increases by 18 percent, price also increases by 18 percent.
2) No. Since the demand curve is downward sloping, an 18 percent increase in MC will cause the price to increase by less than 18 percent.
3) No. Since the demand curve is downward sloping, an 18 percent increase in MC will cause the price to increase by more than 18 percent.
4) Yes. Since the price elasticity of demand is constant, P = 1.8 MC. Thus, if MC increases by 18 percent, price also increases by 18 percent.

Answer 1

A monopolist firm with a demand elasticity of -1.8 would not increase prices by the same percentage as an 18 percent increase in marginal costs due to the elastic nature of the demand. Hence, the price would increase by less than 18 percent.

Step-by-step explanation:

The student asked whether an 18 percent increase in marginal cost (MC) would lead to an 18 percent increase in the price charged by a monopolist firm with a demand curve that has a constant elasticity of -1.8. Given this scenario, and knowing that the firm sets prices to maximize profit, the answer to the student's question is: No. If the demand curve is downward sloping and has a constant elasticity that is not unitary (not equal to -1), the monopolist would increase the price, but not necessarily by the same percentage as the increase in marginal cost.

Since the demand elasticity is -1.8, this means that a 1 percent increase in price leads to a 1.8 percent decrease in quantity demanded. Therefore, if marginal costs were to increase by 18 percent, the monopolist would raise prices, but because the demand is elastic, the percentage increase in price would be less than the percentage change in MC to avoid losing proportionally more in the quantity sold. Hence, the correct answer to the student's multiple-choice question is likely, Option 2.