Econ midterm hw 7

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At a given level of labor​ employment, knowing the difference between the average product of labor and the marginal product of labor tells you

how increasing labor use alters the average product of labor.

You operate a car detailing business with a fixed amount of machinery​ (capital), but you have recently altered the number of workers that you employ per hour. As you increased the number of employees hired per hour from three to​ five, your total output increased by 5 cars to 15 cars per hour. What is the average product of labor at the new levels of​ labor?

AP​ = 3 cars per worker

Joe owns a coffee house and produces coffee drinks under the production​ function: q​ = 5KL where q is the number of cups generated per​ hour, K is the number of coffee machines​ (capital), and L is the number of employees hired per hour​ (labor). What is the average product of​ labor?

AP​ = 5K

Which of the following examples represents a​ fixed-proportion production system with capital and labor​ inputs?

Clerical staff and computers ​Horse-drawn carriages and carriage drivers Airplanes and pilots

Consider the following statements when answering this​ question: I. Whenever the marginal product of labor curve is a​ downward-sloping​ curve, the average product of labor curve is also a​ downward-sloping curve that lies above the marginal product of labor curve. II. If a firm uses only labor to​ produce, and the production function is given by a straight​ line, then the marginal product of labor always equals the average product of labor as labor employment expands.

I is​ false, and II is true.

Use the following two statements to answer this​ question: I. If the marginal product of labor is​ zero, the total product of labor is at its maximum. II. If the marginal product of labor is at its​ maximum, the average product of labor is falling.

I is​ true, and II is false.

You operate a car detailing business with a fixed amount of machinery​ (capital), but you have recently altered the number of workers that you employ per hour. Three employees can generate an average product of 4 cars per person in each​ hour, and five employees can generate an average product of 3 cars per person in each hour. What is the marginal product of labor as you increase the labor from three to five​ employees?

MP​ = 1.5 cars

What describes the graphical relationship between average product and marginal​ product?

Marginal product cuts average product from​ above, at the maximum point of average product.

For many​ firms, capital is the production input that is typically fixed in the short run. Which of the following firms would face the longest time required to adjust its capital​ inputs?

Nuclear power plant

Which of the following is NOT related to the slope of​ isoquants?

The fact that input prices are positive

The short run is

a time period in which at least one input is fixed.

If the law of diminishing marginal returns applies to​ labor, then

after some level of​ employment, the marginal product of labor must fall

If we take the production function and hold the level of output​ constant, allowing the amounts of capital and labor to​ vary, the curve that is traced out is called

an isoquant

Assume that average product for six workers is fifteen. If the marginal product of the seventh worker is​ eighteen,

average product is rising.

As we move downward along a typical​ isoquant, the slope of the isoquant

becomes flatter

An examination of the production isoquants in the figure at right reveals that

capital and labor will be used in fixed proportions.

Which of the following inputs is variable in the long​ run?

capital, equipment, plant size, and labor

If the isoquants in an isoquant map are downward sloping but bowed away from the origin​ (i.e., concave to the​ origin), then the production technology violates the assumption of

diminishing marginal returns.

an isoquant

is a curve that shows all the combinations of inputs that yield the same total output.

When the average product is​ decreasing, marginal product

is less than average product.

The function that shows combinations of inputs that yield the same output is called​ a(n)

isoquant curve

A firm uses two factors of production. Irrespective of how much of each factor is​ used, both factors always have positive marginal​ products, which imply that

isoquants have a negative slope

A production function in which the inputs are perfectly substitutable would have isoquants that are

linear.

The rate at which one input can be reduced per additional unit of the other​ input, while holding output​ constant, is measured by the

marginal rate of technical substitution.

A function that indicates the maximum output per unit of time that a firm can​ produce, for every combination of inputs with a given​ technology, is called

production function

Joe owns a small coffee​ shop, and his production function​ is: q​ = 3KL where q is total output in cups per​ hour, K is the number of coffee machines​ (capital), and L is the number of employees hired per hour​ (labor). If​ Joe's capital is currently fixed at K​ = 3​ machines, what is his​ short-run production​ function?

q=9L

If capital is measured on the vertical axis and labor is measured on the horizontal​ axis, the slope of an isoquant can be interpreted as the

rate at which the firm can replace capital with labor without changing the output rate.

The marginal rate of technical substitution is equal to the

ratio of the marginal products of the inputs.

A production function assumes a given

technology

The marginal product of an input is

the addition to total output due to the addition of the last unit of an​ input, holding all other inputs constant.

When labor usage is at 12​ units, output is 36 units. From​ this, we may infer that

the average product of labor is 3.

In a certain textile​ firm, labor is the only​ short-term variable input. The manager notices that the marginal product of labor is the same for each unit of​ labor, which implies that

the average product of labor is always equal to the marginal product of labor.

An examination of the production isoquants in the figure at right reveals that

the isoquants have a constant MRTS. and capital and labor are perfectly substitutable.

According to the law of diminishing returns

the marginal product of an input will eventually decline.

If the isoquants are straight​ lines, then

the marginal rate of technical substitution of inputs is constant.

The marginal rate of technical substitution is equal to

the ratio of the marginal products of the inputs. and the absolute value of the slope of an isoquant.

A​ firm's marginal product of labor is 4 and its marginal product of capital is 5. If the firm adds one unit of labor but does not want its output quantity to​ change, the firm should

use 0.8 fewer units of capital.

A​ straight-line isoquant

would indicate that capital and labor are perfect substitutes in production.

An​ L-shaped isoquant

would indicate that capital and labor cannot be substituted for each other in production.

The MRTS for isoquants in a​ fixed-proportion production function is

zero or undefined.

Writing total output as​ Q, change in output as Δ​Q, total labor employment as​ L, and change in labor employment as Δ​L, the marginal product of labor can be written algebraically as

ΔQ ​/ ΔL.

Joe owns a coffee house and produces coffee drinks under the production function q​ = 5KL where q is the number of cups generated per​ hour, K is the number of coffee machines​ (capital), and L is the number of employees hired per hour​ (labor). The average product of labor and the marginal product of labor are both equal to AP​ = MP​ = 5K. Does labor exhibit diminishing marginal returns in this​ case?

​No, the marginal product of labor is constant​ (for a given​ K).

A construction company builds roads with machinery​ (capital, K) and labor​ (L). If we plot the isoquants for the production function so that labor is on the horizontal​ axis, then a point on the isoquant with a small MRTS​ (in absolute​ value) is associated with high​ __________ use and low​ __________ use.

​labor; capital


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