1. A firm has the following production function:
q = LK.
The firm wants to produce a target output level of q=200. The costs of the two inputs are r=$2 (for capital K) and w=$1(for labor L).
a. What is the Marginal Rate of Technical Substitution between labor and capital?
b. What is the least cost method of producing the target level of output (i.e., what are the optimal choices of K and L to minimize costs)?
c. Suppose now a payroll tax is imposed on the firm, so that the firm must pay $3 per unit of labor to the government. How does this payroll tax affect the cost minimizing combinations of L and K if the firm still wants to produce q=200? Explain your answer.
d. How much revenue does the government raise? Do the costs to the firm rise? If so, by how much? Explain your answer.
e. How would your answer to part (a)-(d) be affected if the production function changed to q = L + K?