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A.7 Choosing Inputs Review Questions

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Lesson Topics

Profit Maximization (3) through choosing each input into production balances the value of the marginal product of each input with the marginal cost of each input. Cost Minimization (7) balances the marginal product per dollar invested into an input across all inputs. Cost minimization makes the most of the resources devoted to charity. Cost Measures including total cost and marginal cost are alternatives to productivity measures to help firms chose output to maximize profit. They also determine when it is best to shut down production.


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Profit Maximization Question. You are a manager of a firm that sells cotton at a price of $0.50 per pound. Renting one more cotton gin machine (see picture) will increase your firm's output by 200 units per day. Employing one more full-time worker will increase your firm's output by 100 units per day. a. What is the most you should be willing to pay to rent one more cotton gin machine for one day? b. What determines whether or not you actually have to offer that much to the owner of the machine to induce him to rent his machine to your firm? Explain your answers.


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Answer to Question: a. The extra revenue you will earn by renting the machine is 200 × $0.50 = $100 per day. The most you should pay for the machine is $100 per day. b. How much you have to offer the owner of the machine to induce him to rent his machine to your firm depends on how much that owner can get from other firms (his opportunity cost), and depends on the rules for bargaining. For instance, if his opportunity cost is $60 per day and if you can make him a take-it-or-leave-it offer, then you will only have to pay $60.01 to get him to rent to you because he faces the choice between $60.01 renting to you versus $60 renting to some other firm.


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Profit Maximization Question. The A-1 Corporation supplies airplane manufacturers with preformed sheet metal panels that are used on the exterior of aircraft. Manufacturing these panels requires only five sheet metal-forming machines, which cost $300 each, and workers. These workers can be hired on an as-needed basis in the labor market at $7,000 each. Given the simplicity of the manufacturing process, the preformed sheet metal panel market is perfectly competitive. Therefore, the market price for one of A-1’s panels is a constant, $50. Based on the production data in the following table, how many workers should A-1 hire to maximize its profits?

Machines Workers Output

5 0 0

5 1 600

5 2 1,000

5 3 1,290

5 4 1,480

5 5 1,600

5 6 1,680


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Answer to Question: To maximize profits the firm should continue adding workers so long as the value marginal product of labor exceeds the wage. The value marginal product of labor is defined as the marginal product of labor times the price of output. Here, output sells for $50 per panel, so the value marginal product of the third worker is $50(290) = $14,500. The table below summarizes the VMPL for each choice of labor. Since the wage is $7,000, the profit maximizing number of workers is 4.

Machines Workers Output MPL VMPL Wage

5 0 0 – – –

5 1 600 600 $30,000 $7,000

5 2 1,000 400 $20,000 $7,000

5 3 1,290 290 $14,500 $7,000

5 4 1,480 190 $9,500 $7,000

5 5 1,600 120 $6,000 $7,000

5 6 1,680 80 $4,000 $7,000


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Profit Maximization Question. You are a manager of a firm that sells output at a price of $40 per unit. Renting one more unit of capital will increase your firm's output by 4,000 units per year. Employing one more full-time worker will increase your firm's output by 2,000 units per year. Several other firms also are interested in hiring this worker. a. What is the most you should be willing to pay this full-time worker to come to your firm? b. What determines whether or not you actually have to offer this much to the worker to induce him to join your firm? Explain your answers.


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Answer to Question: a. The extra revenue you will earn by hiring the worker is 2,000 × $40 = $80,000 per year. The most you should pay the worker is an annual salary of $80,000. b. How much you have to offer this worker to induce him to join your firm depends on how much the worker can get from other firms (his opportunity cost) and the rules for bargaining. For instance, if his opportunity cost is $60,000 and if you can make him a take-it-or-leave-it offer, then you will only have to pay $60,000.01 to get him because he faces the choice between $60,000.01 working for you versus $60,000 working for some other firm.


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Cost Minimization Each of the following review questions apply the theory of Cost Minimization to the managerial decision of how best to select labor and capital inputs for given input costs.


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Cost Minimization Question. Fourteen McDonalds in Oregon and southeastern Washington have been linked to the call center operated by SEI-CCS Inc., a Fargo, N.D.-based company that works closely with McDonald's. The call taker in Grand Forks enters your order into a computer and relays it back to the home restaurant, where it pops up on a screen in the kitchen. Meanwhile, a digital camera photographs your car as you drive through. The photo pops up on a separate screen next to the order at the drive-through cashier's window to match the order with the car. The reason for outsourcing is that Oregon and Washington state have minimum wages of $8.55 per hour, which is higher than Federal minimum wages, but North Dakota has minimum wages of $7.25 per hour, which equals Federal minimum wages Let’s see how decreasing the cost of hiring handicapped and unskilled workers would affect the McDonald’s Corporation. McDonald’s currently uses 290,000 handicapped and unskilled workers and 140,000 semiskilled workers to produce fast food in the United States. McDonald’s pays the unskilled workers state minimum wages of $7.25 per hour, down from $8.55 per hour, but the semiskilled workers $14.50 per hour. Predict the implications of decreasing the wage of handicapped and unskilled workers from $8.55 to $7.25 on your company’s optimal mix of inputs in the short run (when you cannot adjust your capital) and in the long run (when you can adjust your capital). Hint: Remember to state any assumptions needed to make your predictions.


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Answer to Question: In the short run, a lower wage paid to handicapped and unskilled labor makes

MPU/wU > MPS/wS (since wU decreases),

which implies that to minimize costs the firm should decrease its use of semi-skilled worker (S) and increase its use of handicapped and unskilled workers (U) to produce the same fixed level of output. In the longer run, to produce the same fixed level of output, the company will also substitute labor for capital (invest in fewer machines to replace labor) assuming capital is a substitute with handicapped and unskilled labor.

This answer assumes you keep the level of output fixed. (We also assume that the optimal mix of unskilled and semi-skilled labor was being used at the time of the decrease in the wage, but that is what we assume in every problem unless we are given explicit data to the contrary.)


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Cost Minimization Question. Minimum Wage Stuck in the 1950s Op-ed by Holly Sklar Distributed by McClatchy Tribune News Service, July 23, 2009 Are you better off than you were 40 years ago? Not if you're a minimum wage worker. It would take $9.92 today to match the buying power of the minimum wage at its peak in 1968, the year Martin Luther King died fighting for living wages for sanitation workers. Let’s see how increasing the national minimum wage from $7.25 to $9.92 would affect the Coca-Cola Company. The Coca-Cola Company’s currently uses 1,689 unskilled workers and 6,832 semiskilled workers to produce and ship Coke Zero worldwide. The Coca-Cola Company pays the unskilled workers minimum wages, but the semiskilled workers $15.87 per hour. Predict the implications of increasing the national minimum wage from $7.25 to $9.92 on your company’s optimal mix of inputs in the short run (when you cannot adjust your capital) and in the long run (when you can adjust your capital). Tip: State any assumptions needed to make your predictions.


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Answer to Question: In the short run, a higher minimum wage paid to unskilled labor makes MPU/wU < MPS/wS, which implies that to minimize costs the retailer should increase its use of semi-skilled worker (S) and decrease its use or unskilled workers (U) to produce the same fixed level of output. In the longer run, to produce the same fixed level of output, the company will also substitute capital for labor (invest in some machines to automate a portion of your boxing needs) assuming unskilled labor and capital are substitutes. This answer assumes you keep the level of output fixed. (We also assume that the optimal mix of unskilled and semi-skilled labor was being used at the time of the increase in the minimum wage, but that is what we assume in every problem unless we are given explicit data to the contrary.)


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Cost Minimization Question. You are the manager of a firm that currently uses 17 unskilled workers and 6 semiskilled workers to ship products that you sell online. Your company pays the unskilled workers minimum wages, but the semiskilled workers $15 per hour. You read an article in The Wall Street Journal that the House of Representatives passed legislation that would increase minimum wages. Discuss the implications of this legislation on your company’s optimal mix of inputs in the short run (when you cannot adjust your capital) and in the long run (when you can adjust your capital). Tip: State any assumptions needed to make your predictions.


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Answer to Question: In the short run, a higher minimum wage paid to unskilled labor makes

MPU/wU < MPS/wS,

which implies that to minimize costs the retailer should increase its use of semi-skilled worker (S) and decrease its use or unskilled workers (U) to produce the same fixed level of output. In the longer run, to produce the same fixed level of output, the company will also substitute capital for labor (invest in some machines to automate a portion of your boxing needs) assuming unskilled labor and capital are substitutes.

This answer assumes you keep the level of output fixed. (We also assume that the optimal mix of unskilled and semi-skilled labor was being used at the time of the increase in the minimum wage, but that is what we assume in every problem unless we are given explicit data to the contrary.)


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Cost Minimization Each of the following review questions apply the theory of Cost Minimization to the public policy decision of how best to help the disabled or unemployed.


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Cost Minimization Question. Consider a handicapped person that values his own time at $9 per hour. Suppose In-N-Out Burger and McDonalds and Burger King each value employing the handicapped person at $7 per hour, for 40 hours per week. Discuss the implications of the government subsidizing the handicapped worker’s employment by giving any employer $3 per hour.

In particular, does the subsidy increase the employment of the handicapped person? Does the subsidy increase the happiness of the handicapped person? Is the subsidy a good idea?


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Answer to Question: Without the subsidy, the handicapped person is not working since he values his time more than potential employers. With the subsidy of $3 per hour, competition among multiple employers means the handicapped person will be offered work at the highest wage that is profitable for the employer. That is the wage of $10 per hour since $10 minus the subsidy of $3 means the employer pays a net wage of $7, which is the value of employing the handicapped person. So, the subsidy increases the employment of the handicapped person, from 0 to the new level of 40 hours per week. Does the subsidy increase the happiness of the handicapped person? Yes, he sells his time for $10 per hour and he values it at $9 per hour, and so gains $1 per hour, which amounts to $40 per week of gain. Is the subsidy a good idea? No. The subsidy benefits the handicapped person $40 per week, but it costs taxpayers $3x40 = $120 per week. Both the handicapped person and taxpayers would be better off (and the potential employers would not care) if the handicapped person did not receive the wage subsidy but, instead, received $80 per week (or any amount between $40 and $120) in welfare.


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Cost Minimization Each of the following review questions apply the theory of Cost Minimization to the managerial decision of how best to run a charity.


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Cost Minimization Question. You have been hired to replace the manager of the Toys for Tots charity that uses only two inputs, labor and capital, to produce and distribute toys to poor children. The charity can hire as much labor as it wants at a wage of $5 per hour and can rent as much capital as it wants at a price of $5 per hour. After you look at the company books, you learn that the charity has been using labor and capital in amounts that imply a marginal product of labor of 50 and a marginal product of capital of 100. a. Is the charity running right? Explain. b. How can the charity be improved? Explain. c. What do Microeconomic assumptions imply about the effectiveness of giving toys to poor children? Explain.


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Answer to Question: a. Is the charity running right?

Answer: Currently, (marginal rate of labor / wage) = 50 / 5 = 10 (marginal rate of capital / rental rate) = 100 / 5 = 20 Since those numbers are different, the firm is not minimizing the cost of producing its current level (call it Q) of toys.

b. How can the charity be improved?

Answer: Since the marginal product per dollar is lower for labor, the firm should use less labor and more capital in order to minimize costs of producing Q toys. There is not enough information to figure out how many toys Q to produce and distribute.

c. What do Microeconomic assumptions imply about the effectiveness of giving toys to poor children?

Answer: 1. If “poor” children are in families lead by rational people, then giving

away toys probably makes the poor family less happy than giving away the cash value of the toys. Toys for Tots is thus not as effective as “Cash” for Tots.

2. If children are treated as commodities to be chosen like cars, then having a lot of children does not make a family poor. Calling a family with a $12,000 yearly income poor if there are 5 kids and not poor if there are no kids makes as much sense as calling a family poor if they bought nice cars. Cash for Tots is thus not as effective as Cash for “Poor People”.

3. Sometimes having a low income is a choice of leisure over other commodities. So when giving Cash to Poor People you should make sure you are not including people that have little income but a lot of leisure time (like Huckleberry Finn wearing rags but happy to float down the Mississippi river).

Comment: Using too much labor is a common mistake for charities that get volunteer labor. They could produce more output if they asked some of


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their volunteers to work extra hours at their day jobs and donate their extra income, which the charity can then use to rent extra capital.


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Cost Minimization Question. Operation Christmas Child was created in 1990 by Dave and Jill Cooke for children in Romania. Each November thousands of churches, groups and individual donors prepare and collect shoeboxes filled with toys to send to poor children in East Asia. You have been hired to the current manager of Operation Christmas Child charity that uses only two inputs, labor and capital, to produce and distribute toys to poor children in East Asia. The charity can hire as much labor as it wants at a wage of $8 per hour and can rent as much capital as it wants at a price of $15 per hour. After you look at the company books, you learn that the charity has been using labor and capital in amounts that imply a marginal product of labor of 40 and a marginal product of capital of 60. a. Is the charity running right? Explain. b. How can the charity be improved? Explain. c. What do Microeconomic assumptions imply about the effectiveness of giving toys to poor children? Explain.


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Answer to Question: a. Is the charity running right?

Answer: Currently, (marginal rate of labor / wage) = 40 / 8 = 5 (marginal rate of capital / rental rate) = 60 / 15 = 4 Since those numbers are different, the firm is not minimizing the cost of producing its current level (call it Q) of toys.

b. How can the charity be improved?

Answer: Since the marginal product per dollar is higher for labor, the firm should use more labor and less capital in order to minimize costs of producing Q toys. There is not enough information to figure out how many toys Q to produce and distribute.

c. What do Microeconomic assumptions imply about the effectiveness of giving toys to poor children?

Answer: 1. If “poor” children are in families lead by rational people, then giving

away toys probably makes the poor family less happy than giving away the cash value of the toys. Toys for Children is thus not as effective as “Cash” for Children.

2. If children are treated as commodities to be chosen like cars, then having a lot of children does not make a family poor. Calling a family with a $12,000 yearly income poor if there are 5 kids and not poor if there are no kids makes as much sense as calling a family poor if they bought nice cars. Cash for Children is thus not as effective as Cash for “Poor People”.

3. Sometimes having a low income is a choice of leisure over other commodities. So when giving Cash to Poor People you should make sure you are not including people that have little income but a lot of leisure time (like Huckleberry Finn wearing rags but happy to float down the Mississippi river).

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