Rensselaer Polytechnic Institute - ACCT ACCT 3371

The Solow Growth Model

1. The Solow model of economic growth
   1. endogenizes labor.
   2. endogenizes physical capital.
   3. exogenizes physical capital.
   4. exogenizes investment.
   5. endogenizes investment.

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2. 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.

3. only consumption.
4. either consumption or investment.
5. tax revenue.

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3. In the corn farm example, saving some of the corn produced
   1. yields future output, which grows over time.
   2. leads to higher consumption in the future.
   3. yields future output, which grows over time.
   4. leads to higher consumption today.
   5. both a and b.

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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.

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

b. Y_t = A±K ^2/3L ^2/3.

d. Y_t = A(±1/3)K_t • (2/3)L_t.

e. Y_t = A(±1/3)K_t + (2/3)L_t.

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7. If C_t denotes consumption, I_t denotes investment, and Y_t

is output, the resource constraint in the Solow model is

1. 1. Y_t = C_t – I_t.
   2. Y_t = C_t + I_t.

d. DK_t = I_t – d±K_t.

e. None of the above.

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8. In the Solow model, in every period, a fraction of total 13. In the Solow model, it is assumed that a(n)

output                , which                .                                                 fraction of capital depreciates regardless

1. 1. is saved; reduces next period’s capital stock
   2. depreciates; adds to next period’s capital stock
   3. is saved; adds to next period’s capital stock
   4. is consumed; adds to next period’s capital stock
   5. is consumed; reduces next period’s capital stock

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9. In the Solow model, the equation of capital accumulation is
   1. DK_t = I_t – d±K_t.
   2. K_{t + 1} = K_t + I_t – dK±_t.
   3. K_{t + 1} = K_t + I_t + dK±_t.
   4. K_{t + 1} = K_t + dK_t – I_t.
   5. Both a and b are correct.

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10. In the Solow model, if I_t > d±K_t, the capital stock
    1. declines.
    2. stays the same.
    3. grows.
    4. Not enough information is given.
    5. None of the above.

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11. In the Solow model, if investment is                    depreciation, the capital stock          .
    1. less than; declines
    2. greater than; grows
    3. greater than; declines
    4. equal to; declines
    5. a and b are correct

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12. In the Solow model, the parameter d±denotes

                  and is                .

1. 1. investment; less than one
   2. the depreciation rate; equal to zero
   3. consumption; greater than one
   4. the depreciation rate; less than one
   5. investment; greater than one

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of the capital stock.

1. increasing
2. constant
3. decreasing
4. undetermined
5. None of the above.

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14. Using the Solow model, if, in time t = 0, the initial capital stock is K₀ = 100, investment is I₀ = 25, and d±= 0.1 is the depreciation rate, capital accumulation is a. DK₀ = 35.

b. DK₀ = –15.

c. DK₀ = 15.

d. DK₀ = 0.

e. DK₀ = 115.

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15. Using the Solow model, if, in time t = 50, the capital stock is K₅₀ = 150, investment is I₅₀ = 15, and d±= 0.1 is the depreciation rate, capital accumulation is

a. DK₅₀ = 5.

b. DK₅₀ = –15.

c. DK₅₀ = 15.

d. DK₅₀ = 120.

e. DK₅₀ = 0.

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16. In the Solow model, defining ¯s as the saving rate, Y_t as output, and I_t as investment, consumption is given by
    1. C_t = ¯sI_t.

b. C_t = (1 – ¯s).

3. C_t = (1 – ¯s)Y_t.
4. C_t = (1 – ¯s)Y_t – I_t.
5. C_t = ¯sY_t.

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17. In the Solow model, defining ¯s as the saving rate, Y_t as output; and C_t as consumption, investment I_t is given by

a. I_t = (1 – ¯s).

2. I_t = ¯sY_t.
3. I_t = (1 – ¯s)C_t.
4. I_t = ¯sY_t – C_t.
5. I_t = (1 – ¯s)Y_t.

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18. The amount of capital in an economy is a (an)

                 , while the amount of investment is a (an)

                 .

1. 1. flow; stock
   2. stock; flow
   3. final good; intermediate good
   4. intermediate good; final good
   5. None of the above.

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19. Capital accumulation is a
    1. stock.
    2. flow.
    3. final good.
    4. intermediate good.
    5. None of the above.

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20. The endogenous variables in the Solow model are
    1. the capital stock, labor, and output.
    2. consumption, investment, the capital stock, labor, and the savings rate.
    3. consumption, investment, the capital stock, labor, and output.
    4. productivity and the depreciation and savings rates.
    5. the capital stock, labor, output, and the savings rate.

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21. Which of the following are an exogenous variable in the Solow model?
    1. productivity
    2. depreciation rate
    3. savings rate
    4. the initial capital stock
    5. All of the above.

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22. The Solow model assumes the saving rate is
    1. zero.
    2. constant.
    3. decreasing as income increases.
    4. increasing as income increases.
    5. larger as the interest rate rises.

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23. In the Solow model, investment, I_t, as a function of savings, ¯s, and output, Y_t = F(K_t,L)±, is written as

a. I_t = ¯s/[F(K_t,L)±].

b. I_t = ¯sF(K_t,L±)].

c. I_t = (1 – ¯s)[F(K_t,L)±].

d. I_t = ¯s – F(K_t,L±).

e. I_t = ¯s + F(K_t,L)±.

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24. A change in the capital stock, DK_t, can be expressed as a function of the saving rate, ¯s, output, F(K_t,L±), the capital stock, K_t, and the depreciation rate, d,±by
    1. DK_t = ¯sF(K_t,L±) + d±K_t.
    2. DK_t = ¯sF(K_t,L±) – dK±_t.
    3. DK_t = dF±(K_t,L±) – ¯sK_t.
    4. DK_t = ¯sF(K_t,L±)/dK±_t.
    5. DK_t = F(K_t,L±) – K_t.

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25. The equation ¯sF(K_t,L±) – d±K_t, is called
    1. saving.
    2. investment.
    3. net investment.
    4. the capital stock.
    5. depreciation.

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26. In the Solow model, net investment is defined as
    1. investment plus capital depreciation.
    2. investment minus capital depreciation.
    3. the savings rate minus the depreciation rate.
    4. the savings rate plus the depreciation rate.
    5. None of the above.

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27. In the Solow model, if net investment is positive,
    1. capital accumulation is zero.
    2. capital accumulation is negative.
    3. capital accumulation is positive.
    4. Not enough information is given.
    5. savings are negative.

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28. In Figure 5.1, if the economy begins with the initial capital stock at K₁, the capital stock will              and the economy will                   .
    1. decrease, grow
    2. increase, grow
    3. stay constant, shrink
    4. decrease, shrink
    5. stay constant, grow

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Figure 5.1: Solow Diagram

31. In Figure 5.1, the capital stock at K₁ is not the steady state because
    1. the savings rate is too low.
    2. the savings 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.

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

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33. The steady state is defined as the point where capital accumulation, DK_t, is equal to
    1. the savings rate.
    2. zero.

K1            K2    K3

CAPITAL, K

1. 3. the depreciations rate.
   4. the productivity growth rate.

29. In Figure 5.1, if the economy begins with the initial capital stock at K₂, the capital stock will              and the economy will                   .
    1. decrease, grow
    2. increase, grow
    3. stay constant; be in its steady state
    4. stay constant, shrink
    5. stay constant, grow

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30. In Figure 5.1, if the economy begins with the initial capital stock at K₁, the capital stock        and the economy                    .
    1. will increase; grow
    2. will decrease; shrink
    3. stay constant; is in its steady state
    4. will decrease; is in its steady state
    5. will stay constant; shrink

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e. the population growth rate.

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34. If we define the saving rate as ¯s, output as F(K_t,L±), and the depreciation rate as d±, and if ¯sF(K_t,L±) – dK±_t = 0, the economy is
    1. contracting.
    2. growing.
    3. at the steady state.
    4. in its short-run equilibrium.
    5. None of the above.

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35. If we define the saving rate as ¯s, output as F(K_t,L±), and the depreciation rate as d±, and if sF(K_t,L)±> dK±_t, the economy is
    1. contracting.
    2. at the steady state.
    3. growing.
    4. in its short-run equilibrium.
    5. None of the above.

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36. The Solow model assumes
    1. the capital stock is constant.
    2. the number of workers is growing.
    3. the number of workers is constant.
    4. the saving rate changes each period.
    5. the depreciation rate changes each period.

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37. In the Solow model, if, in the absence of any shocks, the capital stock remains at K* forever, this rest point is called the  of the Solow model.
    1. savings rate
    2. short-run equilibrium
    3. steady state
    4. the rate of capital accumulation
    5. None of the above.

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38. In the Solow model, if capital is in the steady state, then 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.

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39. In the Solow model, the steady-state level of output per worker is a function of
    1. productivity.
    2. the initial capital stock, productivity, and the savings rate.
    3. the initial capital stock, productivity, and the depreciation rate.
    4. the initial capital stock and the steady-state level of capital stock.
    5. productivity, the depreciation rate, and the savings rate.

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40. In the Solow model, the steady-state capital stock is a function of
    1. productivity.
    2. the initial capital stock, productivity, and the savings 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 savings rate.

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41. Assume a production function is given by Y =

a. 0.3.

b. 1.3.

c. 2.8.

d. 0.8.

e. 1.6.

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42. Assume a production function is given by Y =

a. 0.1.

b. 2.5.

c. 1.6.

d. 8.0.

e. 0.6.

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43. Assume a production function is given by Y =

a. 8.0.

b. 4.0.

c. 45.3.

d. 2.0.

e. 22.6

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47. In Figure 5.2, at K₂, capital accumulation is

savings rate, s, is 20 percent, the depreciation rate, d±, is                                                     ; the economy is                                                                                       ; and

10 percent, and A±= L±= 1, the steady-state level of output is

1. 1.
2. 4.
3. 2.
4. 8.
5. 3.

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

46. In Figure 5.2, at K₁, the difference between ¯sY and d±K

is                 and the difference between Y and ¯sY is

                 .

1. 1. output; investment
   2. net investment; consumption
   3. gross investment; consumption
   4. output; consumption
   5. depreciation; gross investment

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Figure 5.2: Solow Diagram

consumption is              .

1. positive; growing; positive
2. zero; in the steady state; zero
3. negative; growing; positive
4. zero; in the steady state; positive
5. zero; contracting; negative

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48. In the Solow model, it is assumed a(n)        fraction of capital depreciates each period.
    1. zero
    2. increasing
    3. decreasing
    4. constant
    5. None of the above.

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49. An increase in the            leads to a higher steady-state capital stock; and a decline in           leads to a lower steady-state capital stock.
    1. savings rate; depreciation rate
    2. savings rate; productivity
    3. productivity; the initial capital stock
    4. depreciation rate; the labor stock
    5. None of the above.

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50. An increase in the            leads to a higher steady-state level of output; and a decline in

                  leads to a lower steady-state level of output.

1. 1. savings rate; depreciation rate
   2. savings rate; productivity
   3. productivity; the initial capital stock
   4. depreciation rate; the labor stock
   5. None of the above.

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51. An increase in the            leads to a higher

steady-state level of output per worker; and a decline in

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

1. 1. productivity; savings rate
   2. savings rate; productivity

K1                  K2

CAPITAL, K

1. 3. savings rate; depreciation rate
   4. Both a and b are correct.
   5. None of the above.

52. In the standard production model, the productivity parameter enters the equation with an exponent of one, while in the Solow model 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 standard production function model.
    3. the productivity measure is zero in the standard production function model.
    4. the productivity measure is negative in the Solow model.

d. the exogenous level of the capital stock itself depends on productivity.

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53. In the Solow model, the           plays a

                  role than it does in the standard production function model.

1. 1. labor supply; larger
   2. productivity parameter; larger
   3. capital stock; larger
   4. capital stock; smaller
   5. productivity parameter; smaller

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54. 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.
    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 the above is correct.

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

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56. According to the Solow model, in the steady state, countries with high savings rates should have a
    1. low labor-output ratio.
    2. low capital-output ratio.
    3. high capital-output ratio.
    4. high depreciation rate.
    5. None of the above.

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57. Suppose you are given the data for Brazil and Portugal. In Brazil, the savings rate is 0.1 and the depreciation rate is 0.1, while in Portugal the savings 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.

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58. 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. the steady-state capital stock.
    2. the initial capital stock and savings rates.
    3. differences in productivity and savings rates.
    4. the labor stock and savings rates.
    5. None of the above.

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Section: 5.

59. If we define ¯s₁/¯s₂ as the savings rates in Countries 1 and 2, respectively; d₁±= d±₂ as the depreciation rates in Countries 1 and 2; A₁±/A₂±as productivity in Countries 1 and 2; and the production function per worker is

62. 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.

y∗    ?

?3/2  

? s  ?1/2

1. 5. None of the above is correct.

×?     1 ?   .

2    ?? A2 ??

?? s 2 ??

.

y∗    ?

?3/2  

? s  ?1/2

×?   1 ?   .

63. An implication of the Solow model is that, once an

2 ??                        ?? s 2 ??

economy reaches the steady state,

y^∗    ? s

?3/2 ?

?1/2

1. 1. per capita consumption is constant.

×? A1 ?   .

∗   ?? s 2 ??

?? A2 ??

1. 2. per capita output is constant.
   3. per capita capital is constant.

y∗   ? d

?3/2  

1. 4. per capita consumption continues to grow.

∗   ?? d

2 ??

?1/2  

1. 5. a, b, and c are correct.

.

∗   ?? s 2 ??

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60. If we define ¯s₁/¯s₂ as the savings rates in Countries 1 and 2, respectively, and A₁±/A±₂ as productivity in Countries 1 and 2, in the Solow model, the equation       predicts that         contributes the majority to differences in steady-state output per worker.

64. A central lesson of the Solow model is a bit of a surprise:
    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. Capital accumulation is the only engine of short-run per capita economic growth.

productivity differences

1. 4. Savings rates serve as the engine of long-run per capita economic growth.

b.  ^y∗    =( A  )3/2  ×( s  )1/2; savings rate differences

e. Both a and c are correct.

^∗      A2       s 2

5. ^y∗    =( s  )1/2; savings rate differences

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65. In the Solow model, saving and investing in additional factories and computers does       . But in the long-run, the        accumulation leads the

^∗      s 2

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61. If the depreciation and savings rate are constant, the economy eventually will settle in 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.

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return to these investments to fall.

1. lead output to grow in the medium run; diminishing returns to capital
2. lead output to grow in the long run; increasing returns to capital
3. lead output to grow in the medium run; increasing returns to capital
4. not lead output to grow in the medium run; diminishing returns to capital
5. not lead output to grow in the long run; diminishing returns to capital

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66. Which of the following best answers the question, Can growth in the labor force lead 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 total production can grow as the population of the economy grows.
    3. Never—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. a and b are correct.

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67. 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 with no growth in output per person.
    3. the economy eventually settles down to a steady state with no growth in output per person.
    4. the economy eventually settles down to a steady

69. Consider the Solow model exhibited in Figure 5.3. 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.

0. 2. For any single country, the movement from point c to b is due to an increase in capital stock for the savings rate ¯s₂ .
   3. If ¯s₁/¯s₂ stands for the saving rates in Countries 1 and 2, respectively, Country 2 has a lower savings rate.
1. i
2. ii
3. iii
4. i and ii
5. i, ii, and iii

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70. 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

state with no growth in aggregate output.                                level of total output and         

e. None of the above is correct.

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68. Consider Figure 5.3, which 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
    2. 1; higher
    3. 2; higher
    4. 1; lower
    5. Not enough information is given.

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Figure 5.3: Solow Diagram

rate of growth of output as (than) the country with the lower saving rate.

1. a higher; a higher
2. higher; the same
3. a lower; a higher
4. a higher; a lower
5. the same; the same

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71. 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. moves from a relatively low steady state to one that is higher.
    5. stays at a constant steady state.

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CAPITAL, K

72. A decline in the investment rate causes
    1. the steady-state level of output and capital to rise.
    2. the steady-state level of output to rise and capital to fall.
    3. the steady-state level of output and capital to fall.
    4. the steady-state level of output and capital to remain constant.
    5. the steady-state level of output to rise and capital to remain constant.

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73. Consider the Solow model exhibited in Figure 5.4. Which of the following are true?

1. If 1 denotes Country 1 and 2 denotes Country 2, Country 1 has a higher savings 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
2. ii
3. iii
4. ii and iii
5. i, ii, and iii

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Figure 5.4: Solow Diagram

CAPITAL, K

74. Consider Figure 5.4, which 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
    2. 1; lower
    3. 2; higher
    4. 2; lower
    5. Not enough information is given.

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75. Immediately following the increase in the investment rate, output grows rapidly. As the economy approaches its new steady state,
    1. the growth rate gradually increases.
    2. the growth rate gradually declines.
    3. the growth rate is constant.
    4. the growth rate is negative.
    5. None of the above is correct.

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76. The analysis of how an economy approaches the steady state is called
    1. investment.
    2. economic growth.
    3. transition dynamics.
    4. savings.
    5. depreciation.

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77. 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. the further below its steady state an economy is, the slower the economy will grow.

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78. Consider Figure 5.5. If K_SK is the current capital stock           80. Among the OECD countries, those that were relatively

in South Korea and K_CH is the current capital stock in                   in 1960                between 1960 and

China, according to principle of transition dynamics

1. 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.

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Figure 5.5: Solow Diagram

2000.

1. poor; grew slowly
2. rich; grew quickly
3. poor; grew quickly
4. rich; did not grow
5. poor; did not grow

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81. Among the world as a whole, there is        correlation between how poor a country was in 1960 and how fast it             from 1960 to 2000.
    1. almost no; grew
    2. a strong positive; grew
    3. a strong positive; contracted
    4. a strong negative; contracted
    5. almost no; contracted

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82. Among the world as a whole, there is        correlation between how rich a country is and how fast it                   from 1960 to 2000.
    1. a strong positive; grew
    2. almost no; grew
    3. a strong positive; contracted
    4. a strong positive; contracted

KCH    KSK

CAPITAL, K

1. 5. almost no; contracted

79. If the current capital stock in South Korea is greater than the current capital stock in China, according to 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.

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83. If both rich and poor countries grow at the same rate, on average, this suggests that
    1. most countries are contracting.
    2. most countries still are growing.
    3. no countries have reached their steady state.
    4. most countries have reached their steady state.
    5. most countries are unproductive.

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84. If South Korea’s steady state GDP per worker is higher than that of the Philippines, you might conclude that
    1. the investment rate in South Korea is higher than in the Philippines.
    2. South Korea is more productive than the Philippines.
    3. the depreciation rate in South Korea is higher than in the Philippines.
    4. a and b are correct.
    5. None of the above is correct.

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