Question

Short-Run Firm Supply. Florida is the biggest sugar-producing state, but Michigan and Minnesota are home to thousands of sugar beet growers. Sugar prices in the United States average about 20¢ per pound, or more than double the worldwide average of less than 10¢ per pound given import quotas that restrict imports to about 15 percent of the U.S. market. Still, the industry is perfectly competitive for U.S. growers who take the market price of 20¢ as fixed. Thus, P = MR = 20¢ in the U.S. sugar market. Assume that a typical sugar grower has fixed costs of $30,000 per year. Total variable cost (TVC), total cost (TC), and marginal cost (MC) relations are TVC = $15,000 + $0.02Q + $0.0000001802 TC = $45,000 + $0.02Q + $0.0000001802 MC=aTC/aQ=$0.02 + $0.00000036Q where Q is pounds of sugar, total costs include a normal profit. A. Using the firm's marginal cost curve, calculate the profit-maximizing short-run supply curve for a typical grower. B. Calculate the average variable cost curve for a typical grower, and verify that average variable costs are less than price at this optimal activity level.

Answer 1

A. As the market is perfectly competitive, the profit maximizing level of output is where Price = marginal cost

Marginal cost = $0.02+0.00000036Q

P = 20¢ = $ 0.20

P = MC

0.20 = 0.02 + 0.00000036* Q

0.18 = 0.00000036*Q

Q = 500,000

So, supply for a typical grower in the short run, Q = 500,000.

B.

The average variable curve is determined by dividing total variable cost by output:

AVC - 15,000/Q + 0.02 +0.00000018Q

At the Q= 500,000

AVC = 15,000/500,000 + 0.02 +0.00000018*500,000

AVC = 0.14

Because P = MR = MC = 0.20 and P > AVC ( 0.20 >0.14) at the 500,000 pounds per year.

This proof that AVC is less than Price at the optimal activity level.