The price elasticity of demand at the profit-maximizing quantity, where the firm's marginal cost is $40 and the price is $60, can be calculated using the relationship of marginal revenue and marginal cost, leading to a price elasticity of demand of -3.
The student wants to find out the price elasticity of demand at the profit-maximizing quantity when the firm's marginal cost is $40 and the price charged is $60.
To calculate the price elasticity of demand, we use the formula which is the percentage change in quantity demanded divided by the percentage change in price.
We are not directly provided with the changes in quantity demanded or price.
However, we can infer from the given situation, as the firm is profit maximizing, that they are operating where marginal revenue (MR) equals marginal cost (MC).
At this point, we know that the price elasticity of demand (PED) can be related to MR and MC through the relationship MR = P (1 + 1/PED), where P is the price.
Since the firm is charging a price of $60 and has a marginal cost of $40, and knowing that MR=MC at the profit-maximizing level, we can deduce that MR is also $40.
Using the formula MR = P (1 + 1/PED) and the given values, we can formulate:
40 = 60 (1 + 1/PED)
2/3 = 1 + 1/PED
1/PED = -1/3
PED = -3
Thus, the correct answer is option b) -3, meaning that the price elasticity of demand at the profit-maximizing quantity is -3.
Question:
at the profit maximizing quantity the firms marginal cost is $40 and it changes a price of $60. what is the price elasticity of demand at the profit-maximizing quantity?
a) -0.5
b) -3
c) -0.67
d) -1.5