# Question: The Ajax Coal Company is the only employer in its

The Ajax Coal Company is the only employer in its area. Its only variable input is labor, which has a constant marginal product equal to 5. Because it is the only employer in the area, the firm faces a supply curve for labor given by W = 10 + L, where W is the wage rate and L is the number of person- hours employed. This supply curve yields the marginal factor cost curve MFC = 10 + 2L. Suppose the firm can sell all it wishes at a constant price of 8.

a. How much labor does the firm employ, how much output does it produce, and what is the wage?

b. Suppose now the firm sells a special kind of coal such that it faces a downward-sloping demand curve for its output. In particular, assume that Ajax faces the demand curve given by P = 102 - 1.96Q. How much labor does the firm employ, how much output does it produce, what price does it set for the output, and what is the wage?

c. Assume that Ajax still faces the demand curve P = 102 - 1.96Q, but now further assume that Ajax has five laborers under contract to produce coal at a wage of 15. If Ajax has the option of hiring additional laborers at a higher wage without increasing the wage to the five laborers already under hire, will Ajax increase its labor force? Explain.

a. How much labor does the firm employ, how much output does it produce, and what is the wage?

b. Suppose now the firm sells a special kind of coal such that it faces a downward-sloping demand curve for its output. In particular, assume that Ajax faces the demand curve given by P = 102 - 1.96Q. How much labor does the firm employ, how much output does it produce, what price does it set for the output, and what is the wage?

c. Assume that Ajax still faces the demand curve P = 102 - 1.96Q, but now further assume that Ajax has five laborers under contract to produce coal at a wage of 15. If Ajax has the option of hiring additional laborers at a higher wage without increasing the wage to the five laborers already under hire, will Ajax increase its labor force? Explain.

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