Economics

Paul A. Samuelson, William D. Nordhaus

Chapter 6

Production and Business Organization - all with Video Answers

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Chapter Questions

Problem 1

Explain the concept of a production function. Describe the production function for hamburgers, computers, concerts, haircuts, and a college education.

Nick Johnson

Nick Johnson

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Problem 2

Consider a production function of the following form:
$X=100 L^{4},$ where $X=$ output and $L=$ input of labor (assuming other inputs are fixed).
a. Construct a figure like Figure $6-1$ and a table like Table $6-1$ for inputs of $L=0,1,2,3,$ and 4.
b. Explain whether this production function shows diminishing returns to labor. What values would the exponent need to take for this production function to exhibit increasing returns to labor?

Kaylee Mcclellan

Kaylee Mcclellan

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Problem 3

The following table describes the actual production function for oil pipelines. Fill in the missing values for marginal products and average products:
(TABLE CANNOT COPY)

Oluwadamilola Ameobi

Oluwadamilola Ameobi

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Problem 4

Using the data in question $3,$ plot the production function of output against horsepower. On the same graph, plot the curves for average product and marginal product.

Natalie Britton

Natalie Britton

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Problem 5

Suppose you are running the food concession at the athletic events for your college. You sell hot dogs, colas, and potato chips. What are your inputs of capital, labor, and materials? If the demand for hot dogs declines, what steps could you take to reduce output in the short run? In the long run?

Marcus Esteban

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Problem 6

An important distinction in economics is between shifts of the production function and movements along the production function. For the food concession in question $5,$ give an example of both a shift of and a movement along the hot-dog production function. Illustrate each with a graph of the relation between hot-dog production and labor employed.

Md.Daniyal Arshad

Md.Daniyal Arshad

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Problem 7

Substitution occurs when firms replace one input for another, as when a farmer uses tractors rather than labor when wages rise. Consider the following changes in a firm's behavior. Which represent substitution of one factor for another with an unchanged technology, and which represent technological change? Illustrate each with a graphical production function.
a. When the price of oil increases, a firm replaces an oil-fired plant with a gas-fired plant.
b. A bookseller reduces its sales staff by 60 percent after it sets up an Internet outlet.
c. Over the period $1970-2000,$ a typesetting firm decreases its employment of typesetters by 200 workers and increases its employment of computer operators by 100 workers.
d. After a successful unionization drive for clerical workers, a college buys personal computers for its faculty and reduces its secretarial workforce.

John Lee

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Problem 8

Consider a firm that produces pizzas with capital and labor inputs. Define and contrast diminishing returns and decreasing returns to scale. Explain why it is possible to have diminishing returns for one input and constant returns to scale for both inputs.

Md.Daniyal Arshad

Md.Daniyal Arshad

Numerade Educator

Problem 9

Show that if the marginal product is always decreasing, the average product is always above the marginal product.

Md.Daniyal Arshad

Md.Daniyal Arshad

Numerade Educator

Problem 10

Review the example of a network shown in Figure $6-4$ Assume that only one person can join the network each month, starting with Adam and proceeding clockwise.
a. Construct a table showing the value to the joining person as well as the external value to others (i.e., the value to all others in the network) when an additional person joins. (Hint: The entries for Ed are $\$ 4 \text { and } \$ 4 .)$ Then calculate the total social value for each level of membership. Graph the relationship between the size of the network and the total social value. Explain why this shows increasing returns rather than diminishing returns.
b. Assume that the cost of joining is $\$ 4.50 .$ Draw a graph which shows how membership changes over time if six people are in the network to begin with. Draw another one which shows what happens if there are initially three people in the network. What is the point at which the equilibrium "tips" toward universal membership?
c. Suppose you are the sponsor of the network shown in Figure $6-4 .$ What kind of pricing could you use to get the network started when there are only one or two members?

Oluwadamilola Ameobi

Oluwadamilola Ameobi

Numerade Educator