A farmer uses three inputs to produce vegetables: land, capital, and labor. The production function for the farm exhibits diminishing marginal rate of technical substitution.
a) In the short run the amount of land is fixed. Suppose the prices of capital and labor both increase by 5 percent. What happens to the cost-minimizing quantities of labor and capital for a given output level? Remember that there are three inputs, one of which is fixed.
b) Suppose only the cost of labor goes up by 5 percent. What happens to the cost-minimizing quantity of labor and capital in the short run?