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Wize University Microeconomics Textbook > Production and Costs

Cost Minimization in the Long Run

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Cost Minimization in the Long Run

  • In order to maximize profits the firm must minimize costs.
  • For this, they have to have technical efficiency. This is when the firm is producing at the lowest cost for a given output.

Cost Minimization

In order to minimize costs the firm has to produce where:
MPLPL=MPKPK\frac{MP_L}{P_L}=\frac{MP_K}{P_K}

MPL = Marginal Product of Labor
MPK = Marginal Product of Capital
PL = Price of Labor
PK = Price of Capital

Example: If the price of labor is $10 and the price of capital is $5, while the marginal product of labor is 100 and marginal product of capital is 50 then the business is minimizing their costs. The logic is that if labor is twice as expensive as capital then it should be twice as productive also.



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Example: Cost Minimization in the Long Run


The current wage for an employee at Wizedemy is $20 while the cost for a unit of capital is $10. The current marginal product of labor is 90 units and marginal product of capital is 30 units. To minimize costs Wizedemy should:
A) hire more capital
B) hire more labor
C) keep the current level of inputs
D) none of the above

B.
Using the formula MPL/PL = MPK/PK we get:
90/20 = 30/10
4.5 = 3
Since the two sides are not equal it means they are not currently minimizing their costs. You should get more of whichever side is bigger. In this case 4.5 > 3 and 4.5 goes with labor so get more labor. The logic is that labor is twice as expensive as capital (20>10) but it is 3 times as productive (90>30) so labor is giving you more value per dollar.