University of California, Santa Cruz - ECON 100B

CHAPTER 5: The Solow Growth Model

MULTIPLE CHOICE

1)In 1960, the Philippines had a per capita income   South Korea’s. In 2014,           .

1. 1. lower than; this situation had reversed
   2. lower than; per capita income was equal in both countries
   3. equal to; South Korea had higher per capita income
   4. higher than; this situation had reversed
   5. higher than; this difference was even more pronounced

                                

 

2. In 2014, the Philippines per capita GDP was about          , while in South Korea it was             . a. $6,600; over $35,000

b. $10,000; $15,000

c.   half that of the United States; twice that of the United States

d. $1,000; $2,000

e.   $35,000; the same

                                

 

3. The Solow model of economic growth:
   1. endogenizes labor.                                  d. exogenizes investment.
   2. endogenizes physical capital.                 e.   endogenizes investment.
   3. exogenizes physical capital.

                                

 

4. The key insight in the Solow model is that:
   1. saving rates are determined in a particular manner.
   2. savings have no impact on economic growth.
   3. capital depreciation enhances economic growth.
   4. the relationship between capital and output is static.
   5. capital accumulation contributes to economic growth.

                                

 

5. The Solow model describes:
   1. how saving rates are determined.
   2. the static relationship between capital and output.
   3. how savings, population growth, and technological change affect output over time.
   4. how savings, population growth, and technological change affect output in a single period.
   5. what constitutes technological change.

                                

 

6. In the corn farm example, corn can be used as:
   1. only investment.                                     d. either consumption or investment.

1. 2. either saving or depreciation.                e.   tax revenue.
   3. only consumption.

                                

 

7. In the corn farm example, saving some of the corn produced:
   1. future output, which grows over time.
   2. lower consumption in the future.
   3. future output, which declines over time.
   4. higher consumption today.
   5. technological change.

                                

 

8. The production function used in the Solow model is:

   1. 

      

      .                                   d.                                       .

   2. 

      

      .                                          e.                                       .

 

c.

 

.

                                

 

9. If C_t denotes consumption, I_t denotes investment, and Y_t is output, the resource constraint in the Solow model is:

   1. 

      Y_t = C_t ? I_t.                                                d.                        .

   2. 

      

      .                                              e.   None of these answers is correct. c.

.

                                

 

10. In the Solow model, in every period, a fraction of total output      , which                next period’s capital stock.
    1. is saved; reduces                                     d. is consumed; adds to
    2. depreciates; adds to                               e.   is consumed; reduces
    3. is saved; adds to

                                

 

11. In the Solow model, the equation of capital accumulation is:

 

a.  

 .                                         d.                                 .

 

 

b.

 .                                 e.                        .

 

c.                               

 .

 

                                

 

12. 

    In the Solow model, if           , the capital stock:
    1. declines.                                                  d.   Not enough information is given.
    2. stays the same.                                       e.   None of these answers is correct.
    3. grows.

                                

 

 

13. In the Solow model, if investment is            depreciation, the capital stock           .
    1. less than; grows                                      d. equal to; declines
    2. greater than; grows                                e.   equal to; grows
    3. greater than; declines

                                

 

 

14. 

    In the Solow model, the parameter                         denotes            and is    .
    1. investment; less than one                       d. the depreciation rate; less than one
    2. the depreciation rate; equal to zero      e.   investment; greater than one
    3. consumption; greater than one

                                

 

 

15. In the Solow model, it is assumed that a(n)          fraction of capital depreciates regardless of the capital stock.
    1. increasing                                               d. undetermined
    2. constant                                                  e.   None of these answers is correct.
    3. decreasing

                                

 

 

16. Using the Solow model, if, in time t = 0, the initial capital stock is K₀ = 100, investment is I₀ = 25, and

 

.1 is the depreciation rate, capital accumulation from period 0 to period 1 is: a.                                                               ?K₁ = 35.            d. ?K₁ = 0.

 

b.   ?K₁ = ?15.                                                e.   ?K₁ = 115.

c.                                ?K₁ = 15.

                                

17.  

18. 

    Using the Solow model, if, in time t = 50, the capital stock is K₅₀ = 150, investment is I₅₀ = 15, and is the depreciation rate, capital accumulation from period 50 to 51 is:

a.   ?K₅₁= 5.                                                   d.   ?K₅₁=120.

b.   ?K₅₁= ?15.                                               e.   ?K₅₁= 0.

c.                                ?K₅₁=15.

                                

 

 

19. In the simple Solow model, we assume:
    1. the depreciation rate is negative.          d. labor is exogenous.

1. 2. net investment is always positive.          e.   the saving rate changes frequently.
   3. TFP equals one.

                                

 

 

20. 

    In the Solow model, defining as the saving rate, Y_t as output, and I_t as investment, consumption is given by:

    1. 

       

       .                                                    d.                            .

    2. 

       

       .                                               e.               .

    3. 

       .

                                

 

 

21. 

    In the Solow model, defining as the saving rate, Y_t as output, and C_t as consumption, investment I_t is given by:

    1. 

       

       .                                                d.                     .

    2. 

       

       .                                                    e.                      .

    3. 

       .

                                

 

 

22. The amount of capital in an economy is a(n)         , while the amount of investment is a(n)

               .

1. 1. flow; stock                                               d. intermediate good; final good
   2. stock; flow                                               e.   None of these answers is correct.
   3. final good; intermediate good

                                

 

 

23. Capital accumulation is a(n):
    1. stock.                                                       d. intermediate good.
    2. flow.                                                        e.   None of these answers is correct.
    3. final good.

                                

 

24. Which of the following is/are left out of the Solow model?
    1. productivity                                             d. the saving rate
    2. consumption                                           e.   depreciation
    3. real interest rates

                                

 

 

25. The endogenous variables in the Solow model are:
    1. the capital stock, labor, and output.
    2. consumption, investment, the capital stock, labor, and the saving rate.
    3. consumption, investment, the capital stock, labor, and output.

1. 4. productivity and the depreciation and saving rates.
   5. the capital stock, labor, output, and the saving rate.

                                

 

 

26. Which of the following is an exogenous variable in the Solow model?
    1. productivity                                             d. the initial capital stock
    2. the depreciation rate                              e.   All of these answers are correct.
    3. the saving rate

                                

 

 

27. The Solow model assumes the saving rate is:
    1. zero.                                                        d. increasing as income increases.
    2. constant.                                                 e.   larger as the interest rate rises.
    3. decreasing as income increases.

                                

 

 

28. 

    

    In the Solow model, investment, I_t, as a function of saving,   , and output,         , is written as:

    1. 

       

       .                                       d.                           .

    2. 

       

       .                                           e.                           .

    3. 

       .

                                

 

 

29. 

    

    A change in the capital stock, ?K_t, can be expressed as a function of the saving rate, ; output,

 

; the capital stock, K_t ; and the depreciation rate, , by:

 

a.  

                                  d.

 

 

b.                                    .                               e. c.                                  

 

                                

 

 

30. 

    The equation                       is called:
    1. saving.                                                     d. the capital stock.
    2. investment.                                             e.   depreciation.
    3. net investment.

                                

 

31. In the Solow model, net investment is defined as:
    1. investment plus capital depreciation.
    2. investment minus capital depreciation.
    3. the saving rate minus the depreciation rate.

1. 4. the saving rate plus the depreciation rate.
   5. None of these answers is correct.

                                

 

 

32. In the Solow model, if net investment is positive:
    1. capital accumulation is zero.                  d. savings are negative.
    2. capital accumulation is negative.           e.   Not enough information is given.
    3. capital accumulation is positive.

                                

 

 

Refer to the following figure when answering the following questions.

 

Figure 5.1: Solow Diagram

 

33. In Figure 5.1, if the economy begins with the initial capital stock at K₁, the capital stock will   

and the economy will             .

1. 1. decrease; grow                                       d. decrease; shrink
   2. increase; grow                                        e.   stay constant; grow
   3. stay constant; shrink

                                

 

34. In Figure 5.1, if the economy begins with the initial capital stock at K₂, the capital stock will   

and the economy will             .

1. 1. decrease; grow                                       d. stay constant; shrink
   2. increase; grow                                        e.   stay constant; grow
   3. stay constant; be in its steady state

                                

 

35. In Figure 5.1, if the economy begins with the initial capital stock at K₃, the capital stock will   

and the economy will             .

1. 1. increase; grow                                        d. decrease; be in its steady state
   2. decrease; shrink                                      e.   stay constant; shrink
   3. stay constant; be in its steady state

                                

 

36. In Figure 5.1, the capital stock at K₁ is not the steady state because:
    1. the saving rate is too low.
    2. the saving rate is too high.
    3. the depreciation rate is too low.
    4. gross investment is higher than capital depreciation.
    5. gross investment is lower than capital depreciation.

                                

 

 

37. In Figure 5.1, at K₁, net investment is            and the economy             .
    1. negative; will grow                                 d. positive; will grow
    2. positive; is in its steady state                  e.   negative; will contract
    3. zero; is in its steady state

                                

 

 

38. The steady state is defined as the point where capital accumulation, ?K_t, is equal to:
    1. the saving rate.                                       d. the productivity growth rate.
    2. zero.                                                        e.   the population growth rate.
    3. the depreciation rate.

                                

 

 

39. 

    

    

    

    If we define the saving rate as   , output as      , and the depreciation rate as         and if

, the economy is:

1. 1. contracting.                                             d. in its short-run equilibrium.
   2. growing.                                                  e.   None of these answers is correct.
   3. at the steady state.

                                

 

 

40. 

    

    

    

    If we define the saving rate as   , output as      , and the depreciation rate as         and if

, the economy is:

1. 1. contracting.                                             d. in its short-run equilibrium.
   2. at the steady state.                                 e.   None of these answers is correct.
   3. growing.

                                

 

 

41. The Solow model assumes the:
    1. capital stock is constant.                         d. saving rate changes each period.
    2. number of workers is growing.              e.   depreciation rate changes each period.
    3. number of workers is constant.

                                

 

42. In the Solow model, if, in the absence of any shocks, the capital stock remains at K* forever, this rest point is called the:
    1. saving rate.                                             d. rate of capital accumulation.
    2. short-run equilibrium.                            e.   dynamic system.
    3. steady state.

                                

 

 

43. In the Solow model, if capital is in the steady state, output:
    1. will continue to grow.
    2. is also in the steady state.
    3. will continue to grow, but its rate of growth will slow down.
    4. will decline, but its rate of growth will be positive.
    5. will begin to contract.

                                

 

 

Refer to the following figure when answering the following questions.

 

Figure 5.2

 

44. In Figure 5.2, steady-state consumption is represented by:

    1. 

       a      b.                                                     d. b.

    2. 

       

       c      a.                                                     e.   a      d.
    3. Consumption is not represented.

 

 

45. 

    

    In Figure 5.2, steady-state investment is represented by:

Investment is not represented. a. c       d.

a b.

b.

 

46. In the Solow model, the steady-state level of output per worker is a function of:
    1. productivity and the initial capital stock.
    2. the initial capital stock, productivity, and the saving rate.
    3. the initial capital stock, productivity, and the depreciation rate.

1. 4. the initial capital stock and the steady-state level of capital stock.
   5. productivity, the depreciation rate, and the saving rate.

                                

 

47. In the Solow model, the steady-state capital stock is a function of:
    1. productivity and the initial capital stock.
    2. the initial capital stock, productivity, and the saving rate.
    3. the initial capital stock, productivity, and the depreciation rate.
    4. the labor stock and the steady-state level of capital stock.
    5. productivity, the depreciation rate, the labor stock, and the saving rate.

                                

 

48. 

    

    

    

    Assume a production function is given by                . If               , the depreciation rate is         , and the saving rate is                the steady-state level of capital is about:

a.   0.3.                                                          d.   0.8.

b.   1.3.                                                          e.   1.6.

c.                                2.8.

                                

 

49. 

    

    

    

    Assume a production function is given by                . If          and        , the depreciation rate is

 

, and the saving rate is       , the steady-state level of capital is about: a.      0.1.                                                          d. 8.0.

 

b.   2.5.                                                          e.   0.6.

c.                                1.6.

                                

 

50. 

    

    

    Assume a production function is given by                . If          and        , and the steady-state capital stock is 8.0, the steady-state level of output is about:

a.   8.0.                                                          d. 2.0.

b.   4.0.                                                          e.   22.6.

c.                                45.4.

                                

 

51. 

    

    

    If the production function is given by                , the saving rate, s, is 20 percent; the depreciation rate,   , is 10 percent; and          , the steady-state level of output is:

a.   1.4.                                                          d.   8.0.

b.   4.0.                                                          e.   3.5.

c.                                2.0.

                                

 

52. 

    The steady-state level of output per worker in the Solow model, with the production function

, is given by:

1. 1. 

      

      d.

 

.                                                                         .

1. 2. 

      

      e.

 

.                                                               .

 

c.

 

 

.

                                

 

 

Refer to the following figure when answering the following questions.

 

Figure 5.3: Solow Diagram

53. In Figure 5.3, at K₁, the difference between           and            is       , and the difference between Y and is         .

    1. 

       

       

       output; investment                                  d. output; consumption
    2. net investment; consumption                 e.   depreciation; gross investment
    3. gross investment; consumption

                                

 

 

54. In Figure 5.3, at K₂, capital accumulation is          , the economy is             , and consumption is

               .

1. 1. positive; growing; positive                      d. zero; in the steady state; positive
   2. zero; in the steady state; zero                e.   zero; contracting; negative
   3. negative; growing; positive

                                

 

 

 

55. In the Solow model, it is assumed a(n)           fraction of capital depreciates each period.
    1. zero                                                         d. constant
    2. increasing                                               e.   None of these answers is correct.

1. 3. decreasing

                                

 

56. An increase in               leads to a higher steady-state capital stock, and a decline in      leads to a lower steady-state capital stock.
    1. the saving rate; the depreciation rate   d. the depreciation rate; the labor stock
    2. the saving rate; productivity                   e.   None of these answers is correct.
    3. productivity; the initial capital stock

                                

 

 

57. An increase in               leads to a higher steady-state level of output, and an increase in    

leads to a lower steady-state level of output.

1. 1. the saving rate; the depreciation rate   d. the depreciation rate; the labor stock
   2. the saving rate; productivity                   e.   None of these answers is correct.
   3. productivity; the initial capital stock

                                

 

58. An increase in               leads to a higher steady-state level of output per worker, and a decline in the

                leads to a lower steady-state level of output per worker.

1. 1. productivity; saving rate                         d. the initial capital stock; saving rate
   2. the saving rate; initial capital stock       e.   None of these answers is correct.
   3. the saving rate; depreciation rate

                                

 

59. In the standard production model’s production function, the productivity parameter enters the equation with an exponent of one, while in the Solow model’s equation for the steady-state stock of capital it is greater than one because:
    1. the endogenous level of the capital stock itself depends on productivity.
    2. there is no productivity parameter in the production function model.
    3. the productivity measure is zero in the production function model.
    4. the productivity measure is negative in the Solow model.
    5. the exogenous level of the capital stock itself depends on productivity.

                                

 

 

60. In the Solow model, the             plays a                role than it does in the standard production function model.
    1. labor supply; larger                                d. capital stock; smaller
    2. productivity parameter; larger              e.   productivity parameter; smaller
    3. capital stock; larger

                                

 

61. If a natural disaster destroys a large portion of a country’s capital stock but the saving and depreciation rates are unchanged, the Solow model predicts that the economy will grow and eventually reach:
    1. the same steady-state level of output as it would have before the disaster.

1. 2. a higher steady-state level of output than it would have before the disaster.
   3. a lower steady-state level of output than it would have before the disaster.
   4. Not enough information is given.
   5. None of these answers is correct.

                                

 

62. The key difference between the Solow model and the production model is that the:
    1. Solow model endogenizes the process of capital accumulation.
    2. production function model endogenizes the process of capital accumulation.
    3. Solow model uses different values for the capital share.
    4. Solow model does not contain a productivity measure.
    5. Solow model exogenizes the process of capital accumulation.

                                

 

63. Over the past 30 years,            has averaged a saving rate of           percent.
    1. Japan; 15                                                 d. South Korea; 35
    2. Russia; 5                                                  e.   China; 12.5
    3. the United States; 15

                                

 

64. Over the past 30 years,            has averaged a saving rate of           percent.
    1. Japan; 15                                                 d. South Korea; 45
    2. Russia; 5                                                  e.   China; 12.5
    3. the United States; 25

                                

 

65. According to the Solow model, in the steady state, countries with high saving rates should have a:
    1. low labor-output ratio.                           d. high depreciation rate.
    2. low capital-output ratio.                         e.   high A.
    3. high capital-output ratio.

                                

 

66. Suppose you are given the data for Brazil and Portugal. In Brazil, the saving rate is 0.1 and the depreciation rate is 0.1, while in Portugal the saving rate is 0.2 and the depreciation rate is 0.1. Using the Solow model, you conclude that in the steady state:
    1. Brazil has a higher level of output than Portugal.
    2. Brazil has a higher capital-output ratio than Portugal.
    3. Portugal has a higher level of output than Brazil.
    4. Portugal has a higher capital-output ratio than Brazil.
    5. Portugal and Brazil have the same capital-output ratio.

                                

 

67. In the Solow model, if we assume that capital depreciation rates are the same across all countries, differences in per capita output can be explained by:

1. 1. the steady-state capital stock.
   2. the initial capital stock and saving rates.
   3. differences in productivity and saving rates.
   4. the labor stock and saving rates.
   5. None of these answers is correct.

                                

 

68. 

    

    

    

    

    

    If we define    and     as the saving rates,          as the depreciation rates, and and     as productivity in Countries 1 and 2, respectively, and the production function per capita is given by

in both countries, the Solow model predicts that the ratio of GDP per worker in Country 1 relative to Country 2 is:

1. 1. 

      

      d.

 

.                                                     .

1. 2. 

      

      e.

 

.                                                    .

 

c.

 

 

.

                                

 

69. 

    

    

    

    

    If we define    and     as the saving rates in Countries 1 and 2, respectively,    as the

depreciation rates in Countries 1 and 2, respectively, and                              and    as productivity in Countries 1 and 2, respectively, in the Solow model, the equation                  predicts that                                                                                        differences contribute the most to differences in steady-state output per worker.

 

a.

 

 

; productivity

 

b.

 

 

; saving rate

 

c.

 

 

; productivity

 

d.

 

 

; productivity

 

e.

 

 

; saving rate

                                

 

70. If the depreciation and saving rates are constant, the economy eventually will reach the steady state in the Solow model because of:
    1. the lack of productivity.
    2. increasing returns to capital in production.
    3. constant returns to capital in production.
    4. diminishing returns to capital in production.
    5. increasing returns to labor in production.

                                

 

71. An implication of the Solow model is that once an economy reaches the steady state:
    1. long-term growth continues indefinitely.
    2. long-term growth does not continue.
    3. long-term growth accelerates.
    4. long-term growth decelerates.
    5. None of these answers is correct.

                                

 

72. An implication of the Solow model is that once an economy reaches the steady state, per capita:
    1. consumption is constant.
    2. output is constant, but per capita capital is not.
    3. capital is variable.
    4. consumption continues to grow.
    5. consumption is growing.

                                

 

 

73. A central lesson of the Solow model is that:
    1. capital accumulation cannot serve as the engine of long-run per capita economic growth.
    2. capital accumulation is the only engine of long-run per capita economic growth.
    3. consumption is the only engine of short-run per capita economic growth.
    4. saving rates serve as the engine of long-run per capita economic growth.
    5. the initial capital stock plays a large part in long-run economic growth.

                                

 

74. In the Solow model, saving and investing in additional factories and computers does        output to grow in the                  run if the economy is below Y*. But, in the long run, the         returns to capital accumulation lead the return to these investments to fall.
    1. lead; medium; diminishing                     d. not lead; medium; diminishing
    2. lead; long; increasing                             e.   not lead; long; increasing
    3. lead; medium; increasing

                                

 

 

75. Which of the following best answers whether growth in the labor force leads to overall economic growth?
    1. Population growth can produce growth in the Solow model in the aggregate but not in output per person.
    2. Total capital and production per worker can grow as the population of the economy grows.
    3. It never does—only capital contributes to aggregate economic growth.
    4. Population growth can produce growth in the Solow model in the aggregate and in output per person.
    5. Population growth increases output per person but not aggregate output.

                                

 

76. In the Solow model, with population growth:
    1. there is no steady state in output per person.
    2. the economy never settles down to a steady state and exhibits growth in output per person.
    3. the economy eventually settles down to a steady state in output per person.
    4. the economy eventually settles down to a steady state with no growth in aggregate output.
    5. None of these answers is correct.

                                

 

Refer to the following figure when answering the following questions.

 

Figure 5.4: Solow Diagram

 

77. Figure 5.4 represents two countries, 1 and 2. Country        has a higher saving rate and will have a                  steady state than the other country.
    1. 2; lower                                                   d. 1; lower
    2. 1; higher                                                  e.   Not enough information is given.
    3. 2; higher

                                

 

78. Consider the Solow model exhibited in Figure 5.4. Which of the following is/are true?

1. For any single country, the movement from point a to b is due to an increase in the saving rate, s₁ > s₂.
2. For any single country, the movement from point c to b is due to an increase in capital stock for the saving rate, s₂.

3. If s₁ and s₂ stand for the saving rates in Countries 1 and 2, respectively, Country 2 has a lower saving rate.

1. i                                                               d. i and ii
2. ii                                                              e.   i, ii, and iii
3. iii

 

 

79. Consider the Solow model exhibited in Figure 5.4. If a country’s saving rate increases from s₁ to s₂, the economy would:
    1. move from point a to point b.                d. move from point a to point c.
    2. move from point c to point a.                 e.   stay at point b.
    3. move from point c to point b.

                                

 

80. Assume two economies are identical in every way except that one has a higher saving rate. According to the Solow growth model, in the steady state, the country with the higher saving rate will have

                level of total output and             rate of growth of output than/as the country with the lower saving rate.

1. 1. a higher; a higher                                   d. a higher; a lower
   2. a higher; the same                                  e.   the same; the same
   3. a lower; a higher

                                

 

81. In the Solow model, if a country’s saving rate increases, the country:
    1. moves from a relatively low steady state to one that is lower.
    2. moves from a relatively low steady state to one that is higher.
    3. moves from a relatively high steady state to one that is lower.
    4. stays at a constant high steady state.
    5. stays at a constant low steady state.

                                

 

82. A decline in the saving rate causes the steady-state level of output:
    1. and capital to rise.                                  d. and capital to remain constant.
    2. to rise and capital to fall.                       e.   to rise and capital to remain constant.
    3. and capital to fall.

 

 

83. Immediately following the increase in the saving rate, output grows rapidly. As the economy approaches its new steady state, the growth rate:
    1. gradually increases.                                d. is negative.
    2. gradually declines.                                  e.   None of these answers is correct.
    3. is constant.

                                

 

Refer to the following figure when answering the following questions.

 

Figure 5.5: Solow Diagram

 

84. Consider the Solow model exhibited in Figure 5.5. Which of the following is/are true?

1. If 1 denotes Country 1 and 2 denotes Country 2, Country 1 has a higher saving rate.
2. If 1 denotes Country 1 and 2 denotes Country 2, Country 1 has a lower depreciation rate.
3. If 1 denotes Country 1 and 2 denotes Country 2, Country 2 has a lower steady state.

1. i                                                               d. ii and iii
2. ii                                                              e.   i, ii, and iii
3. iii

 

 

85. Figure 5.5 represents two countries, 1 and 2. Country        has a higher depreciation rate and, therefore, has a             steady state than the other country.
    1. 1; higher                                                  d. 2; lower
    2. 1; lower                                                   e.   Not enough information is given.
    3. 2; higher

                                

 

86. Considering the figure below, the transitional dynamics best describe:

 

Figure 5.6

1. 1. an increase in the depreciation rate.     d. a decrease in the capital stock.
   2. a positive TFP shock.                               e.   both a and c.
   3. a decline in the saving rate.

 

87. Research on the effects of war on economic growth demonstrates that following a war an economy recovers:
    1. recovers within one or two generations.
    2. recovers in less than 10 years.
    3. recovers slowly over the course of 50 years.
    4. never fully recovers.
    5. recovers in more than 50 years.

                                

 

88. The analysis of how an economy approaches the steady state is called:
    1. investment.                                             d. saving.
    2. economic growth.                                   e.   depreciation.
    3. transition dynamics.

                                

 

89. The principle of transition dynamics can be summarized as:
    1. the further below its steady state an economy is, the faster the economy will grow.
    2. the closer to its steady state an economy is, the faster the economy will grow.
    3. the further below its steady state an economy is, the slower the economy will grow.
    4. regardless of how close to its steady state an economy is, the economy grows at the same rate.
    5. if the economy is very close to the steady state, it stops growing.

                                

 

Refer to the following figure when answering the following questions.

 

Figure 5.7: Solow Diagram

 

90. Consider Figure 5.7. If K_SK is the current capital stock in South Korea and K_CH is the current capital stock in China, according to the principle of transition dynamics:
    1. China initially will grow faster than South Korea, but each will have the same steady state.
    2. China initially will grow slower than South Korea, but each will have the same steady state.
    3. China initially will grow faster than South Korea and will have a higher steady state.
    4. China initially will grow faster than South Korea and will have a lower steady state.

1. 5. both South Korea and China initially will grow at the same rate and have the same steady state.

                                

 

91. Consider Figure 5.7. If K_SK is the current capital stock in South Korea and K_CH is the current capital stock in China, according to the principle of transition dynamics:
    1. South Korea will be richer than China, forever.
    2. South Korea will initially grow slower, but incomes in China and South Korea will converge.
    3. China and South Korea have different steady states.
    4. South Korea will initially grow faster, but incomes in China and South Korea will converge.
    5. China will initially grow slower, but incomes in China and South Korea will converge.

                                

 

92. If the current capital stock in South Korea is greater than the current capital stock in China, and total factor productivity is the same in both countries, according to the principle of transition dynamics:
    1. China initially will grow faster than South Korea, but each will have the same steady state.
    2. China initially will grow slower than South Korea, but each will have the same steady state.
    3. China initially will grow faster than South Korea and will have a higher steady state.
    4. China initially will grow faster than South Korea and will have a lower steady state.
    5. both South Korea and China initially will grow at the same rate and have the same steady state.

                                

 

93. Among the OECD countries, those that were relatively         in 1960                between 1960 and 2010.
    1. poor; grew slowly                                   d. rich; did not grow
    2. rich; grew quickly                                   e.   poor; did not grow
    3. poor; grew quickly

                                

 

94. Among OECD countries, there is             correlation between how poor a country was in 1960 and how fast it               from 1960 to 2010.
    1. almost no; grew                                      d. a strong negative; contracted
    2. a strong; grew                                         e.   almost no; contracted
    3. a strong positive; contracted

                                

 

95. Among the world as a whole, there is           correlation between how rich a country is and how fast it               from 1960 to 2010.
    1. a strong positive; grew                           d. a strong negative; contracted
    2. almost no; grew                                      e.   almost no; contracted
    3. a strong positive; contracted

                                

 

96. On average, if both rich and poor countries grow at the same rate, this suggests that:
    1. most countries are contracting.
    2. most countries still are growing.
    3. no countries have reached their steady states.
    4. most countries have reached their steady states.
    5. most countries are unproductive.

                                

 

97. If South Korea’s steady-state GDP per worker is higher than that of the Philippines, you might conclude that    , ceteris paribus.
    1. the investment rate in South Korea is higher than in the Philippines
    2. South Korea is less productive than the Philippines
    3. the depreciation rate in South Korea is higher than in the Philippines
    4. South Korea has a larger population
    5. None of these answers is correct

                                

 

98. For which of the following does the Solow model NOT provide adequate explanations?
    1. why saving rates differ across countries
    2. the cause of productivity differences across countries
    3. why population growth rates differ across countries
    4. what causes long-term economic growth
    5. All of these answers are correct.

                                

 

TRUE/FALSE

 

1. In the corn farm example, corn can be used as either saving or depreciation.

 

                                

 

 

2. The Solow model of economic growth endogenizes the savings rate.

 

                                

 

3. 

   In the Solow model, the equation of capital accumulation is                      .

 

 

 

 

4. In the Solow model, if gross investment is greater than capital depreciation, the economy accumulates new capital.

 

 

5. In the Solow model, if gross investment is equal to capital depreciation, the economy accumulates new capital.

 

                                

 

6. In the Solow model, it is assumed that a constant fraction of capital depreciates in each period.

 

 

 

7. For any given saving rate, depreciation rate, and production function, changing the initial capital stock yields a different steady state.

 

                                

 

 

8. 

   

   In the Solow model, defining as the saving rate and Y_t as output, consumption is given by .

 

                                

 

 

9. The amount of capital in an economy is a flow, while new investment is a stock.

 

                                

 

 

10. In the Solow model, the saving rate is an endogenous variable.

 

                                

 

 

11. 

    

    

    

    If we define the saving rate as   , output as      , and the depreciation rate as , and if

, the economy is in the steady state.

 

                                

 

 

12. 

    

    

    

    If    is the saving rate,          is the production function, and is the depreciation rate, the growth of capital can be expressed as                               .

 

 

13. 

    

    

    

    

    

    A change in the capital stock,      , can be expressed as a function of the saving rate,                             output, the capital stock,    ; and the depreciation rate,   , as       .

                                

 

 

 

14. In the steady state, capital accumulation is zero.

 

 

 

 

15. In the steady state, capital accumulation is positive.

 

 

16. In the Solow model, we generally assume that the capital depreciation rate is the same across all countries.

 

 

 

 

17. In the steady state, gross investment is less than capital depreciation.

 

                                

 

18. The Solow model assumes the saving rate decreases as income increases.

 

                                

 

19. In the steady state, output per person is growing.

 

                                

 

20. A decline in the saving rate will cause the steady state level of output and capital to rise.

 

                                

 

21. If South Korea’s steady-state GDP per worker is higher than that in the Philippines, you might conclude that the saving/depreciation rate in South Korea is higher/lower than in the Philippines.

 

 

 

22. Immediately following the increase in the investment rate, output grows rapidly. As the economy approaches its new steady state, the growth rate gradually declines.

 

 

 

23. The key difference between the Solow and production models is that the Solow model endogenizes the saving rate.

 

                                

 

24. 

    The productivity parameter, , plays a larger role in the Solow model than it does in the production model.

 

 

 

25. A surprising result of the Solow model is that capital accumulation cannot serve as the engine of growth in the long run.

 

 

 

26. If we include population growth in the Solow model, we can model this concept by thinking of population growth as capital depreciation per person.

 

 

 

SHORT ANSWER

 

1. What are the key assumptions of the Solow growth model?

 

 

 

2. 

   Show the transition dynamics in the Solow model if         .

 

 

 

 

3. 

   

   Suppose that rather than the Cobb-Douglas production function being given as           it is given by                                        . Find the steady-state level of capital and output in the Solow model.

 

 

 

 

4. 

   

   

   Given a production function                   , if                               , and            :

1. Calculate the steady-state level of capital and output.
2. Does the above production function exhibit constant returns to scale, or does it exhibit diminishing marginal returns? Explain, and define the difference between these two concepts.

 

                                                                                                                ).

 

 

5. 

   Use the Solow model, using the production function given by                , to determine which country has the highest steady-state level of capital and output using the data below. Assume that labor is fixed and we can define population of any country in such a way that it is equal to one (1). Which country has the highest, and lowest, steady-state capital stock and output? What is likely driving your answer?

 

Table 5.1
				?
China	0.79	0.32	0.05	0.35
Hungary	0.95	0.20	0.04	0.40
South Korea	0.84	0.35	0.06	0.45

Mexico                 1.12      0.20      0.04      0.45

(Source: Penn World Tables 9.0)

 

 

 

6. Consider the data in Figure 5.9 below, which shows the growth rates for three countries that were involved in World War II. How does the basic Solow model explain the trends in growth rates for each of these countries?

 

Figure 5.9: Economic Growth Rates in France, Germany, and Japan, 1951–2014

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(

 

7. You are asked to make comparisons of two pairs of countries. The first pair is the Latin American countries of Chile and Argentina; the second pair is France and Germany. You are given the following information: the average saving rate in Argentina is 23.3 percent, in Chile it is 28.7 percent, in France it is 21.1 percent, and in Germany it is 20.8 percent. Assuming the countries are identical in every other way, which country would the Solow model predict to have the higher per capita real GDP? However, you find out the steady-state real per capita GDP in each of the countries is $13,300 in Argentina, $12,500 in Chile, $31,300 in France, and $34,000 in Germany. What is the primary factor that the simple Solow model uses to describe these differences? Give an example.

 

 

 

8. The Syrian civil war, which began following the “Arab Spring” in 2011, is undoubtedly a terrible tragedy. However, let us consider the economic impacts of this civil war. Use the Solow model to discuss the impacts of the war on economic growth both during the war and when the war ends.

 

 

 

9. Figure 5.10 shows the investment, or saving, rates for Albania, Botswana, and Turkey. If this were the only data to which you had access, using the Solow model, which country, during which period, would you anticipate to have the highest growth rate? Assume factor productivity and depreciation rates are the same.

Figure 5.10: Investment Rates, 1970–2014