You are the manager of a Mom and Pop store that can buy milk from a supplier at $3.00 per gallon.If you believe the elasticity of demand for milk by customers at your store is −4,then your profit-maximizing price is:
A) $2.00.
B) $2.50.
C) $4.00.
D) $5.00.

Question

Quizplus · Accepted Answer

The formula for profit maximization is Marginal Revenue = Marginal Cost. Here, the supplier price is $3.00 per gallon, so the marginal cost is $3.00. 
We need to find the profit maximizing price using the elasticity of demand formula: 
Elasticity = (% Change in Quantity Demanded) / (% Change in Price)
-4 = (% Change in Quantity Demanded) / (% Change in Price)
We know that our goal is to increase revenue, so we want to increase the price. Given the elasticity of demand, a 1% increase in price leads to a 4% decrease in quantity demanded. This means that when we increase the price from $3.00 to $4.00, the quantity demanded will decrease by 16%. 
Now, let's look at the revenue and profit. 
At $3.00 price: Quantity demanded = Q1
Revenue = $3.00 * Q1
Profit = Revenue - Cost = $3.00 * Q1 - $3.00 * Q1 = $0
At $4.00 price: Quantity demanded = Q2 = 0.84Q1 (Q1 decreases by 16%)
Revenue = $4.00 * Q2 = $4.00 * 0.84Q1 = $3.36Q1
Profit = Revenue - Cost = $3.36Q1 - $3.00 * Q1 = $0.36Q1

Since we want to maximize profit, we need to choose the price that gives us the highest profit. In this case, the profit maximizing price is $4.00. Therefore, the answer is (C) $4.00.

You Are the Manager of a Mom and Pop Store