Deck 7: Technology and Production

Question 1

Suppose that a firm uses both labor (L)and capital (K)as inputs.The firm's long-run production function is Q = F(L,K)= 5√L√K.If the firm has 100 units of capital,what is its short-run production function?

A) Q = F(K) = 50√K
B) Q = F(L) = 500√L
C) Q = F(L,K) = 50√L√K
D) Q = F(L) = 50√L

Answer 1

Q = F(L) = 50√L

Question 2

A firm's _______ shows the amount of output a firm can produce from given amounts of inputs using efficient production methods.

A) production possibilities set
B) efficient production frontier
C) production function
D) production possibilities curve

Answer 2

production function

Question 3

In the short run:

A) the firm is free to change the amount of capital it uses.
B) all inputs are variable.
C) there are no variable inputs.
D) at least one input is fixed.

Answer 3

at least one input is fixed.

Question 4

The average product of labor is defined as:

A) the additional output produced by the last ∆L units of labor hired.
B) the amount of output divided by the amount of capital used to produce the output.
C) the amount of output produced multiplied by the last ∆L units of labor hired.
D) the amount of output divided by the number of workers employed.

Question 5

A firm's _______ contains all combinations of inputs and outputs that are possible given the firms' technology.

A) production possibilities set
B) efficient production frontier
C) production function
D) production possibilities curve

Question 6

As long as a firm can freely dispose of any extra inputs it may have:

A) its production function must slope downward.
B) its production function must be concave.
C) its production function must slope upward.
D) its production function must be convex.

Question 7

Suppose that a firm uses both labor (L)and capital (K)as inputs.The firm's long-run production function is Q = F(L,K)= 8√L√K.The firm has _____ units of capital.If the firm uses an efficient production method and hires _____ workers,it can produce _____ units of output.

A) 100; 100; 1,200
B) 100; 225; 800
C) 225; 100; 1,200
D) 225; 225; 1,000

Question 8

Which of the following is a short-run decision?

A) Because of an increase in enrollment, the economics department hires two new professors.
B) After a new classroom building is built, the economics department hires two new professors.
C) Your college builds a new classroom building.
D) The economics department buys new computers for the professors.

Question 9

Refer to Table 7.1.What is the average product of the 4^th worker?

A) 4 units of output
B) 3 units of output
C) 16 units of output
D) 6 units of output

Question 10

Suppose that a firm uses both labor (L)and capital (K)as inputs.The firm's long-run production function is Q = F(L,K)= 5√L√K.The firm has 100 units of capital.If the firm uses an efficient production method,how much output does it produce in the short run if it hires 25 workers?

A) 250 units
B) 1,250 units
C) 2,500 units
D) 50 units

Question 11

A firm's _______ contains all combinations of inputs and outputs that the firm can achieve using efficient production methods.

A) production possibilities set
B) efficient production frontier
C) production function
D) production possibilities curve

Question 12

Refer to Table 7.1.What is the average product of the 5^th worker?

A) 4.4 units of output
B) 1.17 units of output
C) 6 units of output
D) 17 units of output

Question 13

Refer to Table 7.1.What is the marginal product of the 3^rd worker?

A) 4 units of output
B) 3 units of output
C) 15 units of output
D) 5 units of output

Question 14

The long run refers to a period of time over which:

A) the firm can change its level of output.
B) only one input is fixed.
C) production technology increases.
D) all inputs are variable.

Question 15

The marginal product of labor is defined as:

A) the additional output produced by the last ∆L units of labor hired.
B) the amount of output divided by the amount of capital used to produce the output.
C) the amount of output produced multiplied by the last ∆L units of labor hired.
D) the amount of output divided by the number of workers employed.

Question 16

Refer to Table 7.1.What is the marginal product of the 6^th worker?

A) 1 unit of output
B) 6 units of output
C) 22 units of output
D) 23 units of output

Question 17

Suppose that a firm uses both labor (L)and capital (K)as inputs.The firm's long-run production function is Q = F(L,K)= 4√L√K.The firm has _____ units of capital.If the firm uses an efficient production method and hires _____ workers,it can produce _____ units of output.

A) 100; 100; 40,000
B) 100; 225; 90,000
C) 225; 100; 400
D) 225; 225; 900

Question 18

A firm's _______ summarizes all of its possible methods of producing its output.

A) production technology
B) efficient production frontier
C) production function
D) production possibilities curve

Question 19

Which of the following is the formula for the marginal product of labor?

A) F(L) - F(L - ∆L)
B) F(L)/L
C) F(L)/∆L
D) [F(L) - F(L - ∆L)]/∆L

Question 20

Refer to Table 7.1.Diminishing returns set in with the ______ worker.

A) third
B) fifth
C) fourth
D) sixth

Question 21

According to the Law of Diminishing Marginal Returns,as additional units of one input are employed as all other inputs are held constant,total output will eventually ______.

A) decrease
B) increase at an increasing rate
C) increase at a decreasing rate
D) increase at a constant rate

Question 22

If hiring one more worker causes the average product of labor to fall,then:

A) the marginal product of labor is less than the average product of labor.
B) the marginal product of labor is equal to the average product of labor.
C) the marginal product of labor is greater than the average product of labor.
D) the marginal product of labor is negative.

Question 23

Which of the following formulas represents the marginal rate of technical substitution of labor for capital?

A) MP_K/MP_L
B) -∆L/∆K
C) ∆K/∆L
D) MP_L/MP_K

Question 24

______ identifies all of the input combinations that efficiently produce a given amount of output.

A) A production function
B) An efficient production frontier
C) A production possibilities curve
D) An isoquant

Question 25

When labor inputs are finely divisible,the average product of labor curve is ______ sloping at L if the marginal product is ______ the average product.

A) downward; above
B) upward; above
C) upward; below
D) vertical; equal to

Question 26

Refer to Figure 7.3.The marginal rate of technical substitution for labor with capital at 120 workers is represented by the slope:

A) of line ac.
B) of line ed.
C) of line ab times negative one.
D) of line ed times negative one.

Question 27

The rate at which one input can be substituted for another is shown by:

A) the slope of a firm's production function.
B) the slope of a firm's efficient production frontier.
C) the slope of a firm's isoquants.
D) the shape of a firm's production function.

Question 28

Isoquants are the ______ created by the ______.

A) contour lines; production function
B) contour lines; efficient production frontier
C) tangent lines; production function
D) tangent lines; production possibilities curve

Question 29

When the marginal product of an input is ______ than the average product,the marginal units of the input _____ the average product.

A) larger; lower
B) smaller; raise
C) smaller; do not affect
D) larger; raise

Question 30

Which of the following formulas measures the rate of substitution for labor with capital?

A) -∆L/∆K
B) -∆K/∆L
C) ∆K/∆L
D) ∆L/∆K

Question 31

Refer to Figure 7.1.What is the marginal product of the 25^th worker?

A) 1.1 units of output
B) 22 units of output
C) 2 units of output
D) 10 units of output

Question 32

Which of the following is NOT a property of isoquants?

A) Isoquants curves are thin.
B) Isoquants may slope upward or downward.
C) Isoquants for the same technology never cross.
D) Higher-level isoquants lie farther from the origin.

Question 33

Refer to Figure 7.2.Curve A must be MP_L and Curve B must be AP_L because:

A) the two curves intersect at the maximum of Curve A.
B) everywhere that Curve A is positively-sloped, Curve B is positively-sloped as well, and everywhere that Curve A is negatively-sloped, Curve B is negatively-sloped as well.
C) when Curve A lies above Curve B, Curve B is rising, and when Curve A lies below Curve B, Curve B is falling.
D) when Curve B lies above Curve A, Curve A is rising, and when Curve B lies below Curve A, Curve A is falling.

Question 34

Refer to Figure 7.1.What is the average product of 20 workers?

A) 1.1 units of output
B) 22 units of output
C) 2 units of output
D) 8 units of output

Question 35

Which of the following is the formula for the average product of labor?

A) F(L) - F(L - ∆L)
B) F(L)/L
C) F(L)/∆L
D) [F(L) - F(L - ∆L)]/∆L

Question 36

______ are resources that are fully used up in the production process.

A) Materials
B) Capital inputs
C) Variable inputs
D) Fixed inputs

Question 37

Suppose a manager is deciding how to allocate workers between two plants.The marginal product of labor in plant 1 is 10 units of output.The marginal product of labor in plant 2 is 14 units of labor.What should the manager do?

A) Reallocate workers from plant 1 to plant 2, because MP_L is greater in plant 1 than in plant 2.
B) Reallocate workers from plant 1 to plant 2, because MP_L is greater in plant 2 than in plant 1.
C) Reallocate workers from plant 2 to plant 1, because MP_L is greater in plant 1 than in plant 2.
D) Reallocate workers from plant 2 to plant 1, because MP_L is greater in plant 1 than in plant 1.

Question 38

Refer to Figure 7.3.Suppose a firm moves along the isoquant from point a to point b.The rate of substitution for labor with capital is:

A) 2.
B) -2.
C) ½.
D) -½.

Question 39

Refer to Figure 7.2.Which of the following statements is true?

A) The curve labeled A represents the AP_L.
B) Curves A and B represent short-run production functions.
C) The curve labeled A represents the MP_L.
D) The curve labeled B represents the MP_L.

Question 40

Refer to Figure 7.2.With which worker does diminishing marginal returns set in?

A) The 20^th worker
B) The 30^th worker
C) The 38^th worker
D) The 50^th worker

Question 41

One reason that firms will experience decreasing returns to scale is:

A) the law of diminishing marginal returns.
B) the specialization of inputs as scale increases.
C) there is some fixed input that isn't being taken into consideration.
D) larger firms may be easier to manage effectively.

Question 42

With ______ returns to scale,production is most efficient if there is ______.

A) decreasing; a single producer
B) increasing; a large number of producers
C) constant; a single producer
D) increasing; a single producer

Question 43

Suppose a firm uses only capital and labor to produce output.When the firm doubles the amount of both inputs,output increases by less than double.This firm exhibits:

A) increasing returns to scale.
B) decreasing returns to scale.
C) constant returns to scale.
D) diminishing marginal returns.

Question 44

Refer to Figure 7.5.Which diagram represents isoquants for fixed-proportions technology?

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

Question 45

Refer to Figure 7.6.Which graph represents decreasing returns to scale?

A) A
B) B
C) C
D) Both graph A and graph C

Question 46

Refer to Figure 7.5.Which diagram represents isoquants for inputs that are perfect substitutes?

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

Question 47

Returns to scale is a ______ concept because ______.

A) short-run; it's related to the law of diminishing marginal returns
B) short-run; it deals with varying the level of one input while holding other inputs constant
C) long-run; a firm can change its output level only in the long run
D) long-run; it refers to changes in all of the firm's inputs

Question 48

For the Cobb-Douglas production function F(L,K)= AL^αK^β,a factor-neutral technical change would be represented by:

A) an increase in the value of α.
B) an increase in the value of β.
C) values of α and β for which α + β = 1.
D) an increase in the value of A.

Question 49

Refer to Figure 7.4.This isoquant exhibits:

A) increasing MRTS_LK as we move to the southeast along the isoquant.
B) declining MRTS_LK as we move to the northwest along the isoquant.
C) constant MRTS_LK as we move along the isoquant.
D) declining MRTS_LK as we move to the southeast along the isoquant.

Question 50

Consider the Cobb-Douglas production function F(L,K)= AL^αK^β.Which of the following statements is true?

A) Increases in α increase labor's productivity and raise MRTS_LK.
B) Decreases in α increase labor's productivity and raise MRTS_LK.
C) Increases in α increase labor's productivity and lower MRTS_LK.
D) Changes in α will not affect MRTS_LK.

Question 51

A firm has increasing returns to scale if:

A) a proportional change in the use of all inputs produces a more than proportional change in output.
B) a proportional change in the use of all inputs produces a less than proportional change in output.
C) a proportional change in the use of all inputs produces the same proportional change in output.
D) an increase in capital leads to an increase in output.

Question 52

Two inputs ______ when they must be combined in a fixed ratio.

A) are perfect substitutes
B) are perfect complements
C) represent Cobb-Douglas technology
D) are fixed inputs

Question 53

Suppose that the marginal product of a firm's labor is 10 units of output per hour.Also assume that the marginal product of the firm's capital is 30 units of output per hour.In this case,the marginal rate of technical substitution for labor with capital is:

A) 3.
B) 300.
C) 40.
D) 1/3.

Question 54

Suppose a firm uses 200 units of capital and 1,000 workers to produce 10,000 units of output.When the firm employs 3,000 workers and uses 600 units of capital,output increases to 45,000 units.This firm exhibits:

A) increasing returns to scale.
B) decreasing returns to scale.
C) constant returns to scale.
D) diminishing marginal returns.

Question 55

Refer to Figure 7.6.Which graph represents constant returns to scale?

A) A
B) B
C) C
D) Both graph A and graph C

Question 56

Refer to Figure 7.5.Which diagram represents isoquants for a Cobb-Douglas production function?

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

Question 57

Refer to Figure 7.6.Graph A represents:

A) increasing returns to scale.
B) decreasing returns to scale.
C) constant returns to scale.
D) diminishing marginal returns.

Question 58

Refer to Figure 7.7.A technological improvement is best represented by:

A) a movement from point a to point b.
B) a movement from point d to point a.
C) a movement from point c to point a.
D) a movement from point c to point d.

Question 59

The Cobb-Douglas production function F(L,K)= AL^αK^β will exhibit decreasing returns to scale when:

A) α + β = 1.
B) α + β < 1.
C) α + β > 1.
D) α + β = 0.

Question 60

One reason that firms will experience increasing returns to scale is:

A) the law of diminishing marginal returns.
B) the specialization of inputs as scale increases.
C) there is some fixed input that isn't being taken into consideration.
D) large firms may be difficult to manage effectively.

Question 61

Suppose a firm uses both labor (L)and capital (K)and its long-run production function is given by the expression Q = F(L,K)= 2L × √(L + K).The firm currently uses 10 units of capital.Complete the following table:

Question 62

For the Cobb-Douglas production function F(L,K)= AL^αK^β,a technical change that increases the productivity of capital would be represented by:

A) an increase in the value of α.
B) an increase in the value of β.
C) values of α and β for which β > α.
D) an increase in the value of A.

Question 63

Define decreasing returns to scale,illustrating your definition with isoquants.What are some reasons why firms might experience decreasing returns to scale?

Question 64

Consider the production function Q = F(L,K)= 5L²K².Does this technology have increasing,decreasing or constant returns to scale? Explain your answer in two different ways.

Question 65

Consider the Cobb-Douglas production function F(L,K)= AL^αK^β.Suppose that α = 2,β = 3,the firm has 3 units of capital and the firm's general productivity level is 20.
(a)What is the firm's long-run production function?
(b)What is the firm's short-run production function?
(c)If the firm employs 10 workers,what are the marginal products of labor and capital?
(d)If the firm employs 10 workers,what is the marginal rate of technical substitution for labor with capital?
(e)Does this firm's technology exhibit increasing,decreasing or constant returns to scale?

Question 66

The productivity changes resulting from research and development would be best represented by:

A) an upward shift of a firm's production function.
B) a downward shift of a firm's production function.
C) the firm's isoquants shifting away from the origin.
D) a movement to the northeast along the firm's production function.

Question 67

Suppose you manage a firm with two production plants.The marginal product of labor at plant 1 is MP₁ = 1400 - L₁ where L₁ is the number of workers employed in plant 1.The marginal product of labor at plant 2 is MP₂ = 2000 - L₂ where L₂ is the number of workers employed in plant 2.Given that you have 1,000 workers,what is the best allocation of workers between the two plants?

Question 68

Suppose a firm uses both labor (L)and capital (K)and its long-run production function is given by the expression Q = F(L,K)= L² × √(L + 2K).The firm currently uses 100 units of capital.Assuming labor is finely divisible,graph the firm's short-run production function for the first five workers.

Question 69

If technological change is factor neutral,then the firm's isoquants:

A) shift out away from the origin.
B) shift in toward the origin.
C) do not change in appearance.
D) become flatter.

Question 70

From 1970 to 1984,the productivity of the Lockeed Company increased as the company produced more airplanes.According to the text,Lockeed's experience can best be described as:

A) increasing returns to scale.
B) technological change.
C) learning-by-doing.
D) increasing marginal returns.

Question 71

Which of the following statements regarding comparisons of productivity across two firms is true?

A) The firm with the higher AP_L is the more productive firm.
B) The firm with the higher MP_L is the more productive firm.
C) The firm with the lower MP_L is the more productive firm.
D) The average product of labor can vary with the choice of inputs and the level of outputs, so the firm with the higher AP_L may not be the most productive.

Question 72

Using two carefully-labeled diagrams,explain how MP_L and AP_L can be derived from a firm's production function.In your answer,explain the relationship between average and marginal product.