Chapter 6 Production

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.

What is a production function? How does a long-run production function differ from a short-run production function?

A production function represents how inputs are transformed into outputs by a firm. In particular, a production function describes the maximum output that a firm can produce for each specified combination of inputs. In the short run, one or more factors of production cannot be changed, so a short-run production function tells us the maximum output that can be produced with different amounts of the variable inputs, holding fixed inputs constant. In the long-run production function, all inputs are variable.

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?

A) *AP = 3 cars per worker* B) AP = 5 cars per worker C) AP = 4 cars per worker D) We do not have enough information to answer this question.

Which would not increase the productivity of labor?

A) *An increase in the size of the labor force* B) An increase in the quality of capital C) An increase in the quantity of capital D) An increase in technology E) An increase in the efficiency of energy

Which of the following statements does not explain why US health care expenditures are higher than in other countries?

A) *Government policies have shifted the health care production function downward over time.* B) Consumer incomes have increased, which allows consumers to purchase more health care. C) The US health care system is relatively inefficient compared to other countries. D) Demand for health care in the US has increased, so health care production occurs at a higher point on the total product curve than in other countries.

Refer to Figure 6.2.1 above. At point A, the marginal product of labor is:

A) *rising.* B) at its minimum. C) at its maximum. D) diminishing.

A production function assumes a given:

A) *technology.* B) set of input prices. C) ratio of input prices. D) amount of capital and labor. E) amount of output.

The law of diminishing returns assumes that:

A) *there is at least one fixed input.* B) all inputs are changed by the same percentage. C) additional inputs are added in smaller and smaller increments. D) all inputs are held constant.

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?

A) AP = 5 B) *AP = 5K* C) AP = 5L D) AP = 5K/L

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

A) Average product cuts marginal product from above, at the maximum point of marginal product. B) Average product cuts marginal product from below, at the maximum point of marginal product. C) *Marginal product cuts average product from above, at the maximum point of average product.* D) Marginal product cuts average product from below, at the maximum point of average product. E) Average and marginal product do not intersect.

Use the following two statements to answer this question: I. Production functions describe what is technically feasible when the firm operates efficiently. II. The production function shows the least cost method of producing a given level of output.

A) Both I and II are true. B) *I is true, and II is false.* C) I is false, and II is true. D) Both I and II are false.

Use the following two statements to answer this question: I. The marginal product of labor is the slope of the line from the origin to the total product curve at that level of labor usage. II The average product of labor is the slope of the line that is tangent to the total product curve at that

A) Both I and II are true. B) I is true, and II is false. C) I is false, and II is true. D) *Both I and II are false.*

One of the factors contributing to the fact that labor productivity is higher in the U.S. than in the People's Republic of China is:

A) China's larger stock of capital. B) the higher capital/labor ratio in China. C) *the higher capital/labor ratio in the U.S.* D) China's smaller stock of fossil fuels. E) the fact that much labor in the U.S. is in management.

Which of the following equations based on capital (K) and labor (L) inputs does not represent a plausible production function?

A) F(K,L) = 3KL B) F(K,L) = 3K C) F(K,L) = K + L - 1 D) F(K,L) = 10(KL)^0.5

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?

A) Firm that makes DVD players B) Computer chip fabricator C) Flat-screen TV manufacturer D) *Nuclear power plant*

Consider the following statements when answering this question: 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.

A) I is true, and II is false. B) *I is false, and II is true.* C) Both I and II are true. D) Both I and II are false.

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.

A) I is true, and II is false. B) *I is false, and II is true.* C) Both I and II are true. D) Both I and II are false.

Which of the following inputs are variable in the long run?

A) Labor B) Capital and equipment C) Plant size D) *all of these*

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?

A) MP = 3 cars B) *MP = 1.5 cars* C) MP = 15 cars D) MP = -1 cars

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 marginal product of labor?

A) MP = 5 B) *MP = 5K* C) MP = 5L D) MP = 5K/L

Which of the following actions is NOT an example of the production coordination provided by firms?

A) Manage production activities of workers B) Pay wages to workers C) *Establish industry safety regulations* D) Set the production schedule for each week

Some economists conduct empirical research on the theory of the firm by measuring the degree of technical efficiency achieved by actual firms. What type of research contributions are provided by these studies?

A) Normative B) *Positive* C) Administrative D) Executive

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?

A) Q = 10K10^10L^5 B) *Q = 100KL^0.5* C) Q = 100L^0.5 D) none of the above

Which of the following ideas were central to the conclusions drawn by Thomas Malthus in his 1798 "Essay on the Principle of Population"?

A) Short-run time period B) Shortage of labor C) Law of diminishing resource availability D) *Law of diminishing returns*

As an economy recovers from a recession, the observed level of labor productivity tends to decline. Why?

A) The total product remains the same during the recovery, but the number of workers declines. B) The total product increases during the recovery, but the number of workers declines. C) *The marginal product of labor declines as new workers enter the expanding work force.* D) The marginal product of labor increases at a slower rate than the decline in employment.

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?

A) Yes, if capital also exhibits diminishing marginal returns. B) Yes, this is true for all values of K. C) *No, the marginal product of labor is constant (for a given K).* D) No, the marginal product of labor is increasing (for a given K).

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) an isoquant. B) a production possibility curve. C) *a production function.* D) an isocost function.

A production function defines the output that can be produced:

A) at the lowest cost, given the inputs available. B) for the average firm. C) *if the firm is technically efficient.* D) in a given time period if no additional inputs are hired. E) as technology changes over time.

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

A) average product is maximized. B) *total product is maximized.* C) diminishing returns set in. D) output per worker reaches a maximum. E) All of the above are true.

The slope of the total product curve is the:

A) average product. B) slope of a line from the origin to the point. C) *marginal product.* D) marginal rate of technical substitution.

Technological improvement:

A) can hide the presence of diminishing returns. B) can be shown as a shift in the total product curve. C) allows more output to be produced with the same combination of inputs. D) *All of the above are true.*

When the average product is decreasing, marginal product:

A) equals average product. B) is increasing. C) exceeds average product. D) is decreasing. E) *is less than average product.*

An important factor that contributes to labor productivity growth is:

A) growth in the capital stock. B) technological change. C) the standard of living. D) *A and B only* E) A, B, and C are correct.

The concerns about world food production raised by Malthus have not materialized because:

A) input prices have fallen over time. B) crop prices have risen over time. C) Malthus was wrong about the diminishing returns to labor in agriculture. D) *technological improvements have increased our ability to produce food over time.*

The short run is:

A) less than a year. B) three years. C) however long it takes to produce the planned output. D) *a time period in which at least one input is fixed.* E) a time period in which at least one set of outputs has been decided upon.

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

A) marginal product is rising. B) marginal product is falling. C) *average product is rising.* D) average product is falling.

For consideration of such issues as labor's productivity growth nationwide, the relevant measure is the:

A) marginal product of labor. B) *average product of labor.* C) total product of labor. D) wage. E) cost of capital.

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?

A) q = 3L B) q = 3L^2 C) *q = 9L* D) q = 3K^2

The Malthusian dilemma relates to marginal product in that:

A) starvation can be averted only if marginal product is constant. B) because of diminishing marginal product, the amount of food produced by each additional member of the population increases. C) *because of diminishing marginal product, the amount of food produced by each additional member of the population decreases.* D) because of diminishing marginal product, the wage falls as the population decreases. E) because of diminishing average product, the population will not have additional capital to work with.

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:

A) technically feasible and efficient. B) technically unfeasible and efficient. C) *technically feasible and inefficient.* D) technically unfeasible and inefficient. E) none of the above

We manufacturer 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:

A) technologically efficient. B) *technologically inefficient.* C) maximized. D) optimal.

The link between the productivity of labor and the standard of living is:

A) tenuous and changing. B) inverse. C) *that over the long run, consumers as a whole can increase their rate of consumption only by increasing labor productivity.* D) that over the long run, consumers' rate of consumption is not related to labor productivity. E) that the productivity of labor grows much more erratically than the standard of living.

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:

A) the average product of labor is always greater that the marginal product of labor. B) *the average product of labor is always equal to the marginal product of labor.* C) the average product of labor is always less than the marginal product of labor. D) as more labor is used, the average product of labor falls. E) there is no unambiguous relationship between labor's marginal and average products.

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

A) the marginal product of labor is 3. B) the total product of labor is 1/3. C) *the average product of labor is 3.* D) none of the above

If the law of diminishing returns applies to labor then:

A) the marginal product of labor must eventually become negative. B) the average product of labor must eventually become negative. C) the marginal product of labor must rise and then fall as employment rises. D) the average product of labor must rise and then fall as employment increases. E) *after some level of employment, the marginal product of labor must fall*

The law of diminishing returns can apply to:

A) the short run only. B) the long run only. C) *both the short and the long run.* D) neither the short nor the long run. E) all inputs, with no reference to the time period.

According to the law of diminishing returns:

A) the total product of an input will eventually be negative. B) the total product of an input will eventually decline. C) the marginal product of an input will eventually be negative. D) *the marginal product of an input will eventually decline.* E) none of the above

The marginal product of an input is:

A) total product divided by the amount of the input used to produce this amount of output. B) the addition to total output that adds nothing to total revenue. C) the addition to total output that adds nothing to profit. D) the addition to total output due to the addition of one unit of all other inputs. E) *the addition to total output due to the addition of the last unit of an input, holding all other inputs*

The law of diminishing returns refers to diminishing:

A) total returns. B) *marginal returns.* C) average returns. D) all of these.

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

A) whether increasing labor use raises output. B) whether increasing labor use changes the marginal product of labor. C) whether economies of scale exist. D) whether the law of diminishing returns applies. E) *how increasing labor use alters the average product of labor.*

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

A) ΔQ ∙ L. B) Q / L. C) ΔL / ΔQ. D) *ΔQ / ΔL.*

Explain why the marginal rate of technical substitution is likely to diminish as more and more labor is substituted for capital.

As more and more labor is substituted for capital, it becomes increasingly difficult for labor to perform the jobs previously done by capital. Therefore, more units of labor will be required to replace each unit of capital, and the MRTS will diminish. For example, think of employing more and more farm labor while reducing the number of tractor hours used. At first you would stop using tractors for simpler tasks such as driving around the farm to examine and repair fences or to remove rocks and fallen tree limbs from fields. But eventually, as the number or labor hours increased and the number of tractor hours declined, you would have to plant and harvest your crops primarily by hand. This would take huge numbers of additional workers.

Isoquants can be convex, linear, or L-shaped. What does each of these shapes tell you about the nature of the production function? What does each of these shapes tell you about the MRTS?

Convex isoquants indicate that some units of one input can be substituted for a unit of the other input while maintaining output at the same level. In this case, the MRTS is diminishing as we move down along the isoquant. This tells us that it becomes more and more difficult to substitute one input for the other while keeping output unchanged. Linear isoquants imply that the slope, or the MRTS, is constant. This means that the same number of units of one input can always be exchanged for a unit of the other input holding output constant. The inputs are perfect substitutes in this case. L-shaped isoquants imply that the inputs are perfect complements, and the firm is producing under a fixed proportions type of technology. In this case the firm cannot give up one input in exchange for the other and still maintain the same level of output. For example, the firm may require exactly 4 units of capital for each unit of labor, in which case one input cannot be substituted for the other.

Is it possible to have diminishing returns to a single factor of production and constant returns to scale at the same time? Discuss.

Diminishing returns and returns to scale are completely different concepts, so it is quite possible to have both diminishing returns to, say, labor and constant returns to scale. Diminishing returns to a single factor occurs because all other inputs are fixed. Thus, as more and more of the variable factor is used, the additions to output eventually become smaller and smaller because there are no increases in the other factors. The concept of returns to scale, on the other hand, deals with the increase in output when all factors are increased by the same proportion. While each factor by itself exhibits diminishing returns, output may more than double, less than double, or exactly double when all the factors are doubled. The distinction again is that with returns to scale, all inputs are increased in the same proportion and no inputs are fixed. The production function in Exercise 10 is an example of a function with diminishing returns to each factor and constant returns to scale.

You are an employer seeking to fill a vacant position on an assembly line. Are you more concerned with the average product of labor or the marginal product of labor for the last person hired? If you observe that your average product is just beginning to decline, should you hire any more workers? What does this situation imply about the marginal product of your last worker hired?

In filling a vacant position, you should be concerned with the marginal product of the last worker hired, because the marginal product measures the effect on output, or total product, of hiring another worker. This in turn determines the additional revenue generated by hiring another worker, which should then be compared to the cost of hiring the additional worker. The point at which the average product begins to decline is the point where average product is equal to marginal product. As more workers are used beyond this point, both average product and marginal product decline. However, marginal product is still positive, so total product continues to increase. Thus, it may still be profitable to hire another worker.

Explain the term "marginal rate of technical substitution." What does a MRTS = 4 mean?

MRTS is the amount by which the quantity of one input can be reduced when the other input is increased by one unit, while maintaining the same level of output. If the MRTS is 4 then one input can be reduced by 4 units as the other is increased by one unit, and output will remain the same.

Can an isoquant ever slope upward? Explain.

No. An upward sloping isoquant would mean that if you increased both inputs output would stay the same. This would occur only if one of the inputs reduced output; sort of like a bad in consumer theory. As a general rule, if the firm has more of all inputs it can produce more output

Why is the marginal product of labor likely to increase initially in the short run as more of the variable input is hired?

The marginal product of labor is likely to increase initially because when there are more workers, each is able to specialize in an aspect of the production process in which he or she is particularly skilled. For example, think of the typical fast food restaurant. If there is only one worker, he will need to prepare the burgers, fries, and sodas, as well as take the orders. Only so many customers can be served in an hour. With two or three workers, each is able to specialize, and the marginal product (number of customers served per hour) is likely to increase as we move from one to two to three workers. Eventually, there will be enough workers and there will be no more gains from specialization. At this point, the marginal product will begin to diminish.

Why does production eventually experience diminishing marginal returns to labor in the short run?

The marginal product of labor will eventually diminish because there will be at least one fixed factor of production, such as capital. As more and more labor is used along with a fixed amount of capital, there is less and less capital for each worker to use, and the productivity of additional workers necessarily declines. Think for example of an office where there are only three computers. As more and more employees try to share the computers, the marginal product of each additional employee will diminish.

Faced with constantly changing conditions, why would a firm ever keep any factors fixed? What criteria determine whether a factor is fixed or variable?

Whether a factor is fixed or variable depends on the time horizon under consideration: all factors are fixed in the very short run while all factors are variable in the long run. As stated in the text, "All fixed inputs in the short run represent outcomes of previous long-run decisions based on estimates of what a firm could profitably produce and sell." Some factors are fixed in the short run, whether the firm likes it or not, simply because it takes time to adjust the levels of those inputs. For example, a lease on a building may legally bind the firm, some employees may have contracts that must be upheld, or construction of a new facility may take a year or more. Recall that the short run is not defined as a specific number of months or years but as that period of time during which some inputs cannot be changed for reasons such as those given above

Suppose that output q is a function of a single input, labor (L). Describe the returns to scale associated with each of the following production functions:

a. q = L/2. Let q′ be output when labor is doubled to 2L. Then q′ = (2L)/2 = L. Compare q′ to q by dividing q′ by q. This gives us q′/q = L/(L/2) = 2. Therefore when the amount of labor is doubled, output is also doubled. Hence there are constant returns to scale. b. q = L2 + L. Again, let q′ be output when labor is doubled. q′ = (2L)2 + 2L = 4L2 + 2L. Dividing by q yields q′/q = (4L2 + 2L)/(L2 + L) > 2. To see why this ratio is greater than two, note that it would be exactly two if q′ were to equal 2L2 + 2L, but q′ is larger than that, so the ratio is greater than two, indicating increasing returns to scale. c. q = log(L). In this case, q′ = log(2L) = log(2) + log(L), using the rules for logarithms. Then q′/q = [log(2) + log(L)]/log(L) = log(2)/log(L) + 1. This expression is greater than, equal to or less than 2 when L is less than, equal to or greater than 2. So this production function exhibits increasing returns to scale when L < 2, constant returns to scale when L = 2, and decreasing returns to scale