Chapter 6- ECON 303

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The marginal product of labor in the production of computer chips is 50 chips per hour. The marginal rate of technical substitution ​(MRTS​) of hours of labor for hours of machine capital is 0.40. What is the marginal product of​ capital?

125 chips per hour

Refer to the figure at right. The situation pictured is one of

decreasing returns to​ scale, because doubling inputs results in less than double the amount of output.

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

When the average product is​ decreasing, the marginal product

is less than the average product.

A farmer uses L units of labor and K units of capital to produce Q units of corn using a production function F(K,L). A production plan that uses K'=L'=10 to produce Q' units of corn where Q' < F(10,10) is said to be

technically feasible and inefficient.

According to the law of diminishing returns

the marginal product of an input will eventually decline.

At point A, the marginal product of labor is

rising

Holding capital​ constant, when labor increases from 9 to 10​ units, output increases from 196 to 205 units. The marginal product of labor is ____ units, and when 10 units of labor are​ used, the average product of labor is ______ units.

9; 20.5

The marginal rate of technical substitution is equal to:

A and B only.

What is the difference between a production function and an​ isoquant?

A production function describes the maximum output that can be achieved with any given combination of inputs. An isoquant identifies all of the different combinations of inputs that can be used to produce one particular level of output.

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? What is the marginal product of labor?

AP = 5K MP = 5K

Technological improvement.

All of the above.

Which would not increase the productivity of labor?

An increase in the size of the labor force

Two isoquants, which represent different output levels but are derived from the same production function, cannot cross because

Both B and D are true.

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.

Does this production function exhibit​ increasing, decreasing, or constant returns to​ scale?

Constant returns to scale because a proportionate increase in all inputs results in the same proportionate increase in output.

I. Suppose a semiconductor chip factory uses a technology where the average product of labor is constant for all employment levels. This technology obeys the law of diminishing returns. II. Suppose a semiconductor chip factory uses a technology where the marginal product of labor rises, then is constant and finally falls as employment increases. This technology obeys the law of diminishing returns.

I is false and II is true

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.

I. Isoquants cannot cross one another. II. An isoquant that is twice the distance from the origin represents twice the level of output

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.

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).

Can an isoquant ever slope​ upward? Explain.

No. It would imply that adding more of both inputs keeps output constant.

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 point has the highest marginal productivity of labor?

Point D

Suppose there are ten identical manufacturing firms that produce computer chips with machinery (capital, K) and labor (L), and each firm has a production function of the form q = 10KL0.5. What is the industry-level production function?

Q = 100KL0.5

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 decreases the MPL and increases the MPK. Since the MRTS is the ratio of the former to the​ latter, it will diminish as this substitution occurs.

Can a firm have a production function that exhibits increasing returns to​ scale, constant returns to​ scale, and decreasing returns to scale as output​ increases? Discuss.

Yes. At low levels of​ output, specialization leads to increasing returns to scale. Once specialization has been​ exhausted, proportional increases in all inputs lead to constant returns to scale. And​ finally, for large scale​ operations, logistical and bureaucratic problems can lead to decreasing returns to scale.

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

a production function.

The short run is

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

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 (straight lines)

both B and C are correct.

An examination of the production isoquants in the figure at right reveals that (L shaped)

capital and labor will be used in fixed proportions.

Does this production function exhibit diminishing returns to​ labor? Explain. This production function exhibits

diminishing returns to labor because the additional output produced by each additional worker decreases.

Increasing returns to scale in production means

less than twice as much of all inputs are required to double output.

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

linear.

The slope of the total product curve is the

marginal product

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.

Which of the following production functions exhibits constant returns to​ scale?

q = K + L

The marginal rate of technical substitution is equal to the

ratio of the marginal products of the inputs.

We manufacture automobiles given the production function q = 5KL where q is the number of autos assembled per eight-hour shift, K is the number of robots used on the assembly line (capital) and L is the number of workers hired per hour (labor). If we use K=10 robots and L=10 workers in order to produce q = 450 autos per shift, then we know that production is:

technologically insufficient

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.

The law of diminishing returns applies to

the short run only

Why might you expect the marginal product of additional workers to diminish​ eventually? Eventually, as successive workers continue to be added to the production​ process,

they may no longer be able to specialize​, and output will increase at a diminishing rate.

Marginal product crosses the horizontal axis​ (is equal to​ zero) at the point where

total product is maximized.

You are currently using three printing presses and five employees to print 100 sales manuals per hour. If the MRTS at this point is 0.5 (capital is on the vertical axis of the isoquant map), then you would be willing to exchange ________ employees for one more printing press in order to maintain current output.

two

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.

The menu at Joe​'s coffee shop consists of a variety of coffee​ drinks, pastries, and sandwiches. The marginal product of an additional worker can be defined as the number of customers that can be served by that worker in a given time period. Joe has been employing one​ worker, but is considering hiring a second and a third. Explain why the marginal product of the second and third workers might be higher than the first. The marginal product of the second and third workers might be increasing because

workers can take advantage of existing machinery​, and output will increase at an increasing rate.

Explain intuitively what might cause the marginal product of labor to become negative. The marginal product of labor might become negative due to

workers getting in each other's way within the factory.

An L-shaped isoquant

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


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