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 \, \text{per unit} = $24.00.</li></ul></li></ul><h5id="valueofthemarginalproductvmpcurve">ValueoftheMarginalProduct(VMP)Curve</h5><ul><li>Itisderivedbytransformingmarginalproductunitstothevalueofthemarginalproductforallvariableinputlevels.</li><li>TheVMPcurveissimilartotheMPcurvebutmeasurestheverticalaxisindollarsinsteadofoutputunits(Figure8).</li><li>Itshowstheadditionalrevenuelinkedtoeachadditionalvariableinputunit.</li></ul><h4id="profitmaximizationanalysis">ProfitMaximizationAnalysis</h4><ul><li>TheVMPcurverevealstherevenuesideofthefirmatdifferentvariableinputusagelevels.</li><li>Tocompletetheprofitmaximizationanalysis,weneedtoconsiderthecostsideofthefirm.</li></ul><h5id="perfectlycompetitivemarkets">PerfectlyCompetitiveMarkets</h5><ul><li>Thevariableinputprice(anditscost)isconstant.</li><li>MarginalFactorCost(MFC):Theadditionalcostassociatedwithonemorevariableinputunit;itequalsthevariableinputprice.</li><li>InFigure9,MFCis.</li></ul></li> </ul> <h5 id="valueofthemarginalproductvmpcurve">Value of the Marginal Product (VMP) Curve</h5> <ul> <li>It is derived by transforming marginal product units to the value of the marginal product for all variable input levels.</li> <li>The VMP curve is similar to the MP curve but measures the vertical axis in dollars instead of output units (Figure 8).</li> <li>It shows the additional revenue linked to each additional variable input unit.</li> </ul> <h4 id="profitmaximizationanalysis">Profit Maximization Analysis</h4> <ul> <li>The VMP curve reveals the revenue side of the firm at different variable input usage levels.</li> <li>To complete the profit maximization analysis, we need to consider the cost side of the firm.</li> </ul> <h5 id="perfectlycompetitivemarkets">Perfectly Competitive Markets</h5> <ul> <li>The variable input price (and its cost) is constant.</li> <li>Marginal Factor Cost (MFC): The additional cost associated with one more variable input unit; it equals the variable input price.</li> <li>In Figure 9, MFC is20.00, 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.