Suppose you are a perfectly competitive farmer producing corn. Your costs are gi
ID: 1104827 • Letter: S
Question
Suppose you are a perfectly competitive farmer producing corn. Your costs are given by: C(q, w) wq2-10q 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. . What is your average cost? What is the cost of producing one more unit of output? a. b. c. If the wage rate for farm workers is $1 per hour, what will be the long-rurn equilibrium output for your farm alone? [Hint: There are 2 ways to solve this.] 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]. d.Explanation / Answer
a) Average cost AC = C/q = wq - 10 + 100/q
b) Marginal cost MC = dC/dq = 2wq - 10
c) Long run output can be found by equating AC = MC
2wq - 10 = wq - 10 + 100/q
2q - 10 = q - 10 + 100/q
q^2 = 100
q = 10
In the long run, output will be 10 units for each firm
d) Price = AC = MC = 2*10 - 10 = $10. At this price, Q = 40000-10000 = 30000. Since each farm has 10 units in the long, there will be 30000/10 = 3000 farms in the long run.