Kendra is the owner of Wholesome Farms, a commercial dairy. Kendra employs labor, land, and capital. In her operations, Kendra can substitute between the amount of labor she employs and the amount of capital she employs. That is, to produce the same quantity of output she can use more labor and less land; similarly, to produce the same quantity of output she can use less labor and more land. However, if she uses more land, she must use more of both labor and capital; if she uses less land, she can use less of both labor and capital. Let w* represent the annual cost of labor in the market, let r*L represents the annual cost of a unit of land in the market, and let r*K represent the annual cost of a unit of capital in the market.
a. Suppose that Kendra can maximize her profits by employing less labor and more capital than she is currently using but the same amount of land. What three conditions must now hold for Kendra's operations (involving her value of the marginal product of labor, land, and capital) for this to be true?
b. Kendra believes that she can increase her profits by renting and using more land. What three conditions must hold (involving her value of the marginal product of labor, land, and capital) for this to be true?