Deck 6: Producer Behavior

Question 1

(Figure: Capital and Labor XVI) Consider the production function Q = L^0.5K^0.5, with MP_K = L^0.5/K^0.5 and MP_L = K^0.5/L^0.5. The slope of the isoquant at Point A is ____.

A) -81
B) 81
C) -9
D) 9

Answer 1

A

Question 2

Which of the following statements is (are) TRUE?
I) If labor and capital are perfect substitutes in production, the isoquant is a downward-sloping line.
II) If a company needs to use inputs in fixed proportion such that the capital to labor ratio is always 2, the firm's isoquants are L-shaped.
III) If the production function is given by Q = min(14, 7), the firm can produce, at minimum, 21 units of output.

A) I, II, and III
B) I
C) II
D) I and II

Answer 2

D

Question 3

(Table: Capital and Labor XIV) Consider the production function that this table shows. Suppose the firm is using 3 units of capital and 2 units of labor and then decides to employ a third worker. The marginal product of the third worker is ____.

A) 49.33
B) 40.24
C) 31.78
D) 26.79

Answer 3

B

Question 4

(Figure: Capital and Labor VI) Suppose a firm spends $4,000 per day producing a good. The wage rate per worker is $200 per day and rental rate per unit of capital is $500 per day. The firm's isocost line at the current expenditure level is represented by:

A) C₁.
B) C₂.
C) C₃.
D) C₄.

Question 5

For the production function Q(K,L) = 3K + 2L, the marginal rate of technical substitution MRTS_LK is:

A) 2/3.
B) 3/2.
C) 2L/3K.
D) 3K/2L.

Question 6

(Table: Short-run Production I) The short-run production situation for a firm is listed on this table. The marginal product of labor with one unit of labor is ____.

A) 50
B) 40
C) 30
D) 20

Question 7

(Table: Capital and Labor XIV) Consider the production function that this table shows. Suppose the firm is using 2 units of capital and 1 unit of labor. The marginal product of capital for K = 3 is ____.

A) 41.42
B) 40.24
C) 31.78
D) 26.79

Question 8

(Figure: Production Function I) Which of the following statements is (are) TRUE? I. At L = 5, MPT_L > AP_L.
II) At L = 2, MP_L = AP_L.
III) For this production function, MP_L is greater at L = 2 than at L = 8.
IV) For this production function, MP_L is always greater than AP_L.

A) I and II
B) III
C) I and IV
D) II

Question 9

(Table: Capital and Labor XIV) Consider the production function that this table shows. Suppose the firm is using 3 units of capital and 1 unit of labor. The marginal product of capital for K = 4 is ____.

A) 41.42
B) 40.24
C) 31.78
D) 26.79

Question 10

(Figure: Capital and Labor XII) Which of the following statements is (are) TRUE?
I) Panel a illustrates constant returns to scale.
II) Panel b illustrates decreasing returns to scale.
III) Panel a illustrates increasing returns to scale
IV) Panel b illustrates constant returns to scale.

A) I and IV
B) II and III
C) III and IV
D) I and III

Question 11

Capital cannot be adjusted in the short run because:

A) there is not sufficient time to adjust it.
B) it is too expensive to alter the capital stock.
C) capital markets do not function well enough in the short run.
D) the firm has yet to decide what product to produce, so it does not yet know what kind of capital it needs.

Question 12

(Table: Capital and Labor XIV) Consider the production function that this table shows. With 4 units of labor and 2 units of capital, the level of output is ____.

A) 263.9
B) 246.23
C) 219.46
D) 186.61

Question 13

(Table: Capital and Labor II) Which of the following statements is (are) TRUE? I. A combination of 4 units of capital and 2 units of labor produces the same amount of output as a combination of 3 units of capital and 3 units of labor.
II) If labor is fixed at 3 units, adding more capital increases output at an increasing rate.
III) If capital is fixed at 2 units, adding more labor results in diminishing returns.
IV) A combination of 3 units of capital and 4 units of labor produces 171.4 units of output.

A) I, II, III, and IV
B) II, III, and IV
C) III and IV
D) IV

Question 14

(Table: Short-run Production I) The short-run production situation for a firm is listed on this table. The total output with two units of labor is ____.

A) 80
B) 40
C) 30
D) 20

Question 15

Suppose that a community health center finds that, regardless of the number of physicians or nurse practitioners employed, it can always replace one family practice physician by using two additional nurse practitioners without affecting the quantity or quality of patient office visits. This finding implies that:

A) physicians and nurse practitioners are perfect substitutes in production.
B) physicians and nurse practitioners are perfect complements in production.
C) diminishing returns will occur as the health center hires more nurse practitioners.
D) the marginal product of physicians will increase by two with every nurse practitioner hired.

Question 16

Suppose the production function for a car manufacturer is:
Q = 2K²L²
Where Q is the number of cars produced, K is the number of machine hours used, and L is the number of worker hours used. The function for the marginal product of labor is ____.

A) 4K²L
B) 4KL²
C) 4KL
D) KL^-1

Question 17

Suppose the production function for a coffee shop is:
Q = 2K + 5L
Where Q is the number of cups of coffee produced, K is the number of coffee makers, and L is the number of workers. The function for the marginal product of labor is ____.

A) 5
B) 2.5
C) 2
D) 0.4

Question 18

Suppose the production function for a bakery is:
Q = 4K^0.4L^0.6
Where Q is the number of loaves of bread produced per day, K is the number of ovens, and L is the number of workers employed. The function for the marginal rate of technical substitution is ____.

A) 2.4K^0.4L^-0.4
B) 1.6K^-0.6L0^.6
C) KL
D) (3/2)KL^-1

Question 19

Suppose the production function for a car manufacturer is:
Q = 2K²L²
Where Q is the number of cars produced, K is the number of machine hours used, and L is the number of worker hours used. The function for the marginal rate of technical substitution is ____.

A) 4K²L
B) 4KL²
C) 4KL
D) KL^-1

Question 20

Suppose a firm is producing 2,475 units of output by hiring 50 workers (W = $20 per hour) and 25 units of capital (R = $10 per hour). The marginal product of labor and marginal product of capital are 40 and 25, respectively. Is the firm minimizing the cost of producing 2,475 units of output?

A) Yes, the ratio of the number of workers to the wage equals the ratio of the number of units of capital to the rental rate.
B) No, the firm should use more labor and less capital.
C) No, the firm should use more capital and less labor.
D) No, the firm should use more of both labor and capital.

Question 21

(Figure: Capital and Labor XI) Which of the following statements is (are) TRUE? I. If labor is cheaper than capital, the firm will produce at point B.
II) If capital is more expensive than labor, the firm will produce at point A.
III) At point A, the MRTS_LK = W/R.

A) II and III
B) III
C) I and III
D) I and II

Question 22

(Table: Short-run Production I) The short-run production situation for a firm is listed on this table. The marginal product of labor of the second unit of labor is ____.

A) 50
B) 40
C) 30
D) 20

Question 23

(Figure: Capital and Labor VIII) The movement in the isocost line is caused by a(n):

A) increase in the rental rate of capital.
B) decrease in the rental rate of capital.
C) decrease in the wage rate.
D) increase in the wage rate.

Question 24

(Table: Short-run Production I) The short-run production situation for a firm is listed on this table. The average product of labor with one unit of labor is ____.

A) 50
B) 40
C) 30
D) 20

Question 25

(Figure: Capital and Labor XVI) Consider the production function Q = L^0.5K^0.5, with MP_K = L^0.5/K^0.5 and MP_L = K^0.5/L^0.5. When K = 5 and L = 10, the marginal rate of technical substitution is ____.

A) 2
B) 1
C) 0.5
D) 0.25

Question 26

(Figure: Production Function I) The average product at L = 2 and L = 8, respectively, are:

A) 2 and 1.13.
B) 2 and 0.89.
C) 8 and 72.
D) 1.5 and 1.13.

Question 27

(Table: Short-run Production I) The short-run production situation for a firm is listed on this table. The average product of labor when there are three units of labor is ____.

A) 50
B) 40
C) 33.33
D) 30

Question 28

In the long run, because firms can adjust both capital and labor:

A) firms will grow.
B) production is more expensive because firms must invest in both labor and capital.
C) the impact of diminishing marginal returns is lessened.
D) firms fire workers, replacing the labor productivity with capital.

Question 29

Suppose the firm's production function is Q = K^1/3L^2/3, where the MPK = and MP_L =
)
If the rental rate of capital R is $35 and the wage rate W is $70, how many units of labor and capital should the firm use to produce 12 units of output?

A) L = 18; K = 9
B) L = 9; K = 18
C) L = 12; K = 12
D) L = 24; K = 24

Question 30

(Figure: Capital and Labor XVI) Consider the production function Q = L^0.5K^0.5, with MP_K = L^0.5/K^0.5 and MP_L = K^0.5/L^0.5. The slope of the isoquant at Point B is ____.

A) -9
B) 9
C) -1
D) 1

Question 31

Suppose that a farmer grows corn. The farmer's production function is Q(K,L) = 5K^0.4L^0.6, where K is the number of harvesters and L is the number of farmworker labor hours. The prevailing wage rate is $8 per hour and the rental rate associated with harvesters is $75. The farmer has a goal of delivering 100,000 bushels of corn to market. What Lagrangian equation can be used to solve the farmer's cost minimization problem?

A)
B)
C)
D)

Question 32

In the short run, the marginal product of labor:

A) is always diminishing.
B) will eventually fall.
C) continues to increase as long as the firm adds labor slowly.
D) always increases because laborers become more efficient with experience.

Question 33

Suppose the production function for a coffee shop is:
Q = 2K + 5L
Where Q is the number of cups of coffee produced, K is the number of coffee makers, and L is the number of workers. The function for the marginal product of capital is ____.

A) 5
B) 2.5
C) 2
D) 0.4

Question 34

If a firm is using a lot of capital and just a little labor, the marginal product of labor is_____ relative to the marginal product of capital making it _____ to substitute labor for capital.

A) low; more difficult
B) high; easier
C) high; more difficult
D) low; easier

Question 35

The production function for laser eye surgery is given by Q = 20K^0.5L^0.5, where Q is the number of laser eye surgeries performed per day, K is the number of eye surgery machines (which is fixed at 2 in the short run), and L is the number of employees. The average product of labor for L = 9 is ____.

A) 28.28
B) 11.71
C) 9.43
D) 7.07

Question 36

For the production function Q(K,L) = 3K + 2L, the marginal product of labor is:

A) 2.
B) 3.
C) 2L.
D) 3K.

Question 37

(Figure: Capital and Labor IX) The movement in the isocost line is caused by a(n):

A) decrease in the wage rate.
B) increase in the wage rate or rental rate of capital.
C) increase in the wage rate.
D) decrease in the rental rate of capital.

Question 38

Suppose that a firm's production function is . The marginal rate of technical substitution is ____.

A) 0.5KL
B) KL
C) 2KL^-1
D) 0.5KL^-1

Question 39

Suppose that a firm's production function is given by Q = 1.23KL (MP_K = 1.23L and MP_L = 1.23K), where Q is quantity of output, K is units of capital, and L is units of labor. The price per unit of labor and capital are $30 and $20, respectively. The minimum cost of producing 600 units of output is $____.

A) 2,160
B) 1,080
C) 960
D) 580

Question 40

For the production function Q(K,L) = K^0.5L^0.5, the marginal rate of technical substitution MRTS_LK is:

A) 0.25K/L.
B) 0.25L/K.
C) K/L.
D) L/K.

Question 41

Production is an extremely complicated task, so economists make a number of simplifying assumptions. Which of the following assumptions do economists make in their basic model of producer behavior?
​
I) Multiproduct firms: All firms produce at least two goods.
II) Firms only use two inputs in the production process: capital and labor.
III) Cost minimization: Firms attempt to produce a fixed quantity of output at the lowest possible total cost.
IV) Firms can produce more output by using more inputs.

A) I and IV
B) I, II, III, and IV
C) II, III, and IV
D) I and III

Question 42

Suppose the production function for a bakery is:
Q = 4K^0.4L^0.6
Where Q is the number of loaves of bread produced per day, K is the number of ovens, and L is the number of workers employed. The function for the marginal product of capital is ____.

A) 2.4K^0.4L^-0.4
B) 1.6K^-0.6L0^.6
C) KL
D) (3/2)KL^-1

Question 43

(Table: Short-run Production I) The short-run production situation for a firm is listed on this table. The average product of labor when there are four units of labor is ____.

A) 50
B) 40
C) 33.33
D) 27.5

Question 44

To calculate the firm's expansion path using calculus, we need to solve its:

A) quantity maximization problem.
B) cost minimization problem, with rental cost of capital R and wage W treated as variables.
C) cost minimization problem with quantity Q fixed.
D) cost minimization problem with quantity Q treated as variable.

Question 45

Brenda's Pastry employs three workers who produce 6 dozen pastries per hour. After Brenda hires a fourth worker, the number of pastries produced increases to 7 dozen per hour. Because the marginal product of the fourth worker is _____ than the average product of three workers, the average product must _____.

A) greater; fall
B) less; rise
C) greater; rise
D) less; fall

Question 46

The production function for laser eye surgery is given by Q = 20K^0.5L^0.5, where Q is the number of laser eye surgeries performed per day, K is the number of eye surgery machines (which is fixed at 2 in the short run), and L is the number of employees. The average product of labor for L = 16 is ____.

A) 40
B) 13.33
C) 9.43
D) 7.07

Question 47

The production function given by Q = 10(0.7K² + 0.3L²)^0.5 has _____ returns to scale.

A) constant
B) instant
C) increasing
D) decreasing

Question 48

Which situation will likely give rise to diminishing marginal product of labor?

A) Plasma television manufacturers are going out of business because of increased competition from LCD televisions.
B) Hell's Kitchen, which has enough counter space for three cooks per shift, decides to hire a fourth cook per shift.
C) Nevaeh's Kitchen undertakes a massive expansion, doubling both the size of its kitchen and number of cooks.
D) A landscaping firm replaces all of its self-propelled lawnmowers with push mowers.

Question 49

Suppose a firm's short-run production function is given by Q = 16L^0.8. What is the marginal product of the fourth worker?

A) 36
B) 10
C) 49
D) 1.85

Question 50

Which of the following statements is (are) TRUE, assuming the firm is choosing the optimal bundle of inputs that minimizes the cost of producing a given quantity of output?
​
I) The marginal product per dollar spent on labor equals the marginal product per dollar spent on capital.
II) AP_L = APK
III)
IV) MP_L × W = MP_K × R
​

A) I and II
B) I, II, III, and IV
C) IV
D) I and III

Question 51

(Table: Capital and Labor II) This table illustrates a _____ production function because capital and labor _____.

A) short-run; are used in equal increments
B) long-run; can both be varied
C) long-run; are used in equal increments
D) short-run; can both be varied

Question 52

The production function for laser eye surgery is given by Q = 20K^0.5L^0.5, where Q is the number of laser eye surgeries performed per day, K is the number of eye surgery machines (which is fixed at 2 in the short run), and L is the number of employees. The marginal product of labor for L = 2 is ____.

A) 28.28
B) 11.71
C) 9.43
D) 8.99

Question 53

(Figure: Production Function V) Refer to the production function, which has a slope of 1/L^0.5. The marginal product of labor for L = 1, assuming that labor is infinitely divisible, is ____.

A) 1
B) 0.705
C) 0.577
D) 0.5

Question 54

Which of the following is a Cobb-Douglas production function?

A) Q = f(K, L)
B) Q = 5K + 2.5L
C) Q = K^0.50L^0.75
D) Q = 2K/3L

Question 55

(Figure: Production Function V) Refer to the production function, which has a slope of 1/L^0.5. The average product of labor for L = 2 is ____.

A) 1
B) 0.705
C) 0.577
D) 0.5

Question 56

Suppose that a hot dog vendor uses a cart (K) and his time (L) to make and sell hot dogs. The vendor's production function is , where Q is the number of hot dogs per day. Suppose that the rental on hot dog carts is $50 per day and that the vendor wants to produce 500 hot dogs per day. The demand for labor is ____.

A) L = 1,020.4W^-0.3
B) L = 1,020.4W^-0.7
C) W = 1,020.4L^-0.3
D) L = 1,020.4W^0.3

Question 57

Between 1994 and 2008, the share of the workforce employed in manufacturing _____ and manufacturing output _____.

A) decreased; decreased
B) increased; increased
C) decreased; increased
D) increased; decreased

Question 58

Suppose a firm with a production function given by Q = 4K^0.25L^0.75 produces 100 units of output. The firm pays a wage of $30 per units and pays a rental rate of capital of $10 per unit.
(Note:
)
The minimum cost of producing 100 units of output is:

A) $3,000.
B) $2,250.
C) $800.
D) $1,000.

Question 59

(Table: Production Process I) Diminishing marginal returns to labor occur in production process _____, and diminishing marginal returns to capital occur in production process _____.

A) 1; 3
B) 2; 1
C) 2; 3
D) 1; 1

Question 60

(Table: Capital and Labor I) Which of the following statements is (are) TRUE?

A) At L = 1, marginal product is greater than average product.
B) At L = 3, the quantity of output produced per unit of labor is 82.2.
C) The additional output produced by using the second unit of labor is 86.6.
D) At L = 2, the AP_L = L/Q = 186.6.

Question 61

Suppose the production function for a bakery is:
Q = 4K^0.4L^0.6
Where Q is the number of loaves of bread produced per day, K is the number of ovens, and L is the number of workers employed. The function for the marginal product of labor is ____.

A) 2.4K^0.4L^-0.4
B) 1.6K^-0.6L0^.6
C) KL
D) (3/2)KL^-1

Question 62

MRTS_LK decreases as the firm substitutes labor for capital along the isoquant for all production functions below EXCEPT:

A) .
B) .
C) .
D) .

Question 63

(Table: Short-run Production I) The short-run production situation for a firm is listed on this table. The total output when there are four units of labor is ____.

A) 120
B) 110
C) 100
D) 90

Question 64

(Figure: Capital and Labor V) Put these four panels in order from the easiest case of input substitutability to the hardest case of input substitutability.

A) b, a, c, d
B) a, c, d, b
C) d, c, a, b
D) a, d, c, b

Question 65

Which of the following statements violates the basic assumptions of isoquants?

A) Isoquants cannot cross.
B) Isoquants closer to the origin correspond to lower output levels.
C) Diminishing marginal products imply that isoquants are concave to the origin.
D) Isoquants show all combinations of two inputs that can produce a particular quantity of output.

Question 66

A donut shop has a production function given by Q = 50K^1/3L^1/2, where Q is the number of donuts produced per hour, K is the number of donut fryers (which is fixed at eight in the short run), and L is the number of employed workers. How many donuts can be produced per hour with four workers in the short run?

A) 200
B) 167
C) 320
D) 84

Question 67

A basic assumption of the long run is that a firm:

A) cannot change the amount of labor or capital that it employs.
B) can change the amount of labor and capital that it employs.
C) can change the amount of capital that it employs but not the amount of labor.
D) cannot change the amount of capital that it employs but can change the amount of labor.

Question 68

Which of the following statements best exemplifies the firm's constrained minimization problem?

A) The firm desires to produce a given quantity of output by choosing values of W and R that minimize RK + WL.
B) The firm desires to minimize output subject to the constraint that C = RK + WL.
C) The firm desires to produce as much output as possible by choosing values of L and K that minimize RK + WL.
D) The firm desires to produce a given quantity of output by choosing values of L and K that minimize RK + WL.

Question 69

Suppose the production function for a car manufacturer is:
Q = 2K²L²
Where Q is the number of cars produced, K is the number of machine hours used, and L is the number of worker hours used. The function for the marginal product of capital is ____.

A) 4K²L
B) 4KL²
C) 4KL
D) KL^-1

Question 70

Suppose the slope of a short-run production function is given by 2/L^0.5. Which of the following statements is (are) TRUE?
​
I) The marginal product of the fifth worker is 0.20.
II) The production function exhibits increasing marginal returns.
III) The marginal product of the sixteenth worker is 0.50.
IV) The production function's slope eventually changes from positive to negative as the firm produces more and more.

A) II and III
B) I and IV
C) III
D) I, II, and IV

Question 71

A basic assumption of the short run is that a firm:

A) can employ more workers and add more capital to the production process.
B) cannot adjust its workforce or the amount of capital it uses.
C) can reduce the number of workers it uses, but it cannot adjust how much capital it uses.
D) can freely adjust the amount of labor and capital that it employs.

Question 72

Suppose the production function for a bakery is:
Q = 4K^0.4L^0.6
Where Q is the number of loaves of bread produced per day, K is the number of ovens, and L is the number of workers employed. Suppose that the wage rate is $5 per hour and the rental rate of capital is $10 per hour. The firm's expansion path is ____.

A) K = 0.5L
B) K = L
C) K = 2L
D) K = L²

Question 73

Which of the following is (are) example(s) of production functions?
I) Q = 56K + 18L
II) Q = 2K^0.8L^0.2
III) Q = KL

A) II and III
B) I, II, and III
C) II
D) I

Question 74

Solving for the value of the Lagrange multiplier in the firm's cost minimization problem tells us:

A) average cost.
B) total cost.
C) marginal cost.
D) variable cost.

Question 75

(Figure: Capital and Labor IV) Which of the following statements is (are) TRUE? I. More output is produced at point A than at point B.
II) The ratio of the marginal product of labor to the marginal product of capital is higher at point A than at point B.
III) The MRTS_LK is equal at points A and B.

A) I, II, and III
B) II
C) III
D) II and III

Question 76

Using a Lagrangian equation for a firm's cost minimization problem, you can solve for all of the following EXCEPT:

A) the optimal level of labor input.
B) the average cost of production.
C) the demand function for capital.
D) the equation for the expansion path.

Question 77

(Figure: Production Function II) Which of the following statements are TRUE? I. This production function exhibits diminishing marginal product.
II) At L = 3, MP_L = 1.88 and AP_L = 4.
III) At L = 6, AP_L > MP_L.
IV) At L = 3, MP_L = 4 and AP_L = 1.88.

A) II and III
B) I, II, and III
C) I, III, and IV
D) I and II

Question 78

(Figure: Capital and Labor X) Which of the following statements is (are) TRUE? I. The firm minimizes the cost of producing 10,000 units of output at point C.
II) If the firm chooses an input combination that lies on C₃, the firm will be able to produce 10,000 units of output at a lower cost than at point A.
III) The cost of producing 10,000 units of output is greater at point B than at point A.

A) I and III
B) II and III
C) I
D) I, II, and III

Question 79

Why are the slopes of isocost lines constant?

A) Firms must use capital and labor inputs in fixed proportions.
B) Firms can hire as much of an input as they desire without changing wages or rental rates.
C) Firms must use less labor if employing more capital.
D) The marginal rate of technical substitution of labor for capital is constant.

Question 80

Suppose that a firm's production function is given by Q = KL (MP_K = L and MP_L = K), where Q is quantity of output, K is units of capital, and L is units of labor. The price per unit of labor and capital are $30 and $20, respectively. How many units of labor and capital should the firm use if it wants to minimize the cost of producing 600 units of output?

A) L = 20; K = 30
B) L = 30; K = 20
C) L = 40; K = 60
D) L = 25; K = 25