If the marginal cost of making a photocopy is 2 cents and the elasticity of demand is 2.50, the profit-maximizing price is
A)3 cents.
B)3.33 cents.
C)4 cents.
D)5 cents.
E)6 cents.

Question

Quizplus · Accepted Answer

The profit-maximizing price is where marginal cost equals marginal revenue. Since the marginal cost of making a photocopy is 2 cents, we need to find the marginal revenue. We are given the elasticity of demand which is 2.50. Using the formula for elasticity of demand, we can find the percentage change in quantity demanded when the price changes by 1%.

Elasticity of demand = (% change in quantity demanded) / (% change in price)

2.50 = (% change in quantity demanded) / 1

% change in quantity demanded = 2.50

This means that if the price of a photocopy is increased by 1%, the quantity demanded will decrease by 2.50%.

Now, we can use this information to find the marginal revenue. Marginal revenue is the change in total revenue when one more unit is sold. Since the price will decrease by 2.50% if we increase the quantity sold by one more unit, the marginal revenue is:

Marginal revenue = (Price x (1 - 0.025)) - Price = 0.975 x Price - Price = -0.025 x Price

Setting marginal cost equal to marginal revenue:

2 = -0.025 x Price

Price = 80 cents

However, this cannot be the answer, as the price cannot be negative. Therefore, we need to ensure that the price elasticity of demand is within the range of the answer choices.

The price elasticity of demand is:

% change in quantity demanded / % change in price = 2.50

Rearranging the formula:

% change in price = % change in quantity demanded / 2.50 = 1/2.50 = 0.40

This means that for a 1% increase in price, the quantity demanded will decrease by 0.40%.

Now, we can use this information to calculate the price that maximizes profits.

Marginal revenue = price (1 - 0.40) - price = 0.60 x price

Setting marginal cost equal to marginal revenue:

2 = 0.60 x price

Price = 3.33 cents

Therefore, the profit-maximizing price is 3.33 cents.

If the Marginal Cost of Making a Photocopy Is 2