Download The Cost-Minimizing Input Combinations - Abernathy

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.
 When buyers tend to consume two goods together, the
goods are known as complements.
 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).
• 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.
• Given the relationship between inputs, how does a firm
determine which of the possible combinations to use?
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.
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
 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.
▫ 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