Deck 5: Production and Cost

Question 1

You want to estimate the cost of materials used to produce a particular product. According to accounting reports, you initially paid $50 for the materials that are necessary to produce each unit. Is $50 a good estimate of your current production costs Explain.

Answer 1

The historical cost is not necessarily a good estimate of current production cost. The relevant cost is the current opportunity cost of the materials.

Question 2

Assume Kodak's production function for digital cameras is given by Q = 100(L 0.7 K 0.3 ), where L and K are the number of workers and machines employed in a month, respectively, and Q is the monthly output. Moreover, assume the monthly wage per worker is $3,000 and the monthly rental rate per machine is $2,000. NOTE: Given the production function, the marginal product functions are MPL = 70(L -0.3 K 0.3 ) and MPK = 30(L 0.7 K -0.7 ).

Answer 2

Marginal product is the change is output resulting from employing one more unit of a particular input.
Consider the expression
Here monthly wage per worker is
and monthly rent per machine is
.
The objective is to find the number of workers and machines needs to be deployed for output of
units.
The optimal values of number of worker and machines is obtained as follows
Substituting equation
into production function
with
produces
Substituting
in equation
produces number of machines as
Hence, the number of workers is
. And number of machines is
.
The objective is to find the total cost and the average cost.
Total cost of producing
units is the sum of expenditure made to acquire each of the inputs. So, the total cost is as follows,
Also, the average cost is as follows
Hence, the total cost is
and the average cost is
.

Question 3

You work for an airline company as a ticket operations manager at a major airport. Your unit is responsible for issuing boarding passes to 30,000 customers per day. Currently you employ 80 customer service representatives (CSRs) and 10 electronic ticketing machines to meet this demand. Each CSR is paid wages and fringe benefits of $150/day. It also costs you $150/day to lease each machine (price includes installation, software support, and servicing). A computer vendor has offered to lease you additional electronic ticketing machines at this price. You estimate that by leasing 10 more machines you can meet your service requirements with 30 fewer CSRs. Should you lease the additional machines or continue to service your customers with your current input mix
You conduct additional analysis and estimate that you can service the 30,000 customers with the following combinations of CSRs and machines. Calculate the total costs for each of these combinations. What combination of inputs serves the customers at the lowest possible cost

Answer 3

Factors of production are resources like land, labor, capital, etc. used in production of goods and services. Isocost curve is a curve which shows all the possible combination of inputs which are having same total cost. Isoquant curve is a curve which shows all the possible combinations of inputs which give same level of output.
Show the table showing the total cost at different combinations as follows:
There are two combinations where the total cost is minimum. First combination is 30 CSRs and 30 machines, and second combination is 20 CSRs and 40 machines.

Question 4

Suppose that average cost is minimized at 50 units and equals $1. What is marginal cost at this output level

Question 5

For simplicity, throughout this problem, assume labor ( L ), capital ( K ), and quantity produced ( Q ) can be infinitely divided-that is, it is fine to hire 3.3 workers, rent 4.7 machines, and/or produce 134.2 units. Answer the following questions, assuming the production function for DurableTires Corp. is
where Q is the quantity of tires produced, L is the number
of workers employed, and K is the number of machines rented.
a. What is the quantity of tires produced when the company employs 64 workers and 36 machines
b. What are the average product of labor ( L ) and the average product of machines ( K ) when the input mix is the one given above Clearly and concisely, please explain how you would interpret these numbers.
c. Continue to assume the input mix given above: What is the marginal product of labor ( L ), if the number of workers is increased by 1 unit What is the marginal product of capital ( K ), if the number of machines is increased by 1 unit, instead Clearly and concisely, please explain how you would interpret these numbers.
d. Does DurableTires' production function display increasing, decreasing, or constant returns to scale Explain. Would your answer change, if the production function were
How Explain.
e. Does DurableTires' production function display increasing, decreasing, or constant returns to labor Explain. Would your answer change, if the production function were
How Explain.

Question 6

Proton Holdings Bhd is a national carmaker in Malaysia. In late 2007, the Malaysian government owned 43 percent of the company. The remaining stock of the company traded on public stock exchanges. Proton was among Malaysia's worst performing companies in 2005, after competition from foreign carmakers and a lack of new models cost the firm significant market share and profits. It has since hired a new chief executive, sold its loss-making MV Agusta motorbike firm, and pledged to find a new technology partner. The company has been under substantial pressure, with its share of domestic sales falling to 44 percent from 75 percent over the past decade.
Analysts polled in late 2007 noted that the company's new management had made several moves to revamp the company and that these efforts were bearing fruit in terms of increased sales volume and market share. New models such as the Persona , a sport edition of Savvy, and Satria Neo were relative successes. The management also implemented stringent cost controls. Nonetheless, analysts concluded that Proton's long-run ability to survive depends on whether it can achieve increased production volume and economies of scale. Without sufficient scale it is unlikely that the company will survive the intense local and worldwide competition. The analysts assert that by itself, Proton would find it hard to achieve economies of scale and to develop new technologies.
Suppose that you are hired as a consultant to advise Proton's management. What do the analysts mean when they say that Proton needs to achieve economies of scale to be competitive Discuss at a general level the types of actions that the company might want to consider to achieve the necessary scale.
SOURCE: Kathy Fong (2007), "No Economies of Scale for Proton without Global Partner," StarBiz , thestar online (November 21).

Question 7

What is the difference between economies of scale and economies of scope

Question 8

Answer the following questions, continuing to assume the production function for DurableTires Corp. is
where Q is the quantity of tires produced, L is the number of workers employed, and K is the number of machines rented. Moreover, assume the wage per unit of labor (WL) is $50 and the rental price per machine is $200 (WK).
a. What is the total cost of producing the quantity of tires you found in your answer to question 5-23(a) And the average cost Assuming the number of machines rented does not change, what is the marginal cost of producing one additional tire
b. Given the production function above, the marginal product of labor and the marginal product
of capital are
respectively. Given the wage and rental rate above, is DurableTires Corp. adopting an optimal input mix to produce the quantity of tires found in question 5-23(a) If yes, why If not, why not, and how could DurableTires Corp. save money producing that same quantity of tires Explain.
c. What happens to the optimal input mix you found in question 5-23, if the government introduces a tax that raises the cost of labor to $150 per worker Explain.

Question 9

Gina Picaretto is production manager at the Rich Manufacturing Company. Each year her unit buys up to 100,000 machine parts from Bhagat Incorporated. The contract specifies that Rich will pay Bhagat its production costs plus a $5 markup ( costplus pricing ). Currently, Bhagat's costs per part are $10 for labor and $10 for other costs. Thus the current price is $25 per part. The contract provides an option to Rich to buy up to 100,000 parts at this price. It must purchase a minimum volume of 50,000 parts.
Bhagat's workforce is heavily unionized. During recent contract negotiations, Bhagat agreed to a 30 percent raise for workers. In this labor contract, wages and benefits are specified. However, Bhagat is free to choose the quantity of labor it employs.
Bhagat has announced a $3 price increase for its machine parts. This figure represents the projected $3 increase in labor costs due to its new union contract. It is Gina's responsibility to evaluate this announcement.
Why do many firms use cost-plus pricing for supply contracts

Question 10

What is the difference between economies of scale and learning effects

Question 11

Assume DurableTires Corp. faces the following demand curve, P=250 - 0.1Q. If DurableTires' marginal cost is constant at $35, how many tires should it produce in order to maximize its profits What's DurableTires' profit in this case Should the elasticity of demand be greater, equal, or less than 1 at the profit-maximizing price and quantity Explain ( hint : you may use a graph to support your argument).

Question 12

Distinguish between returns to scale and returns to a factor.

Question 13

Suppose that you can sell as much of a product as you want at $100 per unit. Your marginal cost is: MC = 2Q. Your fixed cost is $50. What is the optimal output level What is the optimal output, if your fixed cost is $60

Question 14

You work for an airline company as a ticket operations manager at a major airport. Your unit is responsible for issuing boarding passes to 30,000 customers per day. Currently you employ 80 customer service representatives (CSRs) and 10 electronic ticketing machines to meet this demand. Each CSR is paid wages and fringe benefits of $150/day. It also costs you $150/day to lease each machine (price includes installation, software support, and servicing). A computer vendor has offered to lease you additional electronic ticketing machines at this price. You estimate that by leasing 10 more machines you can meet your service requirements with 30 fewer CSRs. Should you lease the additional machines or continue to service your customers with your current input mix
Plot the input combinations in the table on a graph that contains CSRs on the vertical axis and machines on the horizontal axis. Connect the points by lines to approximate an isoquant as pictured in Figure 5.6. Add the cost minimizing isocost curve to the graph (you can derive this line from the input prices and the total cost of the low-cost input combination). How do the slopes of the isocost curve and isoquant compare at the optimal input combination

Question 15

Discuss two problems that arise in estimating cost curves.

Question 16

Gina Picaretto is production manager at the Rich Manufacturing Company. Each year her unit buys up to 100,000 machine parts from Bhagat Incorporated. The contract specifies that Rich will pay Bhagat its production costs plus a $5 markup ( costplus pricing ). Currently, Bhagat's costs per part are $10 for labor and $10 for other costs. Thus the current price is $25 per part. The contract provides an option to Rich to buy up to 100,000 parts at this price. It must purchase a minimum volume of 50,000 parts.
Bhagat's workforce is heavily unionized. During recent contract negotiations, Bhagat agreed to a 30 percent raise for workers. In this labor contract, wages and benefits are specified. However, Bhagat is free to choose the quantity of labor it employs.
Bhagat has announced a $3 price increase for its machine parts. This figure represents the projected $3 increase in labor costs due to its new union contract. It is Gina's responsibility to evaluate this announcement.
What potential problems do you envision with cost-plus pricing

Question 17

Suppose that the marginal product of labor is: MP = 100 - L, where L is the number of workers hired. You can sell the product in the marketplace for $50 per unit and the wage rate for labor is $100. How many workers should you hire

Question 18

Your company currently uses steel and aluminum in a production process. Steel costs $.50 per pound, and aluminum costs $1.00 per pound. Suppose the government imposes a tax of $.25 per pound on all metals. What affect will this have on your optimal input mix Show using isoquants and isocost lines.

Question 19

Textbook writers typically receive a simple percentage of total revenue generated from book sales. The publisher bears all the production costs and chooses the output level. Suppose the retail price of a book is fixed at $50. The author receives $10 per copy, and the firm receives $40 per copy. The firm is interested in maximizing its own profits. Will the author be happy with the book company's output choice Does the selected output maximize the joint profits (for both the author and company) from the book

Question 20

You work for an airline company as a ticket operations manager at a major airport. Your unit is responsible for issuing boarding passes to 30,000 customers per day. Currently you employ 80 customer service representatives (CSRs) and 10 electronic ticketing machines to meet this demand. Each CSR is paid wages and fringe benefits of $150/day. It also costs you $150/day to lease each machine (price includes installation, software support, and servicing). A computer vendor has offered to lease you additional electronic ticketing machines at this price. You estimate that by leasing 10 more machines you can meet your service requirements with 30 fewer CSRs. Should you lease the additional machines or continue to service your customers with your current input mix
Suppose that the marginal product of CSRs at the optimal input combination is 1,000. Explain in words what this means. What is the marginal product of machines at this point Explain why.

Question 21

Suppose your company produces one product and that you are currently at an output level where your price elasticity is 0.5. Are you at the optimal output level for profit maximization How can you tell

Question 22

Gina Picaretto is production manager at the Rich Manufacturing Company. Each year her unit buys up to 100,000 machine parts from Bhagat Incorporated. The contract specifies that Rich will pay Bhagat its production costs plus a $5 markup ( costplus pricing ). Currently, Bhagat's costs per part are $10 for labor and $10 for other costs. Thus the current price is $25 per part. The contract provides an option to Rich to buy up to 100,000 parts at this price. It must purchase a minimum volume of 50,000 parts.
Bhagat's workforce is heavily unionized. During recent contract negotiations, Bhagat agreed to a 30 percent raise for workers. In this labor contract, wages and benefits are specified. However, Bhagat is free to choose the quantity of labor it employs.
Bhagat has announced a $3 price increase for its machine parts. This figure represents the projected $3 increase in labor costs due to its new union contract. It is Gina's responsibility to evaluate this announcement.
Should Gina contest the price increase Explain.

Question 23

Semiconductor chips are used to store information in electronic products, such as personal computers. One of the early leaders in the production of these chips was Texas Instruments (TI). During the early period in the development of this industry, TI made the decision to price its semiconductors substantially below its production costs. This decision increased sales, but resulted in near-term reductions in profits. Explain why TI might have made this decision.

Question 24

Your company currently uses steel and aluminum in a production process. Steel costs $.50 per pound, and aluminum costs $1.00 per pound. Suppose that inflation doubles the price of both inputs. What affect will this have on your optimal input mix Show using isoquants and isocost lines.

Question 25

The AFL-CIO has been a steadfast proponent of increasing the minimum wage. Offer at least two reasons why they might lobby for such increases.

Question 26

You work for an airline company as a ticket operations manager at a major airport. Your unit is responsible for issuing boarding passes to 30,000 customers per day. Currently you employ 80 customer service representatives (CSRs) and 10 electronic ticketing machines to meet this demand. Each CSR is paid wages and fringe benefits of $150/day. It also costs you $150/day to lease each machine (price includes installation, software support, and servicing). A computer vendor has offered to lease you additional electronic ticketing machines at this price. You estimate that by leasing 10 more machines you can meet your service requirements with 30 fewer CSRs. Should you lease the additional machines or continue to service your customers with your current input mix
Suppose that the cost of leasing a machine declines to $45/day. What is your new optimal input mix How does this affect your graph

Question 27

Mountain Springs Water Company produces bottled water. Internal consultants estimate the company's production function to be Q = 300L 2 K, where Q is the number of bottles of water produced each week, L is the hours of labor per week, and K is the number of machine hours per week. Each machine can operate 100 hours a week. Labor costs $20/hour, and each machine costs $1000 per week.

Question 28

Gina Picaretto is production manager at the Rich Manufacturing Company. Each year her unit buys up to 100,000 machine parts from Bhagat Incorporated. The contract specifies that Rich will pay Bhagat its production costs plus a $5 markup ( costplus pricing ). Currently, Bhagat's costs per part are $10 for labor and $10 for other costs. Thus the current price is $25 per part. The contract provides an option to Rich to buy up to 100,000 parts at this price. It must purchase a minimum volume of 50,000 parts.
Bhagat's workforce is heavily unionized. During recent contract negotiations, Bhagat agreed to a 30 percent raise for workers. In this labor contract, wages and benefits are specified. However, Bhagat is free to choose the quantity of labor it employs.
Bhagat has announced a $3 price increase for its machine parts. This figure represents the projected $3 increase in labor costs due to its new union contract. It is Gina's responsibility to evaluate this announcement.
Is the increase more likely to be justified in the short run or the long run Explain.

Question 29

The Workerbee Company employs 100 high school graduates and 50 college graduates at respective wages of $10 and $20. The total product for high school graduates is 1000 + 100QH, whereas the total product for college graduates is 5000 + 50QC. QH = the number of high school graduates, while QC = the number of college graduates. Is the company hiring the optimal amount of each type of worker If not, has it hired too many high school or too many college graduates Explain.

Question 30

Is the "long-run" the same calendar time for all firms Explain.

Question 31

.

Question 32

You work for an airline company as a ticket operations manager at a major airport. Your unit is responsible for issuing boarding passes to 30,000 customers per day. Currently you employ 80 customer service representatives (CSRs) and 10 electronic ticketing machines to meet this demand. Each CSR is paid wages and fringe benefits of $150/day. It also costs you $150/day to lease each machine (price includes installation, software support, and servicing). A computer vendor has offered to lease you additional electronic ticketing machines at this price. You estimate that by leasing 10 more machines you can meet your service requirements with 30 fewer CSRs. Should you lease the additional machines or continue to service your customers with your current input mix
Are there any other factors that should be considered in making this decision on the optimal mix of machines and CSRs Discuss briefly.

Question 33

Suppose the Jones Manufacturing Company produces a single product. At its current input mix the marginal product of labor is 10 and the marginal product of capital is 20. The per unit price of labor and capital are $5 and $10, respectively. Is the Jones Company using an optimal mix of labor and capital to produce its current output If not, should it use more capital or labor Explain.

Question 34

Gina Picaretto is production manager at the Rich Manufacturing Company. Each year her unit buys up to 100,000 machine parts from Bhagat Incorporated. The contract specifies that Rich will pay Bhagat its production costs plus a $5 markup ( costplus pricing ). Currently, Bhagat's costs per part are $10 for labor and $10 for other costs. Thus the current price is $25 per part. The contract provides an option to Rich to buy up to 100,000 parts at this price. It must purchase a minimum volume of 50,000 parts.
Bhagat's workforce is heavily unionized. During recent contract negotiations, Bhagat agreed to a 30 percent raise for workers. In this labor contract, wages and benefits are specified. However, Bhagat is free to choose the quantity of labor it employs.
Bhagat has announced a $3 price increase for its machine parts. This figure represents the projected $3 increase in labor costs due to its new union contract. It is Gina's responsibility to evaluate this announcement.
How will a $3 increase in the price of machine parts affect Gina's own production decisions

Question 35

Suppose the production function of PowerGuns Co. is given by
Q = 25 LK
where Q is the quantity of guns produced in the month, L is the number of workers employed, and K is the number of machines used in the production. The monthly wage rate is $3,000 per worker and the monthly rental rate for a machine is $6,000. Currently PowerGuns Co. employs 25 workers and 40 machines. Assume perfect divisibility of labor and machines..)