John's Lawn Mowing Service is a small business that acts as a price taker. John's short-run total cost is given by STC = 0.1q2 + 10q + 50, where q is the number of acres John chooses to cut a day. Total fixed cost is TFC = 50 and total variable cost is TVC = 0.1q2 + 10q. The short-run marginal cost is SMC = 0.2q + 10. Assume that all fixed costs are sunk.

1. Suppose the prevailing market price of lawn mowing is P = $20 per acre. How many acres (q) should John choose to cut in order to maximize profit? How much is John's maximum daily profit?

2. What is the average variable cost (AVC) as a function of q? What is the minimum AVC (at which AVC = SMC)? At what prices will this firm shut down in the short run?

3. What is the short-run supply equation of the firm? First, write price P as a function of quantity qs. Then write quantity qs as a function of price P.