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Achieving Cost-Minimization in Input Combos

Learn how firms determine the optimal input mix to minimize costs, explore alternative input combinations, and understand the cost-minimizing rule for hiring inputs.

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Achieving Cost-Minimization in Input Combos

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  1. MODULE 36 (72)The Cost-Minimizing Input Combination

  2. How firms determine the optimal input mix • The cost-minimizing rule for hiring inputs

  3. Alternative Input Combinations • In many instances, a firm can choose among a number of alternative combinations of inputs that will produce a given level of output. • The firm could choose acapital-intensive or labor intensive operation.

  4. Alternative Input Combinations • The concept of complements and substitutes applies to a firm’s purchase of inputs. • Capital and labor can be both substitutes and complements. • Substitute inputs can be used in place of each other. • More teller or ATM machines? • Complement inputs exist when one input increases the productivity of the other. • In a wheat production firm, for every additional tractor, you would need one more driver. • More computers for more workers.

  5. Determining the Optimal Input Mix • How do you decide which combination of inputs to use if the combinations provide the same amount of output? • Find the combination of inputs that costs the least – the cost-minimizing input combination.

  6. Cost Minimization

  7. Cost Minimization Cost of capital 20 x $1,000 = $20,000 Cost of labor 4 x $1,600 = $6,400 TOTAL $26,400 Cost of capital 10 x $1,000 = $10,000 Cost of labor 10 x $1,600 = $16,000 TOTAL $26,000 • If the cost to rent, operate and maintain a self-checkout station for a month is $1,000 and hiring a cashier is $1,600 per month then the cost of each input combination is:

  8. The Cost Minimization Rule • The outcomes from hiring an additional unit of an input is the marginal product (MP) of that input. • Firms want the highest possible marginal product from each dollar spent on inputs. • Firms adjust their hiring of inputs until the marginal product per dollar is equal for all inputs.

  9. The Cost Minimization Rule • Cost-minimizing rule: • If MPL/Wage > MPK/Rental rate then the firm could move $1 from hiring capital to hiring labor and get more output from it. MPL Wage MPK Rental rate =

  10. The Cost Minimization Rule • The firm will continue to substitute labor for capital until the falling marginal product of labor per dollar meets the rising marginal product of capital per dollar.

  11. B C B MU / P P C C Marginal Utility per Dollar Total utility (utils) MU / P P P At the optimal consumption bundle, the marginal utility per dollar spent on clams is equal to the marginal utility per dollar spent on potatoes. 6 If Sammy has, in fact, chosen his optimal consumption bundle, his marginal utility per dollar spent on clams and potatoes must be equal. 5 4 3 C 2 1 0 1 2 3 4 5 Quantity of clams (pounds) 10 8 6 4 2 0 Quantity of potatoes (pounds)

  12. The Cost Minimization Rule • The cost-minimization rule is analogous to the optimal consumption rule (introduced in Module 51) •  which has consumers maximize their utility by choosing the combination of goods so that the marginal utility per dollar is equal for all goods.

  13. Check your understanding • A firm produces its output using only capital and labor. Labor costs $100 per worker per day and capital costs $200 per unit per day. If the marginal product of the last worker employed is 500 and the marginal product of the last unit of capital employed is 1,000, is the firm employing the cost-minimizing combination of inputs? Explain.

  14. Inputs to production can be either substitutes or complements. • The firm will choose the combination of inputs that produces the desired level of outputs in the cheapest way possible. • The firm wants to get the most MP from each unit of input that it hires. Therefore, it will hire labor and capital until MPL/wage = MPK/rental rate, the cost minimization rule.

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