1. In a competitive industry, the short-run average variable cost (AVC) of a firm is:
AVC = 600 – 20Q – 0.5Q2
a. Derive the firm’s short-run supply equation
b. Determine the minimum possible price (shut-down price) for the firm.
Hint: Competitive firm’s short-run supply curve is its MC curve. MC is the derivative of VC.
2. A small tractor producing firm’s total cost and demand equations are as follows
C = 37,500,000 + 5,000Q + 1.5Q2
P = 30,000 – Q
a. Find optimal output and price and its profit.
b. Because of an increased foreign competition, the demand falls permanently to:
P = 20,000 – Q
The firm is considering closing its plan immediately. By doing so, it can save $18 million of its
annual$37.5 million in fixed costs. Alternatively, it can continue to operate the plant for 12 months after
which if it shuts down it can walk away from its labor contracts and lease payments and incur no
continuing costs. Determine its most profitable or least-cost operating strategy.
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