Profit Maximization and Input Use

Profit-Maximizing Level of Input Use

  • Each output level corresponds uniquely to one input level.
  • The question is: What input level maximizes profit?
  • It is the mirror image of finding the profit-maximizing output level.

Profit Maximization: Output Level

  • Compare the marginal revenue of each additional output unit to the marginal cost of producing it.
  • Profit increases as long as additional revenue is greater than the additional cost.

Profit Maximization: Input Use

  • A similar approach is used.
Value of the Marginal Product (VMP)
  • The marginal product (MP) curve indicates the additional output produced by each variable input unit.
    • Example: The 15th input unit yields 8 output units (Figure 7).
  • To analyze profit-maximizing behavior, convert physical data to economic information.
  • The key question is: How much additional revenue do these additional 8 output units generate?
Perfectly Competitive Situation
  • The product price remains constant.
  • VMP is calculated by multiplying the marginal product by the product price.
    • If the product price is 3.00,then3.00, thenVMP = 8 \, \text{units} \times 3.00 per unit=3.00 \, \text{per unit} =24.00.
Value of the Marginal Product (VMP) Curve
  • It is derived by transforming marginal product units to the value of the marginal product for all variable input levels.
  • The VMP curve is similar to the MP curve but measures the vertical axis in dollars instead of output units (Figure 8).
  • It shows the additional revenue linked to each additional variable input unit.

Profit Maximization Analysis

  • The VMP curve reveals the revenue side of the firm at different variable input usage levels.
  • To complete the profit maximization analysis, we need to consider the cost side of the firm.
Perfectly Competitive Markets
  • The variable input price (and its cost) is constant.
  • Marginal Factor Cost (MFC): The additional cost associated with one more variable input unit; it equals the variable input price.
  • In Figure 9, MFC is 20.00, which equals the variable input price.
  • The graph plots both the dollars of marginal revenue and the dollars of marginal factor costs relative to each additional variable input unit.
Economics of Profit-Maximizing Variable Input Use
  • If the 15th variable input unit is employed: VMP (additional revenue) = 24.00, and MFC (additional cost) = $20.00.
  • The manager adds 4.00 to the firm's profit by using the 15th unit.
  • With a profit-maximizing goal, the firm should hire the 15th variable input unit.
  • Similarly, the 16th variable input unit increases profits because additional revenue exceeds additional expenses.
  • The 17th variable input unit represents the profit-maximizing level because VMP = MFC.
  • If the manager hires the 18th input unit, MFC exceeds VMP, and profit drops.
Profit-Maximizing Criterion
  • To maximize profit, use the variable input level where the value of the marginal product (VMP) equals the marginal factor cost (MFC).
  • This mirrors the profit-maximizing output level criterion: marginal revenue = marginal cost.
  • There is a direct correlation between output and variable input.
Marginal Factor Cost
  • The additional cost associated with a unit increase of the variable input; equal to the price of the variable input.