Chapter 6- ECON 303
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.
