I. Components of Marginal Product and Marginal Revenue
The marginal product is the change in output that occurs when one more unit of input (such as a unit of labor) is added.
Marginal revenue is the increase in total revenue that occurs with the production of one more unit of output.
Value of Marginal Product
For a particular resource, the value of marginal product (VMP) is the resource's marginal product multiplied by the product price.
Marginal Revenue Product
The marginal revenue product of a resource is defined as the increase in a firm's total revenue attributable to employing one more unit of that resource. The increase in output due to adding one more resource unit is called the marginal product. The marginal revenue product is calculated as the marginal product times the marginal revenue.
The Relationship Between MRP and Demand
Due to the law of diminishing returns, we expect that both the marginal product and the marginal revenue product for an input will decline as more of the input is deployed.
A firm seeking to maximize profit will increase employment of a variable input unit until the MRP of that input is just equal to what it pays for the input. This rule will be followed by price takers and price searchers.
As the price of an input goes up, fewer units of that resource will generate the MRP needed to entice the firm to employ that resource. The demand curve for a resource will be downward sloping, as shown in figure 4.1 below:
Figure 4.1: Results of Regulating Price and Output
Values for the demand curve will depend upon the price of the good being produced, the productivity of the resource in question, and the amount of other resources used by the firm.
A profit-maximizing firm will continue to employ units of a resource as long as the MRP associated with the unit exceeds the firm's cost. If we assume the units of each resource are perfectly divisible, then the following conditions will apply to a firm with 3 production inputs (A, B, and C).
Pa is equal to the price (or wage rate) of resource A, Pb is equal to the price (or wage rate) of resource B, and Pc is equal to the price (or wage rate) of resource C.
Suppose resource A represents highly skilled labor and resource B represents labor with low skills. If a firm can get 100 units of additional output by purchasing $500 worth of highly skilled labor and only 50 additional units of output by hiring $500 worth of labor with low skills, then per unit costs will be reduced by hiring the highly-skilled labor. Expenses can always be reduced by substituting resources with relatively high marginal product per dollar spent for resources that have a relatively low marginal product per dollar. This substitution will continue to occur if per unit costs are to be minimized until the following relationship is achieved:
MRPa = MRPb = MRPcinan
-------- -------- --------
Pa Pb Pc
Note that this relationship also implies that if skilled laborers are three times as productive as unskilled labor, then firms will be willing to pay skilled laborers three times as much as unskilled labor.
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