Show how the profit-maximizing rule for hiring resources is equivalent to the cost-minimizing rule.

The cost-minimizing rule for hiring resources is to hire resources to the point at which the marginal physical product per last dollar spent on each input is equalized. That is: (MPP of labor/price of labor) = (MPP of capital/price of capital) = (MPP of land/price of land), and so on. The profit-maximizing rule substitutes MRP for MPP in the equations. However, since MRP is the MPP multiplied by the price of the product, which is the same for all the inputs, the two conditions are exactly the same.