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The Cost-Minimizing Input Combinations

The Cost-Minimizing Input Combinations. 1. Alternative Input Combinations. Substitutes and Complements in Factor Markets Review of Substitutes and Complements Two goods are substitutes if a rise in the price of one good makes consumers more willing to buy the other good.

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The Cost-Minimizing Input Combinations

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  1. The Cost-Minimizing Input Combinations

  2. 1. Alternative Input Combinations • Substitutes and Complements in Factor Markets • Review of Substitutes and Complements • Two goods are substitutes if a rise in the price of one good makes consumers more willing to buy the other good. • When buyers tend to consume two goods together, the goods are known as complements.

  3. The concepts of substitutes and complements also apply to a firm’s purchase of inputs. • The price of other inputs can affect a firm’s decision about how much of an input it will use. • In some situations two factors (i.e. capital and labor) can act like substitutes. • Example: if you were a farmer you could produce the same amount of a good (wheat) by substituting more tractors (capital) for fewer farm workers (labor).

  4. Two factors (i.e. capital and labor) can also be complements when more of one increases the marginal product of the other. • Example: going back to a farm. A farm worker is more productive when the farm owner buys a tractor, and each tractor requires a worker to drive it. • In this case the quantity and quality of capital available affect the marginal product of labor, and thus the demand for labor.

  5. Given the relationship between inputs, how does a firm determine which of the possible combinations to use?

  6. 2. Determining the Optimal Input Mix • Cost Minimization • Firms use the least cost-minimizing input combinations to help determine what combinations to use. • Example: Self check outs and cashiers at a new store.

  7. Cashiers and Self-Checkout Stations Capital (self-checkout stations) Labor (cashiers) Rental rate = $1000/month Wage rate= $1600/month a. 20 4 b. 10 10

  8. When firms must choose between alternative combinations of inputs, they evaluate the cost of each combination and select the one that minimizes the cost of production. • This can be done by calculating the total cost of each alternative combination of inputs. • However it is more practical to use marginal analysis to find the cost-minimizing level of output.

  9. The Cost-Minimization Rule • Remember: the additional output that results from hiring an additional unit of an input is the marginal product (MP) of that input. • Firms want to receive the highest possible marginal product from each dollar spent on inputs. • To do this, firms adjust their hiring of inputs until the marginal product per dollar is equal for all inputs. This is the cost-minimization rule. • When the inputs are labor and capital this amounts to equating the marginal product of labor (MPL) per dollar spent on wages to the marginal product of capital (MPK) per dollar spent to rent capital. • MPL/W = MPK/rental rate

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