University of California, Santa Cruz - ECON 100B

CHAPTER 4: A Model of Production

MULTIPLE CHOICE

1)A model is a(n)                        representation of               world that we use to study economic phenomena.

1. 1. false; a toy                                               d. mathematical; the real
   2. mathematical; a toy                                  e.   accurate; a toy
   3. accurate; the real

2. The text uses this analogy of the economic model: “As the model-builder,         what actions the robots can take and                         the raw materials that fill the robot world. After constructing the world, you switch on the power source and                   .”
   1. you determine; you provide; you know what happens
   2. reality determines; reality provides; watch what happens
   3. reality determines; reality provides; you know what happens
   4. you determine; you provide; watch what happens
   5. None of these answers is correct.

3. Mathematically, an economic model is:
   1. a fake world.                                           d. a set of equations.
   2. a spreadsheet.                                          e.   the actual macroeconomy.
   3. an accurate representation of reality.

4. Which of the following are we likely going to want to explain with an economic model?

1. Why people in the United States are 50 times richer than Ethiopians.
2. What causes economic growth.
3. What we think politicians should do with taxes.

5. 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 how many 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 these answers is correct.

6. The equation                                   is an example of:
   1. a consumption function.
   2. a utility function.
   3. a production function.
   4. the production possibilities frontier.
   5. a growth model.

7. The equation                                   is an example of :
   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                                  , the “bar” over the A means that it is a:
   1. parameter that is endogenous.
   2. variable that is fixed but not exogenous.
   3. parameter that is variable or exogenous.
   4. variable that is endogenous.
   5. parameter that is fixed and exogenous.

9. In the equation                                   , the “bars” over the A and K mean they are:
   1. parameters that are endogenous.
   2. variables that are fixed but not exogenous.
   3. parameters that are endogenous.
   4. variables that are endogenous.
   5. parameters that are fixed and exogenous.

10. In the equation                                   , the lack of a “bar” over the L means that it is:
    1. an exogenous variable.                            d. constant.
    2. an endogenous variable.                          e.   equal to one.
    3. a parameter.

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

12. Which of the following inputs do we generally consider in a simple production function?
    1. capital                                                      d. utilities
    2. consumption                                            e.   distance
    3. natural resources

13. In the production function                                  ,     represents:
    1. an unknown.                                            d. a productivity parameter.
    2. the amount of capital in an economy.      e.   an error term.
    3. the amount of labor in an economy.

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                                     d. has lower costs of production
    2. is more productive                                   e.   has more workers
    3. has more natural resources

15. Consider two countries, labeled 1 and 2. Each has the production function               , i = 1, 2. If the only difference between the two countries is that A₁ > A₂:
    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                 describes how               can be combined to generate output.
    1. any amount of capital and labor
    2. particular amounts of capital and labor
    3. any amount of capital and a particular amount of labor
    4. any amount of labor and a particular amount of capital
    5. None of these answers is correct.

17. The production function                     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.

1. 4. how any amount of labor and a particular amount of capital can be combined to generate output.
   5. what output would be in a so-called perfect economy.

18. The production function                     describes how               can be combined to generate output.
    1. any amount of labor and a particular amount of capital
    2. particular amounts of capital and labor
    3. any amount of capital and labor
    4. any amount of capital and a particular amount of labor
    5. None of these answers is correct.

19. The equation                   is called the                function.
    1. Lucas expectations                                  d. Cobb-Douglas production
    2. Keynesian welfare                                   e.   Glass-Steagall utility
    3. Friedman-Schwartz money

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 when you:
    1. hold inputs constant—you double the output.
    2. double each input—you more than double the output.
    3. double each input—you less than double the output.
    4. double one input—you double the output.
    5. double each input—you double the output.

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

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

24. Which of the following production functions exhibits constant returns to scale?
    1. d.  
    2. e.   All of these answers are correct.

c.                                

25. Which of the following production functions exhibits increasing returns to scale?
    1. d.  
    2. e.   All of these answers are correct.

c.                                

26. Which of the following production functions exhibits constant returns to scale?

a.                                                                       d.       

b.                                                                             e.        All of these answers are correct.

c.                                

27. If the production function is given by                   and          and K = L = 8, total output equals: a. Y = 2.                                                            d. Y = 8.

b.   Y = 6.                                                      e.   None of these answers is correct.

c.                                Y = 14.

28. If the production function is given by                and K = 27 and L = 8, total output equals: a. Y = 1. d. Y = 8.

b.   Y = 18.                                                    e.   None of these answers is correct.

c.                                Y = 12.

29. If the production function is given by                and K = 81 and L = 2.5, total output equals about: a. Y = 1. d. Y = 6.0.

b.   Y = 0.3.                                                   e.   Y = 82.4.

c.                                Y = 22.1.

30. The firm’s profit maximization problem is:
    1. max ? = F(r, w) ? rK ? wL

{r, w}.

1. 2. max ? = rK + wL ? F(K, L)

{K, L}.

1. 3. max ? = F(K, L) ? rK ? wL

{r, w}.

1. 4. max ? = F(K, L) ? rK ? wL

{K, L}.

1. 5. All of these answers are correct.

31. 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.

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

33. 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.

34. 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.

1. 5. but hold labor constant, output will increase, but at a decreasing rate.

Refer to the following figure when answering the following questions.

35. 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.

36. Consider Figure 4.1. The shape of this production function suggests:
    1. None of these answers is correct.
    2. a diminishing marginal product of labor.
    3. a constant marginal product of capital.
    4. an increasing marginal product of capital.
    5. an increasing marginal product of labor.

37. Consider Figure 4.1. The shape of this production function suggests that ? in the production function is:
    1. equal to one.                                            d. less than one.
    2. greater than one.                                      e.   Not enough information is given.
    3. equal to zero.

Refer to the following figure when answering the following questions.

38. 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.

39. 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 constant marginal product of labor.
    4. an increasing marginal product of capital.
    5. None of these answers is correct.

Figure 4.3: The Production Function

40. 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.

41. The solution to the firm’s profit maximization is:
    1. MPL = w.                                                 d. MPL = w and MPK = 0.
    2. MPL = w and MPK = r.                             e.   MPL > w and MPK = r.
    3. MPL < w and MPK = r.

42. With a Cobb-Douglas production function               , the marginal product of capital is            

and the marginal product of labor is            .

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

b.   MPK = (2/3)(Y/K); MPL = (1/3)(Y/L)      e.   None of these answers is correct.

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

43. 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.

44. If MPK = r, the firm:
    1. should hire more labor.
    2. should hire more capital until MPK= w.
    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.

45. 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.

46. The marginal product of the labor curve represents the:
    1. demand for wages.                                  d. demand for capital.
    2. supply of labor.                                       e.   supply of wages.
    3. demand for labor.

47. The equation MPK = r* yields the:
    1. amount of capital in an economy.
    2. optimal amount of capital, K*, a firm fires.
    3. optimal amount of labor, L*, a firm hires.
    4. quantity of capital a firm wants to hire at any rental rate of capital.
    5. None of these answers is correct.

Figure 4.4: Labor Market

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

49. If           and         , 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.

50. The marginal product of labor is measured in:

51. In the Cobb-Douglas production function                 the ? 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.

1. 5. the share of production contributed by capital.

52. In the Cobb-Douglas production function               , 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 two-thirds.
    4. capital’s share of income is one.
    5. labor’s share of income is three.

53. In the Cobb-Douglas production function               , 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.

54. In the Cobb-Douglas production function               , if a = 1/4, then:
    1. capital’s share of GDP is one-fourth.
    2. labor’s share of GDP is half.
    3. capital’s share of GDP is three-fourths.
    4. labor’s share of income is one-fourth.
    5. capital’s share of GDP is four.

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

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

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

58. In models with perfect competition:
    1. economic profits are always positive.
    2. accounting profits are zero.
    3. income paid to labor is the same as is paid to capital.
    4. the real interest rate is equal to the nominal interest rate.
    5. economic profits are zero.

59. Accounting profit is               and is equal to              .
    1. income paid to capital; r*K*
    2. zero; the real interest rate
    3. equal to two-thirds of national income; r*
    4. the same as economic profit; zero
    5. equal to one-third of the labor income; r*L*

60. A firm’s stock price is equal to:
    1. current revenues divided by the number of stocks being traded.
    2. the present value of all past earnings.
    3. zero, in the long run.
    4. current and expected future accounting profits.
    5. economic plus accounting profits, times the real interest rate.

61. In the Cobb-Douglas production function                 , defining y = Y/L as output per person and

k = K/L as capital per person, the per person production function is:

a.                                                                      d.

b.                                     e.  None of these answers is correct.

c.                               

62. In the Cobb-Douglas production function                  , defining y = Y/L as output per person and

k = K/L as capital per person, the per person production function is:

a.                                                                               d.

b.                                                                   e.   None of these answers is correct.

c.

63. In the Cobb-Douglas production function                 , defining y = Y/L as output per person and

k = K/L as capital per person, the per person production function is:

a.                                                                    d.

b.                                   e.  None of these answers is correct.

c.                               

64. The equation               has what 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. The population tends to be higher when (1) the productivity parameter is higher and (2) the amount of capital per person is higher.

Refer to the following table when answering the following questions.

Observed per          Predicted per capita

                                      capita GDP                  output y_P=k       

South Africa                       0.23                             0.63               (Source: Penn World Tables 9.0)

65. Consider Table 4.1, which compares the model         to actual statistical data on per capita GDP. You observe the model:
    1. consistently underestimates the level of per capita GDP.

1. 2. consistently overestimates the level of per capita GDP.
   3. does a really good job of estimating the level of per capita GDP.
   4. clearly contains all factors that affect per capita GDP.
   5. None of these answers is correct.

66. One explanation for the difference between the predicted output per person and the observed per capita GDP in Table 4.1 is differences in:
    1. per capita capital.                                     d. labor’s share of GDP.
    2. the labor supply.                                      e.   None of these answers is correct.
    3. factor productivity.

67. One explanation for the difference between the predicted output per person and the observed per capita GDP in Table 4.1 is differences in:
    1. the labor supply.                                      d. capital’s share of GDP.
    2. human capital.                                         e.   None of these answers is correct.
    3. per capita capital.

68. One explanation for the difference between the predicted output per person and the observed per capita GDP in Table 4.1 is differences in:
    1. the labor supply.                                      d. capital’s share of GDP.
    2. the state of technology.                            e.   labor’s share of GDP.
    3. per capita capital.

69. Considering the data in Table 4.1, the explanation for the difference between the predicted and actual level of output is called             . If you compare South Africa’s observed and predicted output, this difference is equal to             .
    1. total factor productivity; 0.37                  d.   capital’s share of GDP; one-third
    2. the Solow residual; 2.71                          e.   labor’s share of GDP; two-thirds
    3. Dirac’s delta; 0.14

70. Considering the data in Table 4.1, the explanation for the difference between the predicted and actual level of output is called             . If you compare India’s observed and predicted output, this difference is equal to             .
    1. labor’s share of GDP; two-thirds             d. capital’s share of GDP; one-third
    2. the Solow residual; 4.5                            e.   total factor productivity; 0.22
    3. liquidity; 0.05

71. As a measure for total factor productivity, we can use the quantity of         in an economy.

1. 1. computers                                                d. kilowatt hours used
   2. factories                                                   e.   None of these answers is correct.
   3. machines

72. In the equation             ,     represents:
    1. total factor productivity.                          d. the capital = labor ratio.
    2. physical capital.                                       e.   the real interest rate.
    3. natural resources.

73. In the equation             , 1/3 represents:
    1. total factor productivity.                          d. the output share of capital.
    2. physical capital.                                       e.   the real interest rate.
    3. natural resources.

74. Differences in output across economies with the same per capita capital stock can be explained by:
    1. differences in labor.                                d. differences in resource use.
    2. differences in total factor productivity.   e.   similarities in physical capital.
    3. similarities in total factor productivity.

75. You are an economist working for the International Monetary Fund. Your boss wants to know what the total factor productivity of China is, 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?
    1. d.

b.                                 e.   None of these answers is correct.

c.

76. You are an economist working for the International Monetary Fund. Your boss wants to know what the total factor productivity of India is, 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?
    1. d.

1. 2. e.   None of these answers is correct.

c.

77. 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 0.01; predicted per capita GDP,

given by            , is 0.18. What is total factor productivity? a.      0.44                                                         d. 0.00

b.   0.98                                                         e.   18.00

c.                                0.06

78. As an economist working at the International Monetary Fund, you are given the following data for Japan: observed per capita GDP, relative to the United States, is 0.760; predicted per capita GDP, given

by            , is 1.06. What is total factor productivity?

a.   0.75                                                         d.   0.81

b.   1.05                                                         e.   0.72

c.                                1.39

79. As an economist working at the International Monetary Fund, you are given the following data for Italy: observed per capita GDP, relative to the United States, is 0.69; predicted per capita GDP, given

by            , is 0.98. What is total factor productivity?

a.   0.75                                                         d.   0.81

b.   0.68                                                         e.   0.70

c.                                0.99

80. 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, as given by      , is 0.10, and total factor productivity is 0.083. What is the observed per capita GDP, relative to the United States?

a.   0.008                                                       d.   0.44

b.   0.016                                                       e.   0.62

c.                                0.87

81. As an economist working at the International Monetary Fund, you are given the following data for

Brazil: predicted per capita GDP, relative to the United States, as given by      , is 0.56, and total factor productivity is 0.36. What is the observed per capita GDP, relative to the United States?

a.   0.92                                                         d.   0.56

b.   1.57                                                         e.   0.81

c.                                0.20

82. As an economist working at the International Monetary Fund, you are given the following data for

South Africa: predicted per capita GDP, relative to the United States, as given by      , is 0.55, and total factor productivity is 0.33. What is the observed per capita GDP, relative to the United States?

a.   0.54                                                         d.   0.88

b.   1.68                                                         e.   0.18

c.                                0.82

83. Consider the three production functions in Figure 4.5. Each represents a different country. For any given per capita stock of physical capital, which country has the highest total factor productivity?
    1. A                                                             d. Not enough information is given.
    2. B                                                              e.   They are the same.
    3. C

Figure 4.6: Production Function

84. 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 capita capital stock but different factor productivity.
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.

85. Suppose the total factor productivity in Switzerland, Italy, South Africa, and India is 0.89, 0.70, 0.33, and 0.21, respectively. If the U.S. total factor productivity is 1.00, then the United States is         productive, respectively, than these four countries.
    1. equally as
    2. 89 percentage points, 70 percentage points, 33 percentage points, and 21 percentage points less
    3. 11 percentage points, 30 percentage points, 67 percentage points, and 79 percentage points more
    4. 89 percentage points, 70 percentage points, 33 percentage points, and 21 percentage points more
    5. 11 percentage points, 30 percentage points, 67 percentage points, and 79 percentage points less

86. 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. 1. one-third; wages; two-thirds
   2. one-third; total factor productivity; two-thirds
   3. one-third; total factor productivity; one-third

1. 4. one-third; returns to capital; two-thirds
   5. two-thirds; total factor productivity; one-third

87. In the year 2014 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.   60; 6; 10                                                  d. 18; 108; 6

b.   45; 10; 4.5                                               e.   70; 5; 14

c.                                1.25; 0.25; 5

88. In the year 2014 total factor productivity was about           times                important than capital per person when determining differences in per capita GDP using the production model.
    1. 3; more                                                    d. 108; more
    2. 6; less                                                      e.   10; more
    3. one-third; less

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

.                                                                     .

1. 2. e.

.                                                                             .

c.

.

90. Which of the following do(es) NOT explain differences in total factor productivity?
    1. institutions                                               d. natural resources
    2. the labor stock                                         e.   technology
    3. human capital

91. Which of the following explain(s) differences in total factor productivity?
    1. institutions                                               d. technology
    2. human capital                                          e.   All of these answers are correct.
    3. natural resources

92. Which of the following explain(s) differences in total factor productivity?
    1. institutions                                               d. legal structure
    2. human capital                                          e.   All of these answers are correct.
    3. infrastructure

93. Which of the following do(es) NOT explain differences in total factor productivity?
    1. the labor stock                                         d. the stock of capital
    2. the share of capital in GDP                      e.   All of these answers are correct.
    3. the share of labor in GDP

94. In the United States, the average number of years of education adults over the age of 25 have obtained is about:

a.   13.                                                           d.   12.

b.   9.                                                             e.   14.

c.                                17.

95. In the poorest countries in the world, the average number of years of education is about:

96. In the United States, each year of education increases a worker’s wage by about         percent per year.

a.   7                                                              d. 10

b.   1                                                              e.   None of these answers is correct.

c.                                4

97. Which of the following is an example of technology?
    1. just-in-time inventory                              d.   the Internet
    2. a fork                                                       e.   All of these answers are correct.
    3. improved irrigation

98. The influences of institutions on economic performance can be easily contrasted using:
    1. North and South Korea.                           d. Uzbekistan and the United Kingdom.
    2. France and Germany.                              e.   Earth and Mars.

1. 3. Iowa and Illinois.

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

100. Which of the following is/are essential for economic success?
     1. property rights                                         d. the separation of powers
     2. the rule of law                                         e.   All of these answers are correct.
     3. contract enforcement

101. For efficient allocation of resources             and                must be equal across firms.
     1. the marginal product of capital; the marginal product of labor
     2. nominal wages; real wages
     3. the capital stock; the labor stock
     4. unemployment must be equal to its natural rate; wages
     5. net exports should be zero; the marginal product of capital

102. The case of the economic reforms in Russia and China provides insight into differences in:
     1. the production model and Total Factor Productivity.
     2. the labor market.
     3. the “Big Bang” versus gradualist approach to development.
     4. an export-led development model.
     5. political cronyism.

TRUE/FALSE

1. Exogenous variables are predetermined by the model builder.

2. In the production function                                 ,    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                is called the Cobb-Douglas production function.

5. A production function of the form                exhibits constant returns to scale.

6. The production function of the form                exhibits constant returns to scale.

7. The production function of the form               exhibits constant returns to scale.

8. If the production function is                , then in per worker terms, it can be written as             .

9. In the aftermath of the Black Death in the fourteenth century, wages in Europe were higher than before the Black Death because millions of people died.

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 buy 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 0.33, then the U.S. capital per worker is 67 percentage points more productive than China’s.

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

16. If the production function is given by               , then labor’s share of GDP is one-third.

17. If the production function is given by               , the marginal product of capital is (1/3)(Y/K).

18. The marginal product of the labor curve represents the labor supply curve.

19. If you have data on per capita GDP and capital per worker, to find total factor productivity you can use the equation              , if capital’s share of GDP is one-third.

20. If you have data on per capita GDP and capital per worker, to find total factor productivity you can use the equation              , if capital’s share of GDP is two-thirds.

21. Institutions are one example of factors that influence total factor productivity.

22. In the United States, the average number of years of education adults over the age of 25 have obtained is 18 years.

SHORT ANSWER

1. State whether the following production functions exhibit increasing, constant, or decreasing returns to scale in K and L.

(a)

(b)

(c)

2. Write down the firm’s profit maximizing problem. Be sure to identify the variables the firm can choose and which it takes as given. What should the firm facing the following scenarios do?

• The marginal product of capital is greater than the rental price of capital.
• The marginal product of labor is less than the wage.

3. In the Cobb-Douglas production function           , what do a < 1 and b = 1 ? a reflect? Show how you derive your answer.

4. Convert the Cobb-Douglas production                   into per capita terms. Why might we be more concerned about per capita output rather than total output when discussing the welfare impacts of economic growth?

5. What are the shortcomings of using the production model        ? What might we include in our model to improve the fit of this simple model?

                                                                                                                     if           .

6. What are the three sources of total factor productivity discussed in the text? Can you name other possible sources? Explain your answer.

7. Consider Table 4.2 below. Use the production function model to answer the following questions. All answers should use the United States as the comparison country (i.e., U.S.=1). y_O and k_O are the observed levels of per capita output and capital, respectively. (If an instructor is to assign this question during an exam, given time limitations, choose just a subsample of the countries.)
   1. Fill in the missing cells.
   2. Do any of the countries have higher TFP than the United States?
   3. Using what you know about each country, what might help to explain differences between the predicted per capita GDP ( y_P) and the observed value, y_O?
   4. What might help explain why       ?

Table 4.2: Production Function Model (U.S.=1)

United States                1.00      1.00                                     (Source: Penn World Tables 9.0)

8. Throughout the text, a simplifying assumption was made in the production function model of economic growth: the capital share, ?, is set equal to one-third. But this is not necessarily the case; indeed, ? can be any number greater than zero and less than one. Consider two economies, H and L, with different capital shares, ?_H > ?_L. Which country will get more output for each unit of capital added? Explain.

.

9. Throughout the text, a simplifying assumption was made in the production function model of economic growth: capital and labor shares are identical across all countries. But what if they are not? All answers should use the United States as the comparison country (i.e., U.S.=1). y_O and k_O are the observed levels of per capita output and capital, respectively, and ? is capital’s share of output. (If an instructor is to assign this question during an exam, given time limitations, choose just a subsample of the countries.)

Consider Table 4.3 below.

1. 1. Fill in the missing cells.
   2. Do any of the countries have higher TFP than the United States?
   3. Using what you know about each country, what might help to explain differences between the predicted per capita GDP ( y_P) and the observed value, y_O?
   4. What might help explain why       ?
   5. What might cause the differences in ?? Is there any country with ? equal to what is used in the text?

Table 4.3: Production Function Model (U.S. = 1)

(Source: Penn World Tables 9.0)

10. Table 4.4 shows estimates of total factor productivity (TFP) for seventeen western European countries using data from the Penn World Tables, 9.0. What are possible explanations for these differences in TFP across the various questions? Explain.

Table 4.4