HW 7
The marginal rate of technical substitution is equal to
. the absolute value of the slope of an isoquant. B. the ratio of the marginal products of the inputs.
The marginal product of labor in the production of computer chips is 8080 chips per hour. The marginal rate of technical substitution (MRTS ) of hours of labor for hours of machine capital is 0.100.10. What is the marginal product of capital?
800
An Isoquant
is a curve that shows all the combinations of inputs that yield the same total output.
The rate at which one input can be reduced per additional unit of the other input, while holding output constant, is measured by the
slope of the isocost curve
Can an isoquant ever slope upward? Explain.
No. It would imply that adding more of both inputs keeps output constant.
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 negative slopes
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
Increasing returns to scale in production means
less than twice as much of all inputs are required to double output.
A straight-line isoquant
would indicate that capital and labor are perfect substitutes in production.
When capital is plotted on the vertical axis and labor is plotted along the horizontal axis, the marginal rate of technical substitution (MRTS) of labor for capital along a convex isoquant
A. declines as more and more labor is used. B. equals the negative of the slope of the isoquant. C. equals the marginal product of labor divided by the marginal product of capital.
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
Give an example of a production process in which the short run involves a day or a week and the long run any period longer than a week.
Any process where it takes a week or longer to vary all inputs. Typically this would apply to a small business, such as a neighborhood restaurant or small retail store.
Use the following two statements to answer this question: I. "Decreasing returns to scale" and "diminishing returns to a factor of production" are two phrases that mean the same thing. II. Diminishing returns to all factors of production implies decreasing returns to scale.
Both I and II are false.
Which of the following examples represents a fixed-proportion production system with capital and labor inputs?
Clerical staff and computers. B. Horse-drawn carriages and carriage drivers. C. Airplanes and pilots
The figure at right shows an isoquant for the production of wheat. Which point has the highest marginal productivity of labor?
D
In a production process, all inputs are increased by 10%; but output increases less than 10%. This means that the firm experiences
DECREASING returns to scale
many mining and mineral extraction processes tend to exhibit increasing returns to scale. Suppose copper mines have increasing returns, and the existing copper mines reduce their capital and labor inputs by 25 percent in response to a global recession. What is the expected impact on copper output?
Output decreases by more than 25 percent.
MRTS
The MRTS gives the amount by which the quantity of one input can be reduced when one extra unit of another input is used, so that output remains constant.
Which of the following is NOT related to the slope of isoquants?
The fact that input prices are positive
It is possible to have diminishing marginal returns to a single factor of production and constant returns to scale at the same time. Discuss.
The statement is true. Diminishing marginal returns to a single factor applies to the short run when all other inputs are held fixed. On the other hand, returns to scales applies to the long run when all inputs can be increased.
Explain why the marginal rate of technical substitution is likely to diminish as more and more labor is substituted for capital.
The substitution of labor for capital increases the MPL and decreases the Mpk. Since the MRTS is the ratio of the latter to the former, it will diminish as this substitution occurs.
As we move downward along a typical isoquant, the slope of the isoquant
becomes flatter
An examination of the production isoquants in the figure to the right reveals that:
capital and labor are used in fixed proportions
The textbook discusses the carpet industry situated in the southeastern U.S., and the authors indicate that smaller carpet mills have __________ returns to scale while larger mills have ___________ returns to scale.
constant, increasing
If input prices are constant, a firm with increasing returns to scale can expect
costs to go up less than double as output doubles.
A production function in which the inputs are perfectly substitutable would have isoquants that are
linear
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.
If the isoquants are straight lines, then
the marginal rate of technical substitution of inputs is constant.
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.
An L-shaped isoquant
would indicate that capital and labor cannot be substituted for each other in production.
Does it make sense to consider the returns to scale of a production function in the short run?
No, we cannot change all of the production inputs in the short run.
