Rensselaer Polytechnic Institute - ACCT ACCT 3371

CHAPTER 4

A Model of Production

MULTIPLE-CHOICE

1)A model is a representation of

                  world that we use to study economic phenomena.

1. 1. false; a toy
   2. mathematical; a toy
   3. accurate; the real
   4. mathematical; the real
   5. accurate; a toy

.

2. The text uses this analogy of the economic model: “As the model-builder,      what actions the robots

d. a set of equations

e. the actual macroeconomy

.

3. Mathematically, an economic model is      .
   1. a fake world
   2. a spreadsheet
   3. an accurate representation of reality

.

4. Consider an economy where the only consumption good is ice cream; firms in this economy must
   1. hire all workers and rent all machines available.
   2. choose how many workers to hire and ice cream machines to rent.
   3. choose how many workers to hire and rent all machines available.
   4. hire all workers and choose how many machines to rent.
   5. none of the above.

.

5. Models simplify              of decisions into just a few equations.
   1. tens
   2. hundreds
   3. millions
   4. dozens
   5. thousands

.

6. The following equation is an example of      .

Y = F(K, L) = A±K^aL^{1 – a}

1. 1. a consumption function
   2. a utility function
   3. a production function
   4. the production possibilities frontier
   5. a growth model

.

7. The following equation is an example of      .

Y = F(K, L) = AK±1/3L^2/3

1. 1. a growth model
   2. a utility function
   3. a consumption function
   4. the production possibilities frontier
   5. a production function

.

8. In the equation Y = F(K, L) = A±K^1/3L^2/3, the “bar” over the A means that it is
   1. a parameter that is fixed or exogenous.
   2. a variable that is fixed or exogenous.
   3. a parameter that is variable or exogenous.
   4. a variable that is endogenous.
   5. a and b are correct.

.

9. In the equation Y = F(K, L) = A±K¹±/3L^2/3, the “bars” over the A and K mean that these variables are
   1. parameters that are fixed or exogenous.
   2. variables that are fixed or exogenous.
   3. parameters that are endogenous.
   4. variables that are endogenous.
   5. a and b are correct.

.

10. In the equation Y = F(K, L) = A±K¹±/3L^2/3, the lack of a “bar” over the L means that it is
    1. an exogenous variable.
    2. an endogenous variable.
    3. a parameter.
    4. Both b and c are correct.
    5. None of the above is correct.

.

11. The two main inputs we consider in a simple production function are
    1. land and labor.
    2. capital and land.
    3. capital and labor.
    4. utilities and capital.
    5. natural resources and labor.

.

12. Which of the following inputs do we generally not

consider in a simple production function?

1. 1. capital
   2. labor
   3. natural resources
   4. utilities
   5. Both c and d.

.

13. In the production function Y = F(K, L) = A±K¹±/3L^2/3, A±

represents

1. 1. an unknown.
   2. the amount of capital in an economy.
   3. the amount of labor in an economy.
   4. a productivity parameter.
   5. None of the above.

.

14. Consider two economies. If each country has the same production function and the same amount of capital and labor, the country that     produces more.
    1. is less productive
    2. is more productive
    3. has more natural resources
    4. has lower costs of production
    5. has more workers

.

15. Consider two countries, labeled 1 and 2. If each has the production function

Y = A_i±K±1/3L^2/3, i = 1, 2

the only difference between the two countries is that A₁ > A₂.

1. 1. Country 2 will not produce anything, ceteris paribus.
   2. Country 2 will produce more than Country 1, ceteris paribus.
   3. Country 1 will produce more than Country 2, ceteris paribus.
   4. Each will produce the same amount, ceteris paribus.
   5. Not enough information is given.

.

16. The production function Y = K^1/3L^2/3 describes
    1. how any amount of capital and labor can be combined to generate output.
    2. how particular amounts of capital and labor can be combined to generate output.
    3. how any amount of capital and a particular amount of labor can be combined to generate output.
    4. how any amount of labor and a particular amount of capital can be combined to generate output.
    5. None of the above.

.

17. The production function Y = A±K¹±/3L^2/3 describes
    1. how particular amounts of capital and labor can be combined to generate output.
    2. how any amount of capital and labor can be combined to generate output.
    3. how any amount of capital and a particular amount of labor can be combined to generate output.
    4. how any amount of labor and a particular amount of capital can be combined to generate output.
    5. None of the above.

.

18. The production function Y = AK±1±/3L^2/3 describes
    1. how any amount of labor and a particular amount of capital can be combined to generate output.
    2. how particular amounts of capital and labor can be combined to generate output.
    3. how any amount of capital and labor can be combined to generate output.

1. 4. how any amount of capital and a particular amount of labor can be combined to generate output.
   5. None of the above.

.

19. The equation Y = K^aL^{1 – a} is called
    1. the Lucas production function.
    2. the Keynesian production function.
    3. the Marxian production function.
    4. the Cobb-Douglas production function.
    5. None of the above.

.

20. One of the key characteristics of the Cobb-Douglas production function is
    1. increasing returns to scale.
    2. decreasing returns to scale.
    3. constant returns to scale.
    4. that it compacts all inputs into a single equation.
    5. that it is an exact replication of a firm’s production function.

.

21. A production function exhibits constant returns to scale if,
    1. when you hold inputs constant, you double the output.
    2. when you double each input, you more than double the output.
    3. when you double each input, you less than double the output.
    4. when you double one input, you double the output.
    5. when you double each input, you double the output.

.

22. A production function exhibits increasing returns to scale if,
    1. when you double one input, you double the output.
    2. when you double each input, you double the output.
    3. when you double each input, you less than double the output.
    4. when you double each input, you more than double the output.
    5. when you hold inputs constant, you double the output.

.

23. A production function exhibits decreasing returns to scale if,
    1. when you double each input, you double the output.
    2. when you double each input, you more than double the output.
    3. when you double each input, you less than double the output.
    4. when you double one input, you double the output.
    5. when you hold inputs constant, you double the output.

.

24. Which of the following production functions exhibits constant returns to scale?
    1. Y = K^aL^{1 – a}

b. Y = K1/3L2/3

c. Y = K0.1L0.9

d. Y = K1/4L3/4

e. All of the above.

.

25. Which of the following production functions exhibits increasing returns to scale?

a. Y = K1/2L1/2

b. Y = K^aL^{1 – a}

c. Y = K1/3L2/3

d. Y = K1/2L3/4

e. All of the above.

.

26. Which of the following production functions exhibits constant returns to scale?
    1. Y = K^2/3

b. Y = K1/3L1/3

c. Y = K^aL^{1 – a}

d. Y = K1/4L1/2

e. All of the above.

.

27. If the production function is given by Y = A±K^1/3L^2/3 and

A±= 1 and K = L = 8, total output equals

1. 1. Y = 2.
   2. Y = 6.

c. Y = 14.

d. Y = 8.

e. None of the above.

.

28. If the production function is given by Y = A±K^1/3L^2/3 and

A±= 1, K = 27, and L = 8, total output equals

1. 1. Y = 1.

b. Y = 18.

c. Y = 12.

d. Y = 8.

e. None of the above.

.

29. The firm’s profit maximization problem is
    1. max ? ? F(r? w) ? rK ? wL.

{r? w}

1. 2. max Π = rK + wL − F(K, L).

{K , L}

1. 3. max Π = F(K, L) − rK − wL.

{r, w}

1. 4. max Π = F(K, L) − rK − wL.

{K , L}

1. 5. All of the above are correct.

.

30. A firm’s profit is simply defined as
    1. zero.
    2. revenues plus costs.
    3. revenues minus costs.
    4. the price of output minus labor costs.
    5. the price of output minus labor costs minus capital costs.

.

31. The solution to the firm’s maximization problem is
    1. how much capital and labor to hire given the rental rate of capital and labor’s wage rate.
    2. how much capital and labor to hire given the rental rate of capital only.
    3. how much capital to hire given the rental rate of capital.
    4. how much capital and labor to hire regardless of the rental rate of capital and labor’s wage rate.
    5. how much labor to hire given labor’s wage rate.

.

32. The marginal product of labor is defined as
    1. output divided by labor.
    2. the additional output generated by hiring an additional unit of labor.
    3. the additional output generated by hiring an additional unit of labor and capital.
    4. the additional output generated by hiring an additional unit of capital.
    5. the additional revenue generated by hiring an additional unit of labor.

.

33. The law of diminishing marginal product to capital means that as we add additional units of capital
    1. and labor, output will increase but at a constant rate.
    2. and labor, output will increase but at a decreasing rate.
    3. but hold labor constant, output will increase but at an increasing rate.
    4. but hold labor constant, output will increase but at a constant rate.
    5. but hold labor constant, output will increase but at a decreasing rate.

.

34. Consider Figure 4.1. The shape of this production function suggests
    1. not enough information is given.
    2. a diminishing marginal product of labor.
    3. a constant marginal product of capital.
    4. an increasing marginal product of capital.
    5. a diminishing marginal product of capital.

.

Figure 4.1: Production Function

Y

K

35. Consider Figure 4.2. The shape of this production function suggests
    1. a constant marginal product of capital.
    2. a diminishing marginal product of capital.
    3. a diminishing marginal product of labor.
    4. an increasing marginal product of capital.
    5. not enough information is given.

.

Figure 4.2: The Production Function

Y

L

36. Consider Figure 4.3. The shape of this production function suggests
    1. a diminishing marginal product of capital.
    2. a constant marginal product of capital.
    3. a diminishing marginal product of labor.
    4. an increasing marginal product of capital.
    5. not enough information is given.

.

Figure 4.3: The Production Function

Y

K

37. The solution to the firm’s profit maximization is
    1. MPL = w.
    2. MPL = w and MPK = r.
    3. MPL < w and MPK = r.
    4. MPL = w and MPK = 0.
    5. MPL > w and MPK = r.

.

38. With a Cobb-Douglas production function Y = K^1/3L^2/3, the marginal product of capital is                  and the marginal product of labor is    .

a. MPK = (1/3)(Y/K); MPL = (2/3)(Y/L)

b. MPK = (2/3)(Y/K); MPL = (1/3)(Y/L)

c. MPK = (2/3)(Y/K); MPL = (2/3)(Y/L)

d. MPK = (1/3)(Y/K); MPL = (1/3)(Y/L)

e. None of the above is correct.

.

39. If MPK > r, the firm
    1. should hire more labor.
    2. should hire more capital until MPK = 0.
    3. should get rid of some capital until MPK = r.
    4. should hire more capital until MPK = r.
    5. has the optimal amount of capital.

.

40. If MPK = r, the firm
    1. should hire more labor.
    2. should hire more capital until MPK= r.
    3. should hire more capital until MPK = 0.
    4. should get rid of some capital until MPK = r.
    5. has the optimal amount of capital.

.

41. If MPL < w, the firm
    1. has the optimal amount of labor.
    2. should fire some labor until MPL = w.
    3. should fire some labor until MPL = 0.
    4. should hire more capital until MPK = 0.
    5. should hire more capital until MPL = w.

.

42. The marginal product of labor curve represents
    1. the demand for wages.
    2. the supply of labor.
    3. the demand for labor.

1. 4. the demand for capital.
   5. the supply of wages.

.

43. The equation MPK = r* yields
    1. the amount of capital in an economy.
    2. the optimal amount of capital, K*, a firm fires.
    3. the optimal amount of capital, K*, a firm hires.
    4. the quantity of capital a firm wants to hire at any

rental rate of capital.

1. 5. None of the above.

.

44. In Figure 4.4, MPL represents the         , L±represents the                  , and the intersection of the two yields                    .
    1. labor supply; labor demand; the equilibrium wage
    2. labor demand; labor supply; the equilibrium wage
    3. labor supply; labor demand; the equilibrium rental rate of capital
    4. labor demand; labor supply; the amount of capital hired
    5. None of the above is correct.

.

Figure 4.4: Labor Market

LABOR

45. If K = K±and L = L,±then output is determined by
    1. the total amount of labor in an economy.
    2. the total amount of capital in an economy.
    3. the total amount of capital and labor available in an economy.
    4. a percentage of capital and labor in an economy.
    5. Not enough information is given.

.

46. The marginal product of labor is measured in
    1. dollars.
    2. units of output.
    3. units of output per dollar.
    4. units of capital per dollar.
    5. units of labor per dollar.

.

47. In the Cobb-Douglas production function Y = K^aL^{1 – a}, the a represents
    1. total income.
    2. the share of production contributed by labor.
    3. the total amount of capital in an economy.
    4. the total demand for capital in an economy.
    5. the share of production contributed by capital.

.

48. In the Cobb-Douglas production function Y = K^aL^{1 – a}, if a = 1/3, then
    1. labor’s share of GDP is two-thirds.
    2. labor’s share of GDP is one-third.
    3. capital’s share of GDP is one-third.
    4. capital’s share of income is one.
    5. both a and c are correct.

.

49. In the Cobb-Douglas production function Y = K^1/3L^2/3, labor’s share of GDP is     .
    1. two-thirds regardless of how much labor there is
    2. two-thirds but can change as more laborers are added
    3. one-third regardless of how much labor there is
    4. always equal to one
    5. Not enough information is given.

.

50. In the Cobb-Douglas production function Y = K^aL^{1 – a}, if a = 1/4, then
    1. capital’s share of GDP is one-fourth.
    2. labor’s share of GDP is three-fourths.
    3. capital’s share of GDP is three-fourths.
    4. labor’s share of income is one-fourth.
    5. both a and b are correct.

.

51. Suppose the payments to capital and labor are (w*L*)/Y* = 2/3 and (r*L*)/Y* = 1/3, respectively. One implication of this result is

a. (w*L*/r*K*) = Y*.

b. w*L* – r*K* = Y*.

c. w*L* × r*K* = Y*.

d. w*L* + r*K* = Y*.

e. (w*L*/Y*)(r*K*/Y*) = 0.

.

52. Suppose the payments to capital and labor are (w*L*)/Y* = 2/3 and (r*L*)/Y* = 2/3, respectively.

One implication of this result is

a. w*L* + r*K* < Y*.

b. w*L* + r*K* = Y*.

c. w*L* + r*K* > Y*.

d. (w*L*/r*K*) = Y*.

e. (w*L*/Y*)(r*K*/Y*) = 1.

.

53. Suppose the payments to capital and labor are (w*L*)/Y* = 2/3 and (r*L*)/Y* = 1/3, respectively. One implication of this result is that  and profits are     .
    1. w*L* + r*K* = Y*; positive
    2. w*L* + r*K* = Y*; equal to zero
    3. w*L* + r*K* = Y*; negative
    4. (w*L* – r*K*) = Y*; equal to zero
    5. (w*L*/Y*)(r*K*/Y*) = 0; negative

.

54. In the Cobb-Douglas production function Y = AK±aL^{1 –a}, defining y = Y/L as output per person and k = K/L as capital per person, the per person production function is
    1. y = A±k^–a.
    2. y = A±k^a.
    3. y = A±k^{1 – a}.
    4. y = A/±k^{1 – a}.
    5. None of the above.

.

55. In the Cobb-Douglas production function Y = AK±1/3L^2/3, defining y = Y/L as output per person and k = K/L as capital per person, the per person production function is

a.   y = A±/k^2/3.

b.   y = A±k^–1/3.

c.   y = A±k^2/3.

d.  y = A±k^1/3.

e. None of the above.

.

56. In the Cobb-Douglas production function Y = A±K^1/4L^3/4, defining y = Y/L as output per person and k = K/L

as capital per person, the per person production function is

a.   y = Ak±3/4.

b.   y = Ak±–1/4.

c.   y = A±k^1/4.

d.  y = A/±k^3/4.

e. None of the above.

.

57. The equation y = A±k^1/3 has two important implications:
    1. Output per person tends to be higher when (1) the productivity parameter is higher, and (2) the amount of capital per person is higher.
    2. Output per person tends to be lower when (1) the productivity parameter is higher, and (2) the amount of capital per person is higher.
    3. Output per person tends to be higher when (1) the productivity parameter is lower, and (2) the amount of capital per person is higher.
    4. Output per person tends to be higher when (1) the productivity parameter is higher, and (2) the amount of capital per person is lower.
    5. Output tends to be higher when (1) the productivity parameter is higher, and (2) the amount of capital per person is higher.

.

58. Consider Table 4.1, which compares the model y = k±1/3 to actual statistical data on per capita GDP. You observe
    1. the model consistently underestimates the level of per capita GDP.
    2. the model consistently overestimates the level of per capita GDP.
    3. the model does a really good job of estimating the level of per capita GDP.
    4. the model clearly contains all factors that affect per capita GDP.
    5. None of the above.

.

Table 4.1: Model’s Prediction for Per Capita GDP

59. One explanation for the difference between the predicted output per person and the observed per capita GDP in Table 4.1 is
    1. differences in per capita capital.
    2. differences in the labor supply.
    3. differences in factor productivity.
    4. differences in labor’s share of GDP.
    5. None of the above.

.

60. One explanation for the difference between the predicted output per person and the observed per capita GDP in Table 4.1 is
    1. differences in the labor supply.
    2. differences in human capital.
    3. differences in per capita capital.
    4. differences in capital’s share of GDP.
    5. None of the above.

61. As a measure for total factor productivity, we can use the quantity of         in an economy.
    1. computers
    2. factories
    3. machines
    4. All of the above.
    5. None of the above.

.

62. In the equation y = A±k^1/3, A±represents
    1. total factor productivity.
    2. physical capital.
    3. natural resources.
    4. All of the above.
    5. None of the above.

.

63. Differences in output across economies with the same per capita capital stock can be explained by
    1. differences in labor.
    2. differences in total factor productivity.
    3. similarities in total factor productivity.
    4. differences in physical capital.
    5. similarities in physical capital.

.

64. You are an economist working for the International Monetary Fund. Your boss wants to know what is the total factor productivity of China, but all you have is data on per capita GDP, y, and the per capita capital stock, k. If you assume that capital’s share of GDP is one-third, what would you use to find total factor productivity?

b. A = y × k^1/3

c.  A = k1/3

e. None of the above.

.

65. You are an economist working for the International Monetary Fund. Your boss wants to know what is the total factor productivity of India, but all you have is data on per capita GDP, y, and the per capita capital stock, k. If you assume that capital’s share of GDP is one-fourth, what would you use to find total factor productivity?

66. As an economist working at the International Monetary Fund, you are given the following data for Burundi: observed per capita GDP, relative to the United States, is 0.016; predicted per capita GDP, given by y = k^1/3, is

0.19. What is total factor productivity? a. 0.003

b. 12.04

c. 0.083

d. 0.44

e. 0.25

.

67. As an economist working at the International Monetary Fund, you are given the following data for Burundi: predicted per capita GDP, relative to the United States, is given by y = k^1/3, is 0.19, and total factor productivity is 0.083. What is the observed per capita GDP, relative to the United States?

a. 2.28

b. 0.016

c. 0.87

d. 0.44

e. 0.62

.

68. Consider the three production functions in Figure 4.5. Each represents a different country. For any given per capita stock of physical capital, Country          has the highest total factor productivity.
    1. A
    2. B
    3. C
    4. Not enough information is given.
    5. None of the above,

.

Figure 4.5: Production Function

b. A = y × k^1/4

e. None of the above.

.

k

69. Consider the two production functions in Figure 4.6, representing two countries. Which of the following is true?

1. At points a and b, each country has the same per

72. Suppose the total factor productivity in Switzerland, Italy, South Africa, and India are 0.72, 0.69, 0.44, and 0.23, respectively. If the U.S. total factor productivity is 1.00, then the United States is

capita capital stock but different factor productivity.                    productive, respectively, than these four

2. Points a and c represent the same country but with different factor productivity.
3. Points b and d represent the same country but with different stock of per capita capital.

1. i and iii
2. i only
3. ii only
4. iii only
5. i and ii

.

Figure 4.6: Production Function

k

71. Consider the two production functions in Figure 4.6, representing two countries. Which of the following is not true?
    1. At points a and b, each country has the same per capita capital stock but different factor productivity.
    2. Points a and c represent different countries but with the same factor productivity.
    3. Points b and d represent the same country but with different stock of per capita capital.

1. ii only
2. i only
3. iii only
4. i and ii
5. i and iii

countries.

1. equally as
2. 28 percent, 31 percent, 56 percent, and 73 percent less
3. 28 percent, 31 percent, 56 percent, and 73 percent more
4. 72 percent, 69 percent, 44 percent, and 23 percent more
5. 72 percent, 69 percent, 44 percent, and 23 percent less

.

73. As a rough approximation, differences in capital per person explain about of the difference in incomes between the richest and poorest countries, while differences in     explain           .
    1. one-third; wages; two-thirds
    2. one-third; total factor productivity; two-thirds
    3. one-third; total factor productivity; one-third
    4. one-third; returns to capital; two-thirds
    5. two-thirds; total factor productivity; one-third

.

74. In the year 2000, the five richest countries had a per capita GDP                times higher than the five poorest countries. Differences in capital per worker explain about                  percent of this difference, with total factor productivity making up about     percent of this difference.

a. 10; 2; 10

b. 45; 10; 4.5

c. 35; 3.5; 10

d. 35; 10; 3.5

e. 45; 4.5; 10

.

75. To decompose what explains difference in per capita GDP between any two countries, say, 1 and 2, we would use

3. the share of labor in GDP
4. the stock of capital
5. All of the above.

y∗    A

? k  ?1/3  

.

b.

∗         ?? k

2 ??

80. In the United States, the average number of years of

c.    ¹  =?   1 ?   .

1. 1. 13 years.
   2. 9 years.

y∗    A

2 ??

? k

?1/3  

1. 3. 17 years.
   4. 12 years.

d.     ¹  =     ¹ ÷?     1 ?   .

1. 5. 14 years.

2 ??

2    ? A2 ?

.

76. Which of the following does not explain differences in total factor productivity?
    1. institutions
    2. the labor stock
    3. human capital
    4. natural resources
    5. technology

.

77. Which of the following explain differences in total factor productivity?
    1. institutions
    2. human capital
    3. natural resources
    4. technology
    5. All of the above.

.

78. Which of the following explain differences in total factor productivity?
    1. institutions
    2. human capital
    3. infrastructure
    4. All of the above.
    5. None of the above.

.

79. Which of the following do not explain differences in total factor productivity?
    1. the labor stock
    2. the share of capital in GDP

.

81. In the poorest countries in the world, the average number of years of education for adults over the age of 25 is about
    1. 4 years.
    2. 1 year.
    3. 6 years.
    4. 12 years.
    5. 9 years.

.

82. In the United States, each year of education increases a worker’s wage by about       per year.
    1. 7 percent
    2. 1 percent
    3. 4 percent
    4. 10 percent
    5. None of the above.

.

83. Which of the following are examples of technology?
    1. just-in-time inventory
    2. computer chips
    3. improved irrigation
    4. the Internet
    5. All of the above.

.

84. Both the United States and France, among the richest countries in the world, have similar levels of education and capital per worker, but the U.S. citizens enjoy higher incomes than the French. One explanation might be differences in
    1. war.
    2. institutions.
    3. infrastructure.

1. 4. population size.
   5. labor income shares.

.

85. Which of the following are essential for economic success?
    1. property rights
    2. the rule of law
    3. contract enforcement
    4. the separation of powers
    5. All of the above.

.

TRUE/FALSE—EXPLAIN

1. Exogenous variables are predetermined by the model builder.

2. In the production function Y = F(K, L) = A±K±1/3L^2/3, A±

represents a productivity parameter.

3. The two main inputs we consider in our production function model are labor and land.
4. A production function of the form Y = K^aL^{1 – a} is called the Cobb-Douglas production function.

5. A production function of the form Y = K^aL^{1 – a} exhibits constant returns to scale.

6. The production function of the form Y = K^1/3L^1/3
7. The production function of the form Y = K^1/3L^2/3

8. If the production function is Y = K^1/3L^2/3,, then in per worker terms, it can be written as y = K^1/3/L.
9. After the Black Death in the fourteenth century, wages in Europe were higher than before the Black Death.

10. If the marginal product of labor equals the wages, firms should hire more workers.

11. If the marginal product of capital equals the rental rate of capital, firms should not hire any more capital.

12. Consider two countries, A and B. If each country produces using identical production functions, but y_A > y_B and k_A = k_B, the total factor productivity of country A equals that of B.
13. Consider two countries A and B. If each country produces using identical production functions, but y_A = y_B and k_A = k_B, the total factor productivity of country A equals that of B.

14. If the U.S. total factor productivity is 1.00 and China’s is 0.45, then the U.S. capital per worker is 65 percent more productive than China’s.

15. One explanation of differences in total factor productivity is differences in labor’s share of GDP.

Possible explanations are differences in education, technology, infrastructure, and institutions.