The production function for Superlite Sailboats, Inc., is
Q = 20K0.5L0.5
with marginal product functions
MPK=10L0.5K-0.5 and MPL=10K0.5L-0.5
a. If the price of capital is $5 per unit and the price of labor is $4 per unit, determine the expansion path for the firm.
b. The firm currently is producing 200 units of output per period using input rates of L=4 and K=25. Is this an efficient input combination? Why or why not? If not, determine the efficient input combination for producing an output rate of 200. What is the capital-labor ratio?
c. If the price of labor increases from $4 to $8 per unit, determine the efficient input combination for an output rate of 200. What is the capital-labor ratio now? What input substitution has the firm made?