Suppose you are a perfectly competitive farmer producing corn. Your costs are given by: C(q, w) = wq^2 -10q + 100, where q refers to the quantity that you alone produce and w is the hourly wage rate of your employees. Total market demand is given by: Q = 40,000 - 1000P, where Q denotes the total market output and P is the market price.
a. What is your average cost?
b. What is the cost of producing one more unit of output?
c. If the wage rate for farm workers is $1 per hour, what will be the long-run equilibrium output for your farm alone? [Hint: There are 2 ways to solve this.]
d. Assuming that your industry exhibits constant costs (so that all current and potential farmers in this market have the same cost structure), what will be the long-run equilibrium price and how many corn farmers will there be? [Hint: use your information about the individual farm from part a].