CostMinimization Alternative Input Combinations To produce the optimal

Cost-Minimization

Alternative Input Combinations To produce the optimal quantity of wheat, farmers can choose between a capital-intensive operation (by investing in new tractors) or a laborintensive method (by hiring more workers). Additional capital can take the place of some labor, and vice versa.

Substitutes & Complements in Factor Mkts Capital and labor are substitutes when they can be used instead of each other, and they are complements when more of one increases the marginal product of the other. Capital can often substitute for labor, as when vending machines substitute for human vendors.

Determining the Optimal Input Mix Cost minimization is the process of selecting the combination of factors that produces the optimal output at the lowest possible cost. Firms will hire a factor of production only up to the point at which its MRP is equal to its MFC. This parallels the optimal output rule (MR = MC) for the product market.

Determining the Optimal Input Mix The table above shows two possible combinations of capital (self-checkout stations) and labor (cashiers) for managing customer checkout at a retail store.

The Cost-Minimization Rule A firm determines the costminimizing combination of inputs using the costminimization rule: employ factors so that the marginal product per dollar spent on each factor is the same. Some stores have replaced cashiers with self-checkout stations to reach the cost-minimizing combination of labor and capital.

The Cost-Minimization Rule Said another way, the costminimization rule states that firms should employ factors of labor and capital so that the below equation holds true: Firms adjust their quantities of inputs until the marginal product per dollar spent on each input is the same.

SCENARIO 1 Lets do an example of when the marginal product of labor per dollar is more than the marginal product of capital per dollar Marginal product of labor = 20 units Marginal product of capital = 100 units Wage = $10 Rental rate for capital = $100 MP(input 1) / MRC(input 1) = MP(input 2) / MRC(input MPL / Wage = MPK / Rent 2)

SCENARIO 1 MPL / Wage = MPK / Rent 2 units of output per dollar spent on labor > 1 unit of output per dollar spent on capital The firm would hire more workers and use less capital This would lower the MP of labor per dollar and increase the MP of capital per dollar

SCENARIO 2 Lets do an example of when the marginal product of labor per dollar is less than the marginal product of capital per dollar Marginal product of labor = 20 units Marginal product of capital = 100 units Wage = $10 Rental rate for capital = $25 MPL / Wage = MPK / Rent

SCENARIO 2 MPL / Wage = MPK / Rent 2 units of output per dollar spent on labor < 4 unit of output per dollar spent on capital This firm would use less workers and rent more capital This would increase the MPL/Wage This would decrease the MPK/Rental rate

Marginal Productivity Theory of Income Distribution The marginal productivity theory of income distribution says that the division of income among an economy’s factors of production is determined by each factor’s marginal revenue product at the market equilibrium. Does this theory explain why some workers earn more than others?

Marginal Productivity & Wage Inequality Compensating differentials are wage differences across jobs that reflect the fact that some jobs are less pleasant or more dangerous than others. For example, truckers who haul hazardous chemicals earn more than truckers who only haul bread.

Marginal Productivity & Wage Inequality Some initial reasons for wage differentials include: 1) compensating differentials 2) differences in talent 3) differences in the amount of human capital Wage differences arising from the above are not necessarily fair—differences in talent and human capital can arise from unequal opportunities for different people.

Market Power If factor markets aren’t perfectly competitive, wages can come from market power rather than merely reflect the marginal product of labor. Unions are organizations of workers that try to raise wages and improve working conditions for their members by bargaining collectively. Unions act like a single seller of labor. Through collective bargaining, they represent all workers, making them operate like a labor monopoly.

Efficiency Wages Some employers pay efficiency wages—wages that exceed the market equilibrium wage rate—to motivate hard work and reduce worker turnover.

Discrimination Market competition tends to work against discrimination, however, by providing firms an incentive to reward marginal productivity rather than a discriminatory preference. Despite market incentives, discrimination still persists due to: 1) noncompetitive markets that prevent discriminators from facing competition 2) institutionalized discrimination as a result of government policy

Wage Disparities in Practice The U. S. are labor market Women paid substantially continues to show large less than men; Africandifferencesand across workers American Hispanic according workers are to paid gender substantially and ethnicity. less than White male workers.

Summary and Review 1) What does the marginal revenue product theory of income distribution assert? The division of income among an economy’s factors of production is determined by each factor’s marginal revenue product at the market equilibrium. 2) What are compensating differentials? When wage differences reflect the fact that some jobs are less pleasant or more dangerous than others.

Summary and Review 3) What are three conventional reasons for wage differences? 4) What are three alternative reasons for wage differentials? 5) How do unions use market power to raise wages? 1) Compensating differentials 2) Differences in talent 3) Differences in human capital 1) Market power 2) Efficiency wages 3) Discrimination By representing all workers, unions operate like a labor monopoly.

Summary and Review 6) What are efficiency wages, and in what types of jobs do they tend to be found? Efficiency wages occur when firms pay workers more than the market equilibrium wage rate to motivate hard work and reduce worker turnover.

Summary and Review 7) Does market competition tend to work against or in favor of discrimination based on race, gender, or other characteristics? 8) What two factors can cause discrimination to persist despite market competition? Against. 1) Noncompetitive markets 2) Institutionalized discrimination

Walkthrough: Free-Response Question 1 1. Explain the most likely reason for the wage differences among similar workers in each of the following situations. a. Test pilots for new jet aircraft earn higher wages than airline pilots. b. College graduates usually have higher earnings in their first year on the job than workers without college degrees have in their first year on the job. c. Experienced AP® teachers command higher salaries than new AP® teachers for teaching the same class. (6 points) 1 point: Compensating differentials 1 point: Being a test pilot is more dangerous. 1 point: Differences in human capital 1 point: Education leads to higher productivity. 1 point: Differences in human capital 1 point: On-the-job experience increases the marginal product of experienced teachers.

Summary and Review 1) In the case of robotic machinery replacing assembly line workers, are capital and labor substitutes or complements? 2) In the case of satellite imagery allowing farmers to irrigate cropland more precisely, are capital and labor substitutes or complements? 3) What is the process of selecting the combination of capital and labor that produces the optimal output at the lowest cost? Substitutes. Complements. Costminimization.

Summary and Review 4) A firm will hire a factor of production only up to the point at which its _____ equals its _____. marginal revenue product (MRP); marginal factor cost (MRC) 5) This rule is called the _____. 6) Firms set MRP = MRC to minimize costs in the factor market; what equation does this rule parallel in the product market? cost-minimization rule. MR = MC.

Walkthrough: Free-Response Question 1 1. Answer the following questions under the assumption that firms use only two inputs and seek to maximize profit. a. Would it be wise for a firm that does not have the cost-minimizing combination of inputs to employ more of the input with the highest marginal product and less of the input with the lowest marginal product? Explain. b. What is the cost-minimization rule? c. When a firm hires more labor and rents less capital, what happens to the marginal product of labor per dollar and the marginal product of capital per dollar? Explain. (5 points) 1 point: No, it would not be wise. 1 point: The input with the highest marginal product might be much more expensive than the input with the lowest marginal product, making the marginal product per dollar higher for the input with the lowest marginal product. In this case, costs would be lower if the firm employed more of the input with the lowest marginal product (but the highest marginal product per dollar) and less of the input with the highest marginal product (but the lowest marginal product per dollar. )

Walkthrough: Free-Response Question 1 1. Answer the following questions under the assumption that firms use only two inputs and seek to maximize profit. a. Would it be wise for a firm that does not have the costminimizing combination of inputs to employ more of the input with the highest marginal product and less of the input with the lowest marginal product? Explain. b. What is the costminimization rule? c. When a firm hires more labor and rents less capital, what happens to the marginal product of labor per dollar and the marginal product of capital per dollar? Explain. (5 points) 1 point: The cost-minimization rule says firms should adjust their input combinations to equalize marginal product per dollar spent on each input. 1 point: The marginal product of labor per dollar decreases and the marginal product of capital per dollar increases. 1 point: Each factor has diminishing marginal returns. So when more labor is hired, the marginal product of labor (and thus the marginal product of labor per dollar) decreases. Likewise, when less capital is rented, the marginal product of capital (and thus the marginal product of capital per dollar) increases because the units of capital that are given up had a lower marginal product than those that remain.