Queens College, CUNY - ECON 201

CHAPTER 4: A Model of Production

MULTIPLE CHOICE

1)A model is a           representation of        world that we use to study economic phenomen

1. 1. false; a toy                                              mathematical; the real
   2. mathematical; a toy                                     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 worl 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 are correct.

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

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 fifty 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 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 are correct.

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

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

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

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

10. In the equation                                  , the “bars” over the A and K mean that these variables 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

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

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

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

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

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

16. 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.

17. The production function                 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 these answers are correct.

18. 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
    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 “perfect” economy

19. The production function                     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
    4. how any amount of capital and a particular amount of labor can be combined to generate output
    5. None of these answers are correct.

20. The equation                  is called:
    1. the Lucas production function
    2. the Keynesian production function
    3. the Friedman-Schwartz production function
    4. the Cobb-Douglas production function
    5. the Glass-Steagall production function

21. 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

22. 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

23. 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

24. 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

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

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

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

                                                                                           All of these answers are correct.

28. If the production function is given by                   and         and K = L = 8, total output equals:
    1. Y = 2                                                        Y = 8
    2. Y = 6                                                              None of these answers are correct.
    3. Y = 14

29. If the production function is given by                and K = 27 and L = 8, total output equals:
    1. Y = 1                                                        Y = 8
    2. Y = 18                                                            None of these answers are correct.
    3. Y = 12

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

   Y = 0.3                                                              Y = 82.4

                                   Y = 22.1

31. 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}

4. max ? = F(K, L) – rK – wL

{K, L}

5. All of these answers are correct.

                                   max ? = F(K, L) – rK – wL

{r, w}

32. 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

33. 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

34. 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

1. 5. the additional revenue generated by hiring an additional unit of labor

35. 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

Refer to the following figure when answering the next three questions.

36. 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

37. Consider Figure 4.1. The shape of this production function suggests:
    1. None of these answers are 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

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

Refer to the following figure when answering the next two questions.

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 diminishing marginal product of labor
    4. an increasing marginal product of capital
    5. Not enough information is given.

40. 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 are correct.

Figure 4.3: The Production Function

41. 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.

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

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

and the marginal product of labor is         .

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

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

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

44. 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

45. If MPK = r, the firm:
    1. should hire more labor

1. 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

46. 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

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

48. 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 labor, L*, a firm hires
    4. the quantity of capital a firm wants to hire at any rental rate of capital
    5. None of these answers are correct.

49. In Figure 4.4, MPL represents the           ,    represents the            , and the intersection of the two yields                      .

1. 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 these answers are correct.

50. 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.

51. The marginal product of labor is measured in:
    1. dollars                                                     units of capital per dollar
    2. units of output                                               units of labor per dollar
    3. units of output per dollar

52. 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
    5. the share of production contributed by capital

53. In the Cobb-Douglas production function              , if a = 1/3, then:
    1. labor’s share of GDP is two-thirds          capital’s share of income is one
    2. labor’s share of GDP is one-third                  labor’s share of income is three
    3. capital’s share of GDP is two-thirds

54. 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.

55. 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

56. 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:
    1. 

57. 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:
    1. 

58. 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. ; positive                                                           ; equal to zero
    2. ; equal to zero                                                       ; negative
    3. ; negative

59. 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

60. 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 the labor income; r*L*

61. 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

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:

                                            None of these answers are correct.

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:

                                          None of these answers are correct.

64. 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:

                                          None of these answers are correct.

65. 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 next four questions.

Table 4.1: Production Model’s Prediction for Per Capita GDP (US = 1)

Predicted output

Observed

66. 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
    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 are correct.

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. per capita capital                                    labor’s share of GDP
    2. the labor supply                                            None of these answers are correct.
    3. factor productivity

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                                      capital’s share of GDP
    2. human capital                                               None of these answers are correct.
    3. per capita capital

69. 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                                      capital’s share of GDP
    2. the state of technology                                 labor’s share of GDP

1. 3. per capita capital

70. As a measure for total factor productivity, we can use the quantity of     in an economy.
    1. computers                                               kilowatt hours used
    2. factories                                                        None of these answers are correct.
    3. machines

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

72. 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 resource use
    5. similarities in physical capital

73. You are an economist working for the International Monetary Fun 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. 

                                         None of these answers are correct.

74. You are an economist working for the International Monetary Fun 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. 

1. 2.       None of these answers are correct.

75. Suppose the total factor productivity in Switzerland, Italy, South Africa, and India are 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

76. 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
   4. one-third; returns to capital; two-thirds
   5. two-thirds; total factor productivity; one-third

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

78. Which of the following explain(s) differences in total factor productivity?
    1. institutions                                              legal structure

1. 2. human capital                                               All of these answers are correct.
   3. infrastructure

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

80. In the United States, each year of education increases a worker’s wage by about   per year.
    1. 7 percent                                                 10 percent
    2. 1 percent                                                       None of these answers are correct.
    3. 4 percent

81. Which of the following are examples of technology?
    1. just-in-time inventory                             the Internet
    2. a fork                                                             All of these answers are correct.
    3. improved irrigation

82. The influences of institutions on economic performance can be easily contrasted using:
    1. North and South Korea                           Uzbekistan and the U.K.
    2. France and Germany                                    Earth and Mars
    3. Iowa and Illinois

83. 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

84. The case of the economic reforms in Russia and China provide insight into differences in:
    1. the production model and TFP
    2. labor market differences
    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 lan

                                                                 NOT: We consider labor and capital.

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 scal

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

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

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 die

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  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

13. Consider two countries, A and  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

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-thir

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 curv

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-thir

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 for adults over the age of 25 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?

• If the marginal product of capital is greater than the rental price of capital.
• If the marginal product of labor is less than the wag

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?