Looking for Quiz 6 :
The Theory and Estimation of Production
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Define returns to scale. Why is this considered a long-run phenomenon
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Returns to scale describes what effect on production when all the factor of production are increased. It is a long run phenomena.. There are three types of returns to scale- Increasing return to scale, constant return to scale and diminishing return to scale.
This is to be viewed in a long run phenomenon. All factors of production are variable in the long run. No factor is a fixed factor. Accordingly, scale of production can be changed by changing the quantity of all factors.
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Show what will happen to the diagram above as a result of the changes listed.
a. The firm's budget increases.
b. The price of Y decreases.
c. The price of X decreases.
d. Y becomes more expensive, and X becomes less expensive.
e. Technology makes the Y input more productive.
f. Technology increases the productivity of both inputs by the same proportion.
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b. If price of Y decrease then budget line shift upward toward Y-axis. Now with a lower price of Y the producer will be able to purchase more quantity of Y than before with his given budget.
Effect of price decrease in Y
c. If price of X decrease then budget line shift to upward toward X-axis. Now with a lower price of X the producer will be able to purchase more quantity of Y than before with his given budget.
Effect of price decrease in X
d. If Y becomes more expensive and X becomes less expensive then producer will purchase less quantity of Y and more quantity of X. Budget line shift downward on Y axis and shift upward to X axis.
Effect of change in price of Y and X
e. If technology makes the Y input more productive then produces wants to use more quantity of Y. so, budget line shift to upward toward Y axis. Budget line on X axis remains the same.
Effect of increase in productivity in Y
f. If technology increases the productivity of both input by the same proportion then isoquant shifted upward side. Higher isoquant shows the higher production.
Effect of increase in productivity of both by same proportion
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An American company that sells consumer electronics products has manufacturing facilities in Mexico, Taiwan, and Canada. The average hourly wage, output, and annual overhead cost for each site are as follows:
a. Given these figures, is the firm currently allocating its production resources optimally If not, what should it do (Consider output per person as a proxy for marginal product.)
b. Suppose the firm wants to consolidate all its manufacturing into one facility. Where should it locate Explain.
a. Given these figures, is the firm currently allocating its production resources optimally If not, what should it do (Consider output per person as a proxy for marginal product.)
b. Suppose the firm wants to consolidate all its manufacturing into one facility. Where should it locate Explain. Free
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a.
Let
,
and
denote the wage rate in Mexico, Taiwan and Canada respectively. Let
,
and
denote the marginal product of labor in Mexico, Taiwan and Canada respectively.
Calculate the ratio of marginal product of labor to wage rate for each of the three countries as follows.
Mexico:
Taiwan:
Canada:
For the firm to be optimally allocating its resources, the ratios of the marginal product to wage rate of the three countries should be equal. But that is not the case here, that is, the ratios are different. This implies the firm is not optimally allocating its production resources.
The ratio of marginal product to wage rate (i.e., the units of output yield by the last dollar spent on labor) is highest in Mexico. Therefore, the firm should employ more labor in Mexico.
b.
Suppose for simplicity that the price P of one unit of the firm's output is $1. Suppose the firm manufactures in only one of the three countries - Mexico, Taiwan, and Canada, and the amount of labor employed is L units.
Let
denote the profit of the firm in case the firm manufactures only in Mexico,
denote the profit of the firm in case the firm manufactures only in Taiwan, and
denote the profit of the firm in case the firm manufactures only in Canada.
Scenario 1: The firm manufactures only in Mexico.
Calculate the total cost of the firm by adding the labor cost and the fixed cost.
Calculate the total revenue of the firm by multiplying the price of per unit of output by output produced.
Calculate the profit
by subtracting total cost from total revenue as follows.
Therefore, if the firm bases its manufacturing only in Mexico employing L units of labor, the firm's profit will be equivalent to "
."
Scenario 2: The firm manufactures only in Taiwan.
Calculate the total cost of the firm by adding the labor cost and the fixed cost.
Calculate the total revenue of the firm by multiplying the price of per unit of output by output produced.
Calculate the profit
by subtracting total cost from total revenue as follows.
Therefore, if the firm bases its manufacturing only in Taiwan employing L units of labor, the firm's profit will be equivalent to "
."
Scenario 3: The firm manufactures only in Canada.
Calculate the total cost of the firm by adding the labor cost and the fixed cost.
Calculate the total revenue of the firm by multiplying the price of per unit of output by output produced.
Calculate the profit
by subtracting total cost from total revenue as follows.
Therefore if the firm bases its manufacturing only in Mexico employing L units of labor, the firm's profit will be equivalent to "
."
Observe the following.
In the above inequality, the leftmost expression is
, the middle expression is
and the rightmost expression is
, implying the following.
Therefore, if the firm wants to manufacture only in one location, it should manufacture in Taiwan because there its profit is highest.
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Explain the relationship between marginal product and average product. Why can we expect marginal product to equal average product at average product's maximum point
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According to the rule for optimal input usage, a firm should hire a person as long as her marginal revenue product is greater than her marginal cost to the company. It is well known that many companies have management training programs in which new trainees are paid relatively high starting salaries and are not expected to make substantial contributions to the company until after the program is over (programs may run between 6 to 18 months). In offering such training programs, is a company violating the optimality rule Explain.
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For those of you with current or previous work experience, how is (was) productivity measured in your organization
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A firm has the following short-run production function:
Q = 50 L + 6 L 2 - 0.5 L 3
where Q = Quantity of output per week
L = Labor (number of workers)
a. When does the law of diminishing returns take effect
b. Calculate the range of values for labor over which Stages I, II, and III occur.
c. Assume each worker is paid $10 per hour and works a 40-hour week. How many workers should the firm hire if the price of the output is $10 Suppose the price of the output falls to $7.50. What do you think would be the short-run impact on the firm's production The long-run impact
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The Oceanic Pacific fleet has just decided to use a pole-and-line method of fishing instead of gill netting to catch tuna. The latter method involves the use of miles of nets strung out across the ocean and therefore entraps other sea creatures besides tuna (e.g., porpoises, sea turtles). Concern for endangered species was one reason for this decision, but perhaps more important was the fact that the major tuna canneries in the United States will no longer accept tuna caught by gill netting.
Oceanic Pacific decided to conduct a series of experiments to determine the amount of tuna that could be caught with different crew sizes. The results of these experiments follow.
a. Determine the point at which diminishing returns occurs.
b. Indicate the points that delineate the three stages of production.
c. Suppose the market price of tuna is $3.50/pound. How many fishermen should the company use if the daily wage rate is $100
d. Suppose a glut in the market for tuna causes the price to fall to $2.75/pound. What effect would this have on the number of fishermen used per boat Suppose the price rose to $5.00/pound. What effect would this have on its hiring decision
e. Suppose the firm realizes that to keep up with the demand for tuna caught by the more humane pole-and-line method of fishing, each of its boats must catch at least 1,000 pounds of fish per day. Given the preceding data, what should it consider doing Explain.
a. Determine the point at which diminishing returns occurs.
b. Indicate the points that delineate the three stages of production.
c. Suppose the market price of tuna is $3.50/pound. How many fishermen should the company use if the daily wage rate is $100
d. Suppose a glut in the market for tuna causes the price to fall to $2.75/pound. What effect would this have on the number of fishermen used per boat Suppose the price rose to $5.00/pound. What effect would this have on its hiring decision
e. Suppose the firm realizes that to keep up with the demand for tuna caught by the more humane pole-and-line method of fishing, each of its boats must catch at least 1,000 pounds of fish per day. Given the preceding data, what should it consider doing Explain. Essay
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Explain the difference between a short-run and long-run production function. Cite one example of this difference in a business situation.
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Indicate whether each of the following statements is true or false. Explain why.
a. When the law of diminishing returns takes effect, a firm's average product will start to decrease.
b. Decreasing returns to scale occurs when a firm has to increase all its inputs at an increasing rate to maintain a constant rate of increase in its output.
c. A linear short-run production function implies that the law of diminishing returns does not take effect over the range of output being considered.
d. Stage I of the production process ends at the point where the law of diminishing returns occurs.
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Cite and discuss possible reasons a firm may actually find itself operating in Stage I or Stage III of the short-run production function.
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What are the key points in a short-run production function that delineate the three stages of production Explain the relationship between the law of diminishing returns and the three stages of production.
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The owner of a car wash is trying to decide on the number of people to employ based on the following short-run production function:
Q = 6 L - 0.5 L 2
where Q = Number of car washes per hour
L = Number of workers
a. Generate a schedule showing total product, average product, and marginal product. Plot this schedule on a graph.
b. Suppose the price of a basic car wash (no undercoating, no wax treatment, etc.) in his area of business is $5. How many people should he hire if he pays each worker $6/hour
c. Suppose he considers hiring students on a part-time basis for $4/hour. Do you think he should hire more workers at this lower rate Explain.
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Explain why a firm's adherence to the MRP = MLC rule enables it to find the optimal number of units of a variable input to use in the short-run production process.
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The International Calculator Company of China produces handheld calculators in its plant. It tries to keep the number of workers in the plant constant so the only variable factor that can be measured is materials. Over the last seven monthly periods, the data for materials and quantity produced were the following:
a. Calculate a Cobb-Douglas production function of the form Q = aM b.
b. Discuss the important properties of your results.
c. What is the marginal product of materials
a. Calculate a Cobb-Douglas production function of the form Q = aM b.
b. Discuss the important properties of your results.
c. What is the marginal product of materials Essay
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The Noble Widget Corporation produces just one product, widgets. The company's new economist has calculated a short-run production function as follows:
Q = 7 V + 0.6 V 2 - 0.1 V 3
where Q is the number of widgets produced per day and V is the number of production workers working an 8-hour day.
a. Develop a production schedule with V equaling 1 to 10.
b. Calculate average and marginal products.
c. Draw a graph.
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The Brady Corporation has eleven plants located around the world. In a recent year, the data for each plant gave the number of labor hours (in thousands), capital (total net plant assets, in millions), and total quantity produced:
The plants all operate at a similar level of technology so a production function can be derived from the data.
a. Use a Cobb-Douglas production function to calculate a regression, and discuss the important characteristics of your results, such as the form of the equation, R 2 , and the statistical significance of the coefficients.
b. Calculate the estimated production for each plant.
c. Does the result indicate constant, decreasing, or increasing returns to scale
d. What are the elasticities of production of labor and of capital What is the meaning of the elasticities
e. Is the marginal product of labor decreasing (See Appendix 6C to answer this question.)
The plants all operate at a similar level of technology so a production function can be derived from the data.
a. Use a Cobb-Douglas production function to calculate a regression, and discuss the important characteristics of your results, such as the form of the equation, R 2 , and the statistical significance of the coefficients.
b. Calculate the estimated production for each plant.
c. Does the result indicate constant, decreasing, or increasing returns to scale
d. What are the elasticities of production of labor and of capital What is the meaning of the elasticities
e. Is the marginal product of labor decreasing (See Appendix 6C to answer this question.)
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The owner of a small car rental service is trying to decide on the appropriate numbers of vehicles and mechanics to use in the business for the current level of operations. He recognizes that his choice represents a trade-off between the two resources. His past experience indicates that this trade-off is as follows (see Appendix 6B for help in answering this question):
a. Assume the annual (leasing) cost per vehicle is $6,000 and the annual salary per mechanic is $25,000. What combination of vehicles and mechanics should he employ
b. Illustrate this problem with the use of an isoquant/isocost diagram. Indicate graphically the optimal combination of resources.
a. Assume the annual (leasing) cost per vehicle is $6,000 and the annual salary per mechanic is $25,000. What combination of vehicles and mechanics should he employ
b. Illustrate this problem with the use of an isoquant/isocost diagram. Indicate graphically the optimal combination of resources. Essay
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Suppose Noble's production function (see Problem) is as follows:
Q = 7 V - 0.5 V 2
where Q is the number of widgets produced per day and V is the number of production workers working an 8-hour day.
a. Develop a production schedule with V equaling 1 to 10.
b. Calculate average and marginal products.
c. Draw a graph.
d. Discuss the difference between the form of the production function in this problem and the form in Problem Discuss, among other things, the implications for the three stages of production.
The Noble Widget Corporation produces just one product, widgets. The company's new economist has calculated a short-run production function as follows:
Q = 7 V + 0.6 V 2 - 0.1 V 3
where Q is the number of widgets produced per day and V is the number of production workers working an 8-hour day.
a. Develop a production schedule with V equaling 1 to 10.
b. Calculate average and marginal products.
c. Draw a graph.
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Define the law of diminishing returns. Why is this law considered a short-run phenomenon
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