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Rensselaer Polytechnic Institute  ACCT ACCT 3371
CHAPTER 5
The Solow Growth Model
MULTIPLECHOICE
The Solow model of economic growth
endogenizes labor
Rensselaer Polytechnic Institute  ACCT ACCT 3371
CHAPTER 5
The Solow Growth Model
MULTIPLECHOICE
The Solow model of economic growth
endogenizes labor
Accounting
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Rensselaer Polytechnic Institute  ACCT ACCT 3371
CHAPTER 5
MULTIPLECHOICE
 The Solow model of economic growth
 endogenizes labor.
 endogenizes physical capital.
 exogenizes physical capital.
 exogenizes investment.
 endogenizes investment.
.
 The key insight in the Solow model is that
 saving rates are determined in a particular manner.
 savings have no impact on economic growth
 capital depreciation enhances economic growth.
 the relationship between capital and output is static.
 capital accumulation contributes to economic growth.
 only consumption.
 either consumption or investment.
 tax revenue.
.
 In the corn farm example, saving some of the corn produced
 yields future output, which grows over time.
 leads to higher consumption in the future.
 yields future output, which grows over time.
 leads to higher consumption today.
 both a and b.
.

The production function used in the Solow model is a. Yt = K 1/3L 2/3.
.
 The Solow model describes
 how saving rates are determined.
 the static relationship between capital and output.
 how savings, population growth, and technological change affect output over time.
 how savings, population growth, and technological change affect output in a single period.
 what constitutes technological change.
.
 In the corn farm example, corn can be used as
 only investment.
 either saving or depreciation.
b. Y_{t} = A±K ^{2/3}L ^{2/3}.
c. Y_{t} = AK±1/3L ^{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}.
.
 If C_{t} denotes consumption, I_{t} denotes investment, and Y_{t}
is output, the resource constraint in the Solow model is

 Y_{t} = C_{t} – I_{t}.
 Y_{t} = C_{t} + I_{t}.
c. Y_{t} = AK±1/3L ^{2/3}.
d. DK_{t} = I_{t} – d±K_{t}.
e. None of the above.
.
39
 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

 is saved; reduces next period’s capital stock
 depreciates; adds to next period’s capital stock
 is saved; adds to next period’s capital stock
 is consumed; adds to next period’s capital stock
 is consumed; reduces next period’s capital stock
.
 In the Solow model, the equation of capital accumulation is
 DK_{t} = I_{t} – d±K_{t}.
 K_{t} _{+} _{1} = K_{t} + I_{t} – dK±_{t}.
 K_{t} _{+} _{1} = K_{t} + I_{t} + dK±_{t}.
 K_{t} _{+} _{1} = K_{t} + dK_{t} – I_{t}.
 Both a and b are correct.
.
 In the Solow model, if I_{t} > d±K_{t}, the capital stock
 declines.
 stays the same.
 grows.
 Not enough information is given.
 None of the above.
.
 In the Solow model, if investment is depreciation, the capital stock .
 less than; declines
 greater than; grows
 greater than; declines
 equal to; declines
 a and b are correct
.
 In the Solow model, the parameter d±denotes
and is .

 investment; less than one
 the depreciation rate; equal to zero
 consumption; greater than one
 the depreciation rate; less than one
 investment; greater than one
.
of the capital stock.
 increasing
 constant
 decreasing
 undetermined
 None of the above.
.
 Using the Solow model, if, in time t = 0, the initial capital stock is K_{0} = 100, investment is I_{0} = 25, and d±= 0.1 is the depreciation rate, capital accumulation is a. DK_{0} = 35.
b. DK_{0} = –15.
c. DK_{0} = 15.
d. DK_{0} = 0.
e. DK_{0} = 115.
.
 Using the Solow model, if, in time t = 50, the capital stock is K_{50} = 150, investment is I_{50} = 15, and d±= 0.1 is the depreciation rate, capital accumulation is
a. DK_{50} = 5.
b. DK_{50} = –15.
c. DK_{50} = 15.
d. DK_{50} = 120.
e. DK_{50} = 0.
.
 In the Solow model, defining ¯s as the saving rate, Y_{t} as output, and I_{t} as investment, consumption is given by
 C_{t} = ¯sI_{t}.
b. C_{t} = (1 – ¯s).
 C_{t} = (1 – ¯s)Y_{t}.
 C_{t} = (1 – ¯s)Y_{t} – I_{t}.
 C_{t} = ¯sY_{t}.
.
 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).
 I_{t} = ¯sY_{t}.
 I_{t} = (1 – ¯s)C_{t}.
 I_{t} = ¯sY_{t} – C_{t}.
 I_{t} = (1 – ¯s)Y_{t}.
.
 The amount of capital in an economy is a (an)
, while the amount of investment is a (an)
.

 flow; stock
 stock; flow
 final good; intermediate good
 intermediate good; final good
 None of the above.
.
 Capital accumulation is a
 stock.
 flow.
 final good.
 intermediate good.
 None of the above.
.
 The endogenous variables in the Solow model are
 the capital stock, labor, and output.
 consumption, investment, the capital stock, labor, and the savings rate.
 consumption, investment, the capital stock, labor, and output.
 productivity and the depreciation and savings rates.
 the capital stock, labor, output, and the savings rate.
.
 Which of the following are an exogenous variable in the Solow model?
 productivity
 depreciation rate
 savings rate
 the initial capital stock
 All of the above.
.
 The Solow model assumes the saving rate is
 zero.
 constant.
 decreasing as income increases.
 increasing as income increases.
 larger as the interest rate rises.
.
 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)±.
.
 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
 DK_{t} = ¯sF(K_{t},L±) + d±K_{t}.
 DK_{t} = ¯sF(K_{t},L±) – dK±_{t}.
 DK_{t} = dF±(K_{t},L±) – ¯sK_{t}.
 DK_{t} = ¯sF(K_{t},L±)/dK±_{t}.
 DK_{t} = F(K_{t},L±) – K_{t}.
.
 The equation ¯sF(K_{t},L±) – d±K_{t}, is called
 saving.
 investment.
 net investment.
 the capital stock.
 depreciation.
.
 In the Solow model, net investment is defined as
 investment plus capital depreciation.
 investment minus capital depreciation.
 the savings rate minus the depreciation rate.
 the savings rate plus the depreciation rate.
 None of the above.
.
 In the Solow model, if net investment is positive,
 capital accumulation is zero.
 capital accumulation is negative.
 capital accumulation is positive.
 Not enough information is given.
 savings are negative.
.
 In Figure 5.1, if the economy begins with the initial capital stock at K_{1}, the capital stock will and the economy will .
 decrease, grow
 increase, grow
 stay constant, shrink
 decrease, shrink
 stay constant, grow
.
Figure 5.1: Solow Diagram
INVESTMENT, DEPRECIATION
 In Figure 5.1, the capital stock at K_{1} is not the steady state because
 the savings rate is too low.
 the savings rate is too high.
 the depreciation rate is too low.
 gross investment is higher than capital depreciation.
 gross investment is lower than capital depreciation.
.
 In Figure 5.1, at K_{1}, net investment is and the economy .
 negative; will grow
 positive; is in its steady state
 zero; is in its steady state
 positive; will grow
 negative; will contract
.
 The steady state is defined as the point where capital accumulation, DK_{t}, is equal to
 the savings rate.
 zero.
K1 K2 K3
CAPITAL, K

 the depreciations rate.
 the productivity growth rate.
 In Figure 5.1, if the economy begins with the initial capital stock at K_{2}, the capital stock will and the economy will .
 decrease, grow
 increase, grow
 stay constant; be in its steady state
 stay constant, shrink
 stay constant, grow
.
 In Figure 5.1, if the economy begins with the initial capital stock at K_{1}, the capital stock and the economy .
 will increase; grow
 will decrease; shrink
 stay constant; is in its steady state
 will decrease; is in its steady state
 will stay constant; shrink
.
e. the population growth rate.
.
 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
 contracting.
 growing.
 at the steady state.
 in its shortrun equilibrium.
 None of the above.
.
 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
 contracting.
 at the steady state.
 growing.
 in its shortrun equilibrium.
 None of the above.
.
 The Solow model assumes
 the capital stock is constant.
 the number of workers is growing.
 the number of workers is constant.
 the saving rate changes each period.
 the depreciation rate changes each period.
.
 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.
 savings rate
 shortrun equilibrium
 steady state
 the rate of capital accumulation
 None of the above.
.
 In the Solow model, if capital is in the steady state, then output
 will continue to grow.
 is also in the steady state.
 will continue to grow but its rate of growth will slow down.
 will decline but its rate of growth will be positive.
 will begin to contract.
.
 In the Solow model, the steadystate level of output per worker is a function of
 productivity.
 the initial capital stock, productivity, and the savings rate.
 the initial capital stock, productivity, and the depreciation rate.
 the initial capital stock and the steadystate level of capital stock.
 productivity, the depreciation rate, and the savings rate.
.
 In the Solow model, the steadystate capital stock is a function of
 productivity.
 the initial capital stock, productivity, and the savings rate.
 the initial capital stock, productivity, and the depreciation rate.
 the labor stock and the steadystate level of capital stock.
 productivity, the depreciation rate, the labor stock, and the savings rate.
.
 Assume a production function is given by Y =
A±K ^{1/3}L^{2}±/3. If A±= L±= 1, the depreciation rate is d±= 0.05, and the savings rate is ¯s = 0.1, the steadystate level of capital is about
a. 0.3.
b. 1.3.
c. 2.8.
d. 0.8.
e. 1.6.
.
 Assume a production function is given by Y =
A±K ^{1/3}L^{2}±/3. If A±= 2 and L±= 1, the depreciation rate is d±= 0.05, and the savings rate is ¯s = 0.1, the steadystate level of capital is about
a. 0.1.
b. 2.5.
c. 1.6.
d. 8.0.
e. 0.6.
.
 Assume a production function is given by Y =
A±K ^{1/3}L^{2}±/3. If A±= 2 and L±= 1, and the steady state capital stock is 8.0, the steadystate level of capital is about
a. 8.0.
b. 4.0.
c. 45.3.
d. 2.0.
e. 22.6
.

If the production function is given by Y = A±K ^{1/3}L^{2}±/3, the
47. In Figure 5.2, at K_{2}, 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 steadystate level of output is
 1.
 4.
 2.
 8.
 3.
.
 The steadystate level of output per worker in the Solow model, with the production function Y =
AK±1/3L^{2}±/3, is given by
a. y∗ = A ( s )1/2.
b. Y ∗ = A3/2( s )1/2 L.
c. y∗ = A3/2 ( s )1/2 L.
d. y∗ = A3/2( s )1/2.
e. y∗ = A ( s )1/3.
 In Figure 5.2, at K_{1}, the difference between ¯sY and d±K
is and the difference between Y and ¯sY is
.

 output; investment
 net investment; consumption
 gross investment; consumption
 output; consumption
 depreciation; gross investment
.
Figure 5.2: Solow Diagram
INVESTMENT, DEPRECIATION AND OUTPUT
consumption is .
 positive; growing; positive
 zero; in the steady state; zero
 negative; growing; positive
 zero; in the steady state; positive
 zero; contracting; negative
.
 In the Solow model, it is assumed a(n) fraction of capital depreciates each period.
 zero
 increasing
 decreasing
 constant
 None of the above.
.
 An increase in the leads to a higher steadystate capital stock; and a decline in leads to a lower steadystate capital stock.
 savings rate; depreciation rate
 savings rate; productivity
 productivity; the initial capital stock
 depreciation rate; the labor stock
 None of the above.
.
 An increase in the leads to a higher steadystate level of output; and a decline in
leads to a lower steadystate level of output.

 savings rate; depreciation rate
 savings rate; productivity
 productivity; the initial capital stock
 depreciation rate; the labor stock
 None of the above.
.
 An increase in the leads to a higher
steadystate level of output per worker; and a decline in
leads to a lower steadystate level of output per worker.

 productivity; savings rate
 savings rate; productivity
K1 K2
CAPITAL, K

 savings rate; depreciation rate
 Both a and b are correct.
 None of the above.
 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
 the endogenous level of the capital stock itself depends on productivity.
 there is no productivity parameter in the standard production function model.
 the productivity measure is zero in the standard production function model.
 the productivity measure is negative in the Solow model.
d. the exogenous level of the capital stock itself depends on productivity.
.
 In the Solow model, the plays a
role than it does in the standard production function model.

 labor supply; larger
 productivity parameter; larger
 capital stock; larger
 capital stock; smaller
 productivity parameter; smaller
.
 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
 the same steadystate level of output as it would have before the disaster.
 a higher steadystate level of output than it would have before the disaster.
 a lower steadystate level of output than it would have before the disaster.
 Not enough information is given.
 None of the above is correct.
.
 The key difference between the Solow model and the production model is
 the Solow model endogenizes the process of capital accumulation.
 the standard model endogenizes the process of capital accumulation.
 the Solow model uses different values for the capital share.
 the Solow model does not contain a productivity measure.
 the Solow model exogenizes the process of capital accumulation.
.
 According to the Solow model, in the steady state, countries with high savings rates should have a
 low laboroutput ratio.
 low capitaloutput ratio.
 high capitaloutput ratio.
 high depreciation rate.
 None of the above.
.
 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
 Brazil has a higher level of output than Portugal.
 Brazil has a higher capitaloutput ratio than Portugal.
 Portugal has a higher level of output than Brazil.
 Portugal has a higher capitaloutput ratio than Brazil.
 Portugal and Brazil have the same capitaloutput ratio.
.
 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
 the steadystate capital stock.
 the initial capital stock and savings rates.
 differences in productivity and savings rates.
 the labor stock and savings rates.
 None of the above.
.
Section: 5.
 If we define ¯s_{1}/¯s_{2} as the savings rates in Countries 1 and 2, respectively; d_{1}±= d±_{2} as the depreciation rates in Countries 1 and 2; A_{1}±/A_{2}±as productivity in Countries 1 and 2; and the production function per worker is
y_{t} = A±K ^{1/3}, the Solow model predicts the difference in GDP per worker between Countries 1 and 2 is
 An implication of the Solow model is that, once an economy reaches the steady state,
 longterm growth continues indefinitely.
 longterm growth does not continue.
 longterm growth accelerates.
 longterm growth decelerates.
y∗ ?
?3/2
? s ?1/2

 None of the above is correct.
a. 1 =? A1 ?
×? 1 ? .
b. ^{1} =? d 1 ?
×? 1 ? .
 An implication of the Solow model is that, once an
∗ ?? d
2 ?? ?? s 2 ??
economy reaches the steady state,
y^{∗} ? s
?3/2 ?
?1/2

 per capita consumption is constant.
c. ^{ } ^{1} =? 1 ?
×? A1 ? .
∗ ?? s 2 ??
?? A2 ??

 per capita output is constant.
 per capita capital is constant.
y∗ ? d
?3/2

 per capita consumption continues to grow.
∗ ?? d
y^{∗} ? s
2 ??
?1/2

 a, b, and c are correct.
.
∗ ?? s 2 ??
.
60. If we define ¯s_{1}/¯s_{2} as the savings rates in Countries 1 and 2, respectively, and A_{1}±/A±_{2} as productivity in Countries 1 and 2, in the Solow model, the equation predicts that contributes the majority to differences in steadystate output per worker.
 A central lesson of the Solow model is a bit of a surprise:
 Capital accumulation cannot serve as the engine of longrun per capita economic growth.
 Capital accumulation is the only engine of longrun per capita economic growth.
 Capital accumulation is the only engine of shortrun per capita economic growth.
∗ ( A1 )3/2;
productivity differences

 Savings rates serve as the engine of longrun per capita economic growth.
b. ^{y}∗ =( A )3/2 ×( s )1/2; savings rate differences
e. Both a and c are correct.
.
 If the depreciation and savings rate are constant, the economy eventually will settle in the steady state in the Solow model because of
 the lack of productivity.
 increasing returns to capital in production.
 constant returns to capital in production.
 diminishing returns to capital in production.
 increasing returns to labor in production.
.
return to these investments to fall.
 lead output to grow in the medium run; diminishing returns to capital
 lead output to grow in the long run; increasing returns to capital
 lead output to grow in the medium run; increasing returns to capital
 not lead output to grow in the medium run; diminishing returns to capital
 not lead output to grow in the long run; diminishing returns to capital
.
 Which of the following best answers the question, Can growth in the labor force lead to overall economic growth?
 Population growth can produce growth in the Solow model in the aggregate but not in output per person.
 Total capital and total production can grow as the population of the economy grows.
 Never—only capital contributes to aggregate economic growth.
 Population growth can produce growth in the Solow model in the aggregate and in output per person.
 a and b are correct.
.
 In the Solow model, with population growth,
 there is no steady state in output per person.
 the economy never settles down to a steady state with no growth in output per person.
 the economy eventually settles down to a steady state with no growth in output per person.
 the economy eventually settles down to a steady
 Consider the Solow model exhibited in Figure 5.3. Which of the following is (are) true?
 For any single country, the movement from point a
to b is due to an increase in the saving rate, ¯s_{1} > ¯s_{2}.

 For any single country, the movement from point c to b is due to an increase in capital stock for the savings rate ¯s_{2} .
 If ¯s_{1}/¯s_{2} stands for the saving rates in Countries 1 and 2, respectively, Country 2 has a lower savings rate.
 i
 ii
 iii
 i and ii
 i, ii, and iii
.
 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.
.
 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.
 2; lower
 1; higher
 2; higher
 1; lower
 Not enough information is given.
.
Figure 5.3: Solow Diagram
INVESTMENT, DEPRECIATION
rate of growth of output as (than) the country with the lower saving rate.
 a higher; a higher
 higher; the same
 a lower; a higher
 a higher; a lower
 the same; the same
.
 In the Solow model, if a country’s saving rate increases, the country
 moves from a relatively low steady state to one that is lower.
 moves from a relatively low steady state to one that is higher.
 moves from a relatively high steady state to one that is lower.
 moves from a relatively low steady state to one that is higher.
 stays at a constant steady state.
.
 A decline in the investment rate causes
 the steadystate level of output and capital to rise.
 the steadystate level of output to rise and capital to fall.
 the steadystate level of output and capital to fall.
 the steadystate level of output and capital to remain constant.
 the steadystate level of output to rise and capital to remain constant.
.
 Consider the Solow model exhibited in Figure 5.4. Which of the following are true?
 If 1 denotes Country 1 and 2 denotes Country 2, Country 1 has a higher savings rate.
 If 1 denotes Country 1 and 2 denotes Country 2, Country 1 has a lower depreciation rate.
 If 1 denotes Country 1 and 2 denotes Country 2, Country 2 has a lower steady state.
 i
 ii
 iii
 ii and iii
 i, ii, and iii
.
Figure 5.4: Solow Diagram
INVESTMENT, DEPRECIATION
CAPITAL, K
 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; higher
 1; lower
 2; higher
 2; lower
 Not enough information is given.
.
 Immediately following the increase in the investment rate, output grows rapidly. As the economy approaches its new steady state,
 the growth rate gradually increases.
 the growth rate gradually declines.
 the growth rate is constant.
 the growth rate is negative.
 None of the above is correct.
.
 The analysis of how an economy approaches the steady state is called
 investment.
 economic growth.
 transition dynamics.
 savings.
 depreciation.
.
 The principle of transition dynamics can be summarized as
 the further below its steady state an economy is, the faster the economy will grow.
 the closer to its steady state an economy is, the faster the economy will grow.
 the further below its steady state an economy is, the slower the economy will grow.
 regardless of how close to its steady state an economy is, the economy grows at the same rate.
 the further below its steady state an economy is, the slower the economy will grow.
.
 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

 China initially will grow faster than South Korea, but each will have the same steady state.
 China initially will grow slower than South Korea, but each will have the same steady state.
 China initially will grow faster than South Korea and will have a higher steady state.
 China initially will grow faster than South Korea and will have a lower steady state.
 Both South Korea and China initially will grow at the same rate and have the same steady state.
.
Figure 5.5: Solow Diagram
INVESTMENT, DEPRECIATION
2000.
 poor; grew slowly
 rich; grew quickly
 poor; grew quickly
 rich; did not grow
 poor; did not grow
.
 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.
 almost no; grew
 a strong positive; grew
 a strong positive; contracted
 a strong negative; contracted
 almost no; contracted
.
 Among the world as a whole, there is correlation between how rich a country is and how fast it from 1960 to 2000.
 a strong positive; grew
 almost no; grew
 a strong positive; contracted
 a strong positive; contracted
KCH KSK
CAPITAL, K

 almost no; contracted
 If the current capital stock in South Korea is greater than the current capital stock in China, according to principle of transition dynamics,
 China initially will grow faster than South Korea, but each will have the same steady state.
 China initially will grow slower than South Korea, but each will have the same steady state.
 China initially will grow faster than South Korea and will have a higher steady state.
 China initially will grow faster than South Korea and will have a lower steady state.
 Both South Korea and China initially will grow at the same rate and have the same steady state.
.
 If both rich and poor countries grow at the same rate, on average, this suggests that
 most countries are contracting.
 most countries still are growing.
 no countries have reached their steady state.
 most countries have reached their steady state.
 most countries are unproductive.
.
 If South Korea’s steady state GDP per worker is higher than that of the Philippines, you might conclude that
 the investment rate in South Korea is higher than in the Philippines.
 South Korea is more productive than the Philippines.
 the depreciation rate in South Korea is higher than in the Philippines.
 a and b are correct.
 None of the above is correct.
.
 For which of the following does the Solow model not
provide adequate explanations?

 why savings rates differ across countries
 the cause of productivity differences across countries
 why population growth rates differ across countries
 what causes longterm economic growth
 All of the above.
.