Econ midterm hw 7
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 ΔQ, total labor employment as L, and change in labor employment as ΔL, 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
