Question

A monopolist firm faces a demand with constant elasticity of negative 1.8. It has a constant marginal cost of ​$15 per unit and sets a price to maximize profit. If marginal cost should increase by 20 ​percent, would the price charged also rise by 20 ​percent?

A. Yes. Since the price elasticity of demand is​ constant, Upper P equals 1.8 MC. ​Thus, if MC increases by 20 ​percent, price also increases by 20 percent.

B. Yes. Since the price elasticity of demand is​ constant, Upper P equals 2.25 MC. ​Thus, if MC increases by 20 ​percent, price also increases by 20 percent.

C. No. Since the demand curve is downward​ sloping, a 20 percent increase in MC will cause the price to increase by more than 20 percent.

D. No. Since the demand curve is downward​ sloping, a 20 percent increase in MC will cause the price to increase by less than 20 percent.

Answer 1

Calculate the old profit maximizing price as follows: P-MC_1 Р Е. P-15_1 P 1.8 P-15=P 1.8 2P-27 =P 2P - P = 27 p* = 27 Thus, price is $27. Calculate the new marginal cost if it increases by 20% as follows: New MC =15(1+0.20) = 15x1.2 = $18. Thus, the new marginal cost is $18). Calculate the new profit maximizing price as follows:

P-MC Р P-18 1 Е. 1 P 1.8 P-18= 1.8 2P-32.4 = P 2P - P = 32.4 p* = $32.4 Thus, price is $32.4 Calculate the percentage increase in profit maximizing price as follows: Percentage increase in price = 32.4–27 x 100 27 *100 27 = 0.2x100 = 20% Thus, the percentage increase in profit maximizing profit is 20%. Thus, Yes, since the price elasticity of demand is constant, Upper P equals 1.8 MC. Thus, if MC increases by 20 percent, price also increases by 20 percent.

Thus, the correct answer is option A.