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A manufacturer of laptop computers operates a plant with an annual capacity of 6,630,000 laptop units. One of his models is expected to sell 390,000 units in the coming year. How large should each product lot be if it costs $575 to change production from one model to another. Assume that the manufacturer values each laptop at $280 dollars and it has a holding interest rate of 2%. You should round your answer up to the nearest laptop unit. Please show work using the economic order quality formula.

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Deanna Hettinger
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6 Jun 2019

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Related questions

You're the resident economic expert of Medicine. The CEO, Jeff, is asking you to complete a project that another person, Shawn, had started working on before he retired. The project is time-sensitive. Jeff explains that Medaline has a manufacturing plant that produces a prescription topical cream called DermaPlus, which is used for treating certain skin conditions. Hospitals and pharmacies are the main buyers of DermaPlus. The market for this cream is extremely competitive. Several other firms produce creams that are almost identical to DermaPlus. Medaline's current share of the market for this type of topical cream is so small that it cannot influence the market price. On the other hand, because Medaline is relatively small compared to the size of the market, it can sell as much of the cream as it likes at the prevailing market price. The plant producing DermaPlus has been operating for a little over three years with the same manufacturing equipment. Currently, there are no plans for upgrading or adding to this equipment. Over the last three years, the price of DermaPlus and related creams has been quite volatile and Medaline has tried to react to the changing price by varying its output level to constantly maximize its monthly profit. To date, Medaline has been able to vary monthly production quite easily by taking advantage of a flexible, none union workforce with a large number of part-time workers. However, the workforce at the DermaPlus plant is just about to be unionized. Once that happens, it will become much more difficult to vary the amount of labour used in the short run and therefore much more difficult to vary the monthly production of DermaPlus. Before he left, Shawn had been asked to estimate the short-run cost functions for the DermaPlus manufacturing plant. The goal was to use this information to determine the profit-maximizing output level and use that information to estimate the optimal size for the newly unionized workforce. Jeff tells you that DermaPlus and related products are just about to come under the umbrella of a new reference-based pricing scheme. Under the new scheme, the government will set the price of DermaPlus and competing creams and review that price every two years. Once the price has been set Medaline and other manufacturers simply have to decide how much of the cream, if any, they want to produce and sell. Unfortunately, although the workforce will be unionized in just over a week, the referenced based price for DermaPlus will not be announced for another two months. Consequently, Medaline has to choose the size of its workforce (and therefore its production capacity) before it knows the price it will get for its product. To reduce the uncertainty about this decision, Jeff recently hired a consultant with expertise in the pharmaceutical industry and reference-based pricing to estimate the price that will be announced for DermaPlus. The consultant estimates that there is a 6% chance that the price will be $50 per unit, a 19% chance that the price will be $100 per unit and a 75% chance that the price will be $150 per unit. This is the best estimate the consultant can provide given the lack of information coming from the government about the issue. After giving you this background information, Jeff asks you to complete the following tasks:

1. Determine the profit-maximizing average monthly production capacity for DermaPlus for each of the possible reference-based prices identified by the consultant. Estimate the expected monthly profit in each case.

2. Recommend an average monthly production capacity for the next 12 months given the uncertainty about the price of DermaPlus. Your recommendation will be used to set the size of the manufacturing plant's unionized workforce. (Note: You simply have to determine the best monthly production capacity for the next 12 months, not the number of workers required.)

3. Write a short report summarizing the results of your analysis and any recommendations. Jeff makes it clear to you that he is a risk-neutral person. You only have a week to complete the analysis, interpret the results, and summarize your findings and recommendations in a brief report. When Jeff makes his recommendations about the structure and format of the report you realize that they are much the same for Assignment 1 that you completed at another company. Finally, Jeff gives you a copy of one of Shawn's spreadsheets. This one contains data that Shawn collected on the variables he thought would be needed to estimate the short-run cost functions for DermaPlus and the firm's profit-maximizing output level. Jeff makes it clear that he has complete confidence in Shawn's technical abilities and professional judgment and tells you to take the information in Shawn's spreadsheet at face value and to use it as a starting point for your analysis.

Cray Computer, Inc., located in Colorado Springs, Colorado, is a privately-held producer of high-speed electronic computers with immense storage capacity and computing capability. Although the Crays market is restricted to industrial users and a few large government agencies (e.g., Department of Health, NASA, National Weather Service, etc.), the company has profitably exploited its market niche.

Glen Cray, founder and research director, has recently announced his retirement, the timing of which will, unfortunately, coincide with the expiration of several patents covering key aspects of the Cray computer. Your company, a potential entrant into the market for supercomputers, has asked you to evaluate the short- and longer-run potential of this market. Based on data gathered from your company's engineering department, user surveys, trade associations, and other sources, the following market Demand and cost information has been developed:

P = $54 - $1.5Q

TC = $200 + $6Q + $0.5Q2

where P is the price, Q is units measured by the number of supercomputers, TC is total costs, including a normal rate of return and all figures are in millions of dollars.

A. Assume that these demand and cost data are descriptive of Cray's historical experience.

i.Calculate the profit-maximizing output, price, and economic profit earned by Cray Computer as a monopolist.

ii. What is the point price elasticity of demand at this output level?

Ā 

B. After the patents expire and barriers to entry are eliminated, the market structure changes.

i.If the new entrants have the same total cost structure as Cray, and a competitive equilibrium results.

ii. What will the output of one firm be after all adjustment has taken place; and what will the price be in the market?

iii. What will one firm's profits be?

C. Assume as in B that barriers to entry are eliminated and all entrants have the same cost conditions; however, firms are able to differentiate their products in the eyes of their customers.

i. What will the output of one firm be after all adjustments have taken place?

ii. What will the price be? (Assume that entry causes a parallel shift in the demand curve, as in the monopolistic competitive market).

iii. What will the firm's profits be?

D. Assume that the point price elasticity of demand calculated in part A is a good estimate of the relevant arc price elasticity. What are the estimates for the potential overall market size (i.e., total quantity demanded in the market) for super-computers in B and C?

E.If no other near-term entrants are anticipated, should your company enter the market for supercomputers using the estimates of the market size in D? Why or why not? (Hint: Criterion for entry: if in the longer-run equilibrium the total quantity demanded in the market is greater or equal to the sum of the amounts produced by two firms. There is room for another firm.)

1. Suppose that there is a tax of $1 per unit, and the elasticity of supply is 3 and the elasticity of demand is 2 (in absolute value). How much of the $1 tax is paid by sellers?

$0.60

$0.40

$0.75

$0.67

2. In Market X, the external benefit of consumption is $5. In Market Y, the external cost of consumption is $10. Efficiency in both markets could be achieved by:

a tax of $5 in Market X and a subsidy of $10 in Market Y.

subsidizing both markets.

taxing Market Y and subsidizing Market X.

taxing both markets.

3.Economic theory suggests that a natural monopoly should be:

eliminated whenever it arises.

regulated to take advantage of economies of scale.

left alone to operate with excess capacity.

taken over by the government.

4.When the size of the production is the most efficient:

total cost is at the minimum.

average cost is at the minimum.

marginal cost is at the minimum.

fixed cost is at the minimum.

5.A firm should exit the industry if which of the following conditions apply?

TR > TC

P < AC

Lifetime expected profit is positive.

Prices are low now but expected to rise.

6.Figure: Costs

Reference: Ref 11-6

(Figure: Costs) Use the figure. At a price of $20, the firm earns profit of:

$75.

$300.

$225.

$0, because P = MC at P = $20.

7.When external benefits are present, the market price is ________, however when external costs are present, the market price is ________.

too low; too high

equal to the efficient price; too low

too high; too low

equal to the efficient price; too high

8.Which of the following statements is TRUE?

I. The EPA's tradeable allowances program for sulfur dioxide establishes property rights to pollute and helps reduce transaction costs by distributing allowances, maintaining databases, and monitoring emissions.

II. One criticism of tradeable allowances is that they prohibit non-businesses and environmental groups from purchasing the allowances.

III. The tradeable allowances for sulfur dioxide have performed poorly because electricity output has increased, causing a rise in sulfur dioxide levels.

I only

II and III only

I, II, and III

III only

9.Price floors make it illegal to compete for more customers by lowering prices, so firms compete by offering customers:

various options.

more quantity.

more discount.

higher quality.

10.Figure: Government Price Controls

Reference: Ref 8-3

(Figure: Government Price Controls) Refer to the figure. If the government sets the price ceiling at $31, there will be:

a shortage of 15 units.

a surplus of 15 units.

a supply of 20 units.

no effect on the market.

11.In which of these instances does price function as a signal in the market?

Suppliers invest more in exploration when the price of oil increases.

Consumers complain of price gouging as the price of oil skyrockets.

Government imposes price controls on the skyrocketing price of oil.

All of the answers are correct.

12.Ethanol and sugar are both made from sugar cane, and ethanol can be used as substitute fuel for oil. Increasing oil prices cause the demand for ethanol to increase. This will cause the ______ sugar to ______ and its price to ______.

demand for; decrease; decrease

supply of; increase; increase

supply of; decrease; increase

demand for; increase; increase

13.Why do cotton growers spend billions of dollars to dam rivers and transport water hundreds of miles to grow cotton in California deserts?

Cotton growers in California don't pay payroll taxes.

The water used to grow California cotton is highly subsidized by the government.

Cotton growers in California are mostly operated as nonprofit enterprises.

The water used to grow California cotton is high in mineral contents, making for a bigger cotton yield.

14.Suppose that the equilibrium price in the market is $10. If the current market price is $7.50:

the equilibrium price will fall to $7.50.

competition among buyers will increase the current price.

the current price will fall below $7.50 as sellers compete for market share.

There is not enough information provided to answer the question.

15.Which of the following would increase the demand for beef?

lower pork prices

higher consumer income

higher prices of feed grains used to feed beef cattle

an increase in the price of beef

16.A change in quantity supplied is reflected by a movement along the same supply curve while a change in supply refers to a shift in the entire supply curve.

True

False

17.Table: Production in the United States and Germany

Labor units required to produce:

One Clock

One Sofa

United States

2

5

Germany

3

9

Reference: Ref 2-8

(Table: Production in the United States and Germany) According to the table, the opportunity cost of producing one sofa in the United States is _________, and the opportunity cost of producing one sofa in Germany is _______.

two clocks; three clocks

10 clocks; 27 clocks

0.4 clocks; 0.33 clocks

2.5 clocks; three clocks

18.Mark values his drum set at $800 and Ella values her guitar at $1,000. Suppose that Mark trades his drum set for Ella's guitar.

This trade makes Ella worse off by $200.

This trade makes Mark better off by $200.

Mark must value Ella's guitar for at least $1,000, and Ella must value Mark's drum set for at least $800.

This trade creates value by moving the guitar and drum set to people who value them more.

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