Macroeconomics Quiz: Drivers Of Long Run Growth

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Drivers Of Long Run GrowthQuestion 1 of 20

An economy has the aggregate production function $Y = A K^{0.5} L^{0.5}$ . If the Solow residual is measured to be 1%, the labor force grows at 1%, and the capital stock grows at 4%, what is the growth rate of output per worker?

1.5%

2.0%

2.5%

3.5%

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Macroeconomics Quiz: Drivers Of Long Run Growth

Practice Drivers Of Long Run Growth in Macroeconomics with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Drivers Of Long Run Growth, giving you a quick way to practice the rules, question types, and explanations that matter most for Macroeconomics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

1.5%
2.0%
2.5% (correct answer)
3.5%

Explanation: This problem can be solved in two ways. First, we can find the growth rate of total output (

g_Y

) and then subtract the growth rate of labor (

g_L

). The capital share

\alpha

is 0.5.

g_Y = g_A + \alpha g_K + (1-\alpha)g_L = 1\% + 0.5(4\%) + 0.5(1\%) = 1\% + 2\% + 0.5\% = 3.5\%

. The growth rate of output per worker is

g_{Y/L} = g_Y - g_L = 3.5\% - 1\% = 2.5\%

. Alternatively, we can use the per-worker growth accounting equation:

g_{Y/L} = g_A + \alpha g_{K/L}

. The growth rate of the capital-labor ratio is

g_{K/L} = g_K - g_L = 4\% - 1\% = 3\%

. Plugging this in gives

g_{Y/L} = 1\% + 0.5(3\%) = 1\% + 1.5\% = 2.5\%

. Choice A is only the contribution from capital deepening (

\alpha g_{K/L}

). Choice B is a plausible miscalculation. Choice D is the growth rate of total output, not output per worker.

Question 2

Consider two economies with identical production functions $Y = AK^{0.3}L^{0.7}$ , savings rates, and depreciation rates. Economy X has a population growth rate of 2% while Economy Y has a population growth rate of 4%. If both economies start below their respective steady states, which statement about their long-run growth accounting is most accurate?

Economy Y will have higher steady-state output per worker and higher long-run per capita growth than Economy X
Economy X will have higher steady-state output per worker and both economies will have identical long-run per capita growth rates (correct answer)
Economy Y will have higher steady-state output per worker and both economies will have identical long-run per capita growth rates
Economy X will have higher steady-state output per worker and higher long-run per capita growth than Economy Y

Explanation: In the Solow model, higher population growth reduces steady-state capital per worker because the same amount of investment must be spread across more workers. Economy X (lower population growth) will have higher steady-state capital per worker and thus higher output per worker. However, in the long run, both economies grow at the rate of technological progress (zero here), so per capita growth rates are identical. Choice A incorrectly suggests Y has higher output per worker. Choice C incorrectly suggests Y has higher output per worker. Choice D incorrectly suggests different long-run growth rates.

Question 3

Two countries have identical Cobb-Douglas production functions $Y = K^{\alpha}L^{1-\alpha}$ with $\alpha = 0.3$ . Country A has a savings rate of 20% while Country B has a savings rate of 40%. If both countries are initially at their respective steady states, what is the ratio of output per worker in Country B to output per worker in Country A?

$2^{1/0.7} \approx 2.85$
$2^{1/0.3} \approx 6.35$
$2^{0.3/0.7} \approx 1.52$ (correct answer)
$2^{0.7/0.3} \approx 5.28$

Explanation: In steady state,

k^* = \left(\frac{s}{n+\delta}\right)^{\frac{1}{1-\alpha}}

and

y^* = (k^*)^{\alpha}

. The ratio of capital per worker is

\frac{k_B^*}{k_A^*} = \left(\frac{0.4}{0.2}\right)^{\frac{1}{0.7}} = 2^{1/0.7}

. The ratio of output per worker is

\frac{y_B^*}{y_A^*} = \left(\frac{k_B^*}{k_A^*}\right)^{\alpha} = \left(2^{1/0.7}\right)^{0.3} = 2^{0.3/0.7}

. Choice A gives the capital ratio, not output ratio. Choice B incorrectly uses

1/\alpha

. Choice D incorrectly uses

\alpha/(1-\alpha)

in the wrong position.

Question 4

An economy's aggregate production function exhibits constant returns to scale with output elasticities of 0.4 for capital and 0.6 for labor. Over a five-year period, output grows at 5% annually, the capital stock grows at 7% annually, labor input grows at 2% annually, and measured total factor productivity grows at 2% annually. What does this pattern most likely indicate about the sources of growth?

There is likely measurement error since the calculated contributions sum to 6.0% while actual output growth is only 5%, suggesting either overestimated input growth or unmeasured factor utilization changes (correct answer)
Capital deepening contributes 2.8 percentage points, labor growth contributes 1.2 percentage points, and technological progress contributes 2.0 percentage points to output growth
Capital deepening contributes 2.0 percentage points, labor growth contributes 1.2 percentage points, and technological progress contributes 1.8 percentage points, perfectly accounting for the 5% output growth
The economy is experiencing diminishing returns to capital accumulation since capital grows faster than output, indicating inefficient resource allocation toward investment rather than consumption

Explanation: When you encounter growth accounting questions, you need to apply the fundamental equation: output growth equals the weighted sum of input growth rates plus total factor productivity growth. The weights are the output elasticities. Let's calculate the contributions to growth. With output elasticities of 0.4 for capital and 0.6 for labor, capital contributes

0.4 \times 7\% = 2.8

percentage points and labor contributes

0.6 \times 2\% = 1.2

percentage points. Adding the measured TFP growth of 2%, the total calculated growth is

2.8 + 1.2 + 2.0 = 6.0\%

. However, actual output growth is only 5%, creating a 1 percentage point discrepancy. This discrepancy signals measurement error, making A correct. Real-world data often contains inaccuracies in measuring capital stocks, labor quality changes, or capacity utilization rates that can explain such gaps. B incorrectly states the individual contributions but ignores that they sum to 6%, not the observed 5%. C attempts to force the numbers to add up by arbitrarily reducing TFP's contribution to 1.8%, but this contradicts the given 2% measured TFP growth. D misinterprets the situation entirely—faster capital growth than output growth is normal and doesn't indicate diminishing returns or inefficiency in this context. Remember: in growth accounting problems, always check that your calculated contributions match observed output growth. When they don't align, suspect measurement issues rather than forcing the arithmetic to work by changing given values.

Question 5

In an economy described by the production function $Y = K^{0.25}(AL)^{0.75}$ where technology $A$ grows at rate $g$ , consider the golden rule level of capital. If the economy is currently above the golden rule level and the government wants to reach the golden rule through a change in the savings rate, what will be the short-run and long-run effects on consumption per worker?

Consumption per worker will increase immediately and continue growing at a higher rate in the long run due to optimal capital accumulation
Consumption per worker will decrease initially as savings fall, then increase to a higher long-run level that grows at rate $g$
Consumption per worker will increase immediately as savings fall, then settle at a higher long-run level that grows at rate $g$ (correct answer)
Consumption per worker will remain unchanged in the short run but will grow at a faster rate in the long run due to more efficient capital allocation

Explanation: If the economy is above the golden rule level, the marginal product of capital is below the effective depreciation rate

(n+g+\delta)

. To reach the golden rule, the savings rate must decrease. This immediately increases consumption per worker since less output is saved and more is consumed. In the long run, the economy reaches the golden rule steady state where consumption per worker is maximized and grows at rate

g

. The long-run consumption level is higher than the original steady state. Choice A incorrectly suggests continued higher growth. Choice B incorrectly suggests initial decrease in consumption. Choice D incorrectly suggests no short-run change.

Question 6

In an economy described by the Solow model with technological progress, the effective capital-labor ratio is $\hat{k} = \frac{K}{AL}$ . If the steady-state condition is $s f(\hat{k}^*) = (n + g + \delta)\hat{k}^*$ , and an increase in the technological progress rate $g$ occurs, what is the most likely short-run and long-run impact on actual output per worker?

Short-run decrease in growth rate of output per worker, long-run increase in growth rate of output per worker
Short-run increase in growth rate of output per worker, long-run increase in growth rate of output per worker
Short-run decrease in growth rate of output per worker, long-run increase in level of output per worker growth rate
Short-run decrease in effective capital per worker, long-run increase in growth rate of output per worker (correct answer)

Explanation: An increase in

g

raises

(n+g+\delta)

, making the current

\hat{k}

above the new steady state, causing

\hat{k}

to fall in the short run. However, output per worker

y = Af(\hat{k})

grows at rate

g + f'(\hat{k})\frac{\dot{\hat{k}}}{\hat{k}}

. In the long run,

\frac{\dot{\hat{k}}}{\hat{k}} = 0

and output per worker grows at the higher rate

g

. Choice A misses that the long-run effect is on the growth rate, not a temporary increase. Choice B incorrectly suggests short-run improvement. Choice C incorrectly describes the long-run effect as a 'level of growth rate' rather than recognizing the permanent increase in the growth rate itself.

Question 7

In the context of endogenous growth models, consider an economy where the production function for final goods is $Y = K^{\alpha}(AH)^{1-\alpha}$ , where $H$ is human capital and $A$ represents knowledge. If knowledge accumulation follows $\dot{A} = \delta H_A A$ where $H_A$ is human capital devoted to research, which condition is necessary for sustained per capita growth without diminishing returns?

The parameter $\delta$ must exceed the population growth rate $n$ to ensure knowledge grows faster than population
The share of human capital devoted to research must be constant and $\delta H_A$ must equal $\alpha + n$ for balanced growth
The parameter $\alpha$ must equal $1/2$ to ensure that physical and human capital contribute equally to output growth
The economy must maintain $\delta H_A \geq n$ and human capital must grow at the same rate as knowledge for sustained growth (correct answer)

Explanation: For sustained per capita growth, knowledge must grow at least as fast as population (

\dot{A}/A = \delta H_A \geq n

) to prevent dilution effects. Additionally, in balanced growth, human capital and knowledge must grow at the same rate to maintain constant factor ratios in production. This ensures that the effective labor input

(AH)

grows fast enough to sustain per capita growth. Choice A ignores the role of human capital allocation. Choice B incorrectly specifies the balanced growth condition. Choice C arbitrarily restricts

\alpha

without theoretical justification for the specific value.

Question 8

An economy described by the Solow growth model has a per-worker production function of $y = k^{0.5}$ , a saving rate of 30%, a depreciation rate of 5%, and a population growth rate of 2%. If the economy begins with a capital per worker level of $k=10$ , what is the immediate change in the capital stock per worker ( $\Delta k$ )?

$\Delta k = 1.75$
$\Delta k = 0.25$ (correct answer)
$\Delta k = 9.49$
$\Delta k = -0.40$

Explanation: The fundamental equation for the change in capital per worker in the Solow model is

\Delta k = s y - (\delta + n)k

. First, calculate output per worker,

y

, using the production function

y = k^{0.5}

with

k=10

. This gives

y = \sqrt{10} \approx 3.162

. Next, substitute all the given values into the equation:

\Delta k = (0.30)(3.162) - (0.05 + 0.02)(10)

. This simplifies to

\Delta k = 0.9487 - (0.07)(10) = 0.9487 - 0.7 = 0.2487

. The closest answer is 0.25. Choice A results from miscalculating investment as

sk

instead of

sy

. Choice C represents the gross investment per worker,

sy

, but fails to subtract the amount of investment needed to cover depreciation and population growth. Choice D results from forgetting to apply the production function and calculating

y=k

, leading to

\Delta k = 0.30(10) - (0.07)(10) = -4.0

Question 9

Two countries, A and B, are identical in all respects except for their saving rates and initial capital stocks. Both have the same production function $y=f(k)$ , depreciation rate ( $\delta$ ), and population growth rate ( $n$ ). Country A has a high saving rate ( $s_A$ ) and a high capital stock per worker ( $k_A$ ) and is currently in its steady state. Country B has a lower saving rate ( $s_B$ ) and a much lower capital stock per worker ( $k_B$ ). Which of the following is the most likely scenario regarding their growth rates of output per worker?

Country A will grow faster because its higher saving rate leads to more investment.
Country B will initially grow faster than Country A, but its long-run growth rate will be zero.
Both countries will have a long-run growth rate of zero, and it is ambiguous which country is currently growing faster.
Country A's growth rate is zero, and Country B's growth rate is positive and will remain so until it reaches its own, lower steady state. (correct answer)

Explanation: Country A is in its steady state, so by definition, its capital per worker is constant (

\Delta k = 0

), and its output per worker is also constant. Therefore, its growth rate of output per worker is zero. Country B has a low capital stock, implying it is below its own steady-state level (which is determined by

s_B

). Because it starts with a low

k

, the marginal product of capital is high, and investment

s_B f(k_B)

will be greater than break-even investment

(\delta+n)k_B

. This will cause

k_B

to grow, leading to a positive growth rate of output per worker. This growth will continue until Country B reaches its steady state, at which point its growth will also become zero. Choice A is incorrect because in the steady state, growth is zero regardless of the saving rate. Choice B is partially correct that B will grow faster, but its long-run growth rate is zero, not that it will become zero after an initial period. Choice C is incorrect because we can unambiguously determine that Country B is growing while Country A is not.

Question 10

The Golden Rule level of capital is the steady state that maximizes consumption per worker. An economy is at a steady-state where the marginal product of capital (MPK) is 8%, the depreciation rate is 5%, the population growth rate is 2%, and the rate of technological progress is 2%. To move towards the Golden Rule steady state, the country should:

increase its saving rate, because MPK is greater than the break-even investment growth rate.
decrease its saving rate, because MPK is greater than the depreciation rate.
decrease its saving rate, because the economy has over-accumulated capital. (correct answer)
maintain its current saving rate, as the economy is already dynamically efficient.

Explanation: The Golden Rule steady state, which maximizes consumption per effective worker, is characterized by the condition MPK =

\delta + n + g

. In this economy,

\delta + n + g = 5\% + 2\% + 2\% = 9\%

. The current marginal product of capital is 8%. Since MPK (8%) is less than

\delta + n + g

(9%), the economy has accumulated capital beyond the Golden Rule level. This condition is known as dynamic inefficiency. To increase consumption in the long run, the economy must reduce its steady-state capital stock. This is achieved by decreasing the saving rate. Choice A reaches the wrong conclusion by misinterpreting the inequality. Choice B compares MPK to an incorrect benchmark (just the depreciation rate). Choice D is incorrect because the economy is dynamically inefficient, not at the optimal Golden Rule level.

Question 11

Growth accounting for Japan from 1950-1973 showed extremely high output growth, much of which was attributed to capital accumulation. In contrast, growth from 1973-1990 was slower, with a larger share attributed to Total Factor Productivity (TFP). Which concept best explains this pattern?

Unconditional convergence, as Japan caught up to the United States' TFP level.
Transition dynamics, as Japan moved towards its steady state in the first period and then relied on technological progress. (correct answer)
Golden Rule of savings, indicating Japan over-invested in the first period and corrected in the second.
Mismeasurement of capital, where the quality of capital was not accounted for in the early period.

Explanation: This pattern is a classic example of transition dynamics in the Solow model. After WWII, Japan had a very low capital stock. As it rebuilt, its saving/investment rate allowed for rapid capital accumulation, leading to high growth rates as it moved along its production function toward its steady state. This is the 'catch-up' growth phase. Once Japan approached its steady-state level of capital per worker, the effect of diminishing returns to capital set in, and growth from capital accumulation slowed dramatically. At that point, further growth in living standards depends primarily on TFP growth (technological progress). Choice A is related but less precise; 'transition dynamics' is the specific mechanism within the model that describes this catch-up. Choice C is a specific condition about consumption maximization, not the general growth pattern. Choice D is a potential issue in growth accounting but doesn't explain the broad shift from capital-led to TFP-led growth as well as transition dynamics.

Question 12

An economy is in a steady state with no population growth or technological change. A devastating earthquake destroys half of the nation's capital stock but does not affect the production function, saving rate, or depreciation rate. Immediately following the earthquake, which of the following is true?

The growth rate of output will be negative as the economy adjusts to a new, lower steady state.
The marginal product of capital will be lower, and the economy's growth rate will be zero.
The saving rate will automatically increase to finance the reconstruction of capital.
The growth rate of output will be positive and higher than it was before the earthquake. (correct answer)

Explanation: This question tests your understanding of the Solow growth model and how economies respond to capital shocks. When you see scenarios involving capital destruction and steady states, focus on how the marginal product of capital changes and drives growth dynamics. When the earthquake destroys half the capital stock, the economy suddenly has much less capital relative to its unchanged labor force. This dramatically increases the marginal product of capital - each remaining unit of capital becomes much more productive. In the Solow model, investment equals saving, and with a higher marginal product of capital, the economy will invest more aggressively to rebuild its capital stock. The correct answer is D because the reduced capital stock creates a gap between the current capital level and the steady-state level. Since the production function, saving rate, and depreciation rate haven't changed, the steady state itself remains the same. The economy will now grow rapidly as it rebuilds capital, with output growth being positive and higher than before the earthquake (which was zero in the original steady state). Answer A is wrong because the economy moves toward the same steady state, not a lower one. Answer B incorrectly states the marginal product of capital will be lower - it's actually higher due to less capital per worker. Answer C is incorrect because the saving rate is assumed to remain constant; increased saving comes from higher income, not a higher saving rate. Remember: in growth models, temporary shocks to capital stocks create convergence dynamics. Economies grow faster when they're further below their steady state.

Question 13

An economy's production function is $Y = K^{0.4}(AL)^{0.6}$ . It is in a steady state where the saving rate is 28%, the depreciation rate is 4%, population growth is 1%, and technological progress is 2%. What is the steady-state capital-output ratio (K/Y)?

4.0 (correct answer)
7.0
0.4
2.5

Explanation: For a Cobb-Douglas production function in the Solow model, a useful steady-state relationship is that the capital-output ratio, K/Y, is equal to

s / (\delta + n + g)

. This can be derived from the steady-state condition

s y = (\delta+n+g)k

where variables are per effective worker. Rearranging gives

s(Y/AL) = (\delta+n+g)(K/AL)

. Canceling AL gives

sY = (\delta+n+g)K

, and rearranging yields

K/Y = s / (\delta+n+g)

. Plugging in the given values:

K/Y = 0.28 / (0.04 + 0.01 + 0.02) = 0.28 / 0.07 = 4.0

. Choice B is calculated as

s/\delta = 0.28/0.04 = 7.0

. Choice C is the capital share,

\alpha

. Choice D is a plausible miscalculation.

Question 14

A revised growth accounting study for a country incorporates improvements in the educational attainment and health of the workforce, which were ignored in a previous study. The new study finds a smaller contribution of Total Factor Productivity (TFP) growth to overall economic growth compared to the old study. What is the most logical explanation for this change?

The new study must have used a lower capital share in its calculations.
The old study incorrectly attributed growth from human capital accumulation to the Solow residual. (correct answer)
Technological progress in the country must have slowed down between the two studies.
The old study overestimated the growth of the physical capital stock.

Explanation: The Solow residual, or TFP growth, is the portion of output growth that cannot be explained by the growth of measured inputs (capital and labor). When the measurement of an input is improved to account for quality changes (like education and health improving the quality of labor, i.e., human capital), the measured contribution of that input to growth increases. Since TFP is calculated as a residual, if the contribution of a measured input (like quality-adjusted labor) goes up, the unexplained residual (TFP) must go down. Therefore, the old study was attributing the economic gains from a better-educated and healthier workforce to an unobserved, mysterious source (TFP), when it was actually an investment in human capital. The other choices are not directly related to the specific revision made in the study.

Question 15

Consider two countries, Richland and Poorland, with the same Cobb-Douglas production function, depreciation rate, and rate of technological progress. Richland has a saving rate of 30% and a population growth rate of 1%. Poorland has a saving rate of 15% and a population growth rate of 3%. In the long-run steady state, what can we conclude about their levels of output per effective worker ( $\tilde{y}$ )?

Richland's $\tilde{y}$ will be higher than Poorland's. (correct answer)
Poorland's $\tilde{y}$ will be higher than Richland's.
Their levels of $\tilde{y}$ will be equal due to convergence.
The comparison is ambiguous without knowing their current capital stocks.

Explanation: The steady-state level of capital per effective worker (

\tilde{k}

) is determined by the condition

s f(\tilde{k}) = (\delta+n+g)\tilde{k}

. For a Cobb-Douglas function

\tilde{y}=\tilde{k}^\alpha

, this solves to

\tilde{k}^* = [s / (\delta+n+g)]^{1/(1-\alpha)}

. Output per effective worker is

\tilde{y}^* = (\tilde{k}^*)^\alpha

. A higher saving rate (s) increases

\tilde{k}^*

and

\tilde{y}^*

. A higher population growth rate (n) decreases

\tilde{k}^*

and

\tilde{y}^*

. Richland has a higher saving rate (good for

\tilde{y}

) and a lower population growth rate (also good for

\tilde{y}

) compared to Poorland. Therefore, both factors work in the same direction, and Richland will unambiguously have a higher steady-state level of capital and output per effective worker. The current capital stocks (choice D) only determine their current position relative to the steady state, not the level of the steady state itself.

Question 16

A country's government implements a policy that doubles its national saving rate. According to the Solow growth model, what are the short-run and long-run effects on the growth rate of output per worker?

Short-run: increases; Long-run: increases permanently.
Short-run: no change; Long-run: increases.
Short-run: increases; Long-run: returns to its original rate. (correct answer)
Short-run: decreases; Long-run: returns to its original rate.

Explanation: An increase in the saving rate shifts the investment curve

sf(k)

upward. The economy is no longer in a steady state; investment now exceeds the amount needed to cover depreciation and population growth. This leads to capital accumulation (

k

increases). As

k

increases, output per worker

y

also increases. This period of capital accumulation is characterized by a growth rate of output per worker that is temporarily higher than its long-run rate. This is the short-run effect. However, due to diminishing returns to capital, this higher growth rate is not permanent. The economy eventually converges to a new, higher steady-state level of

k

and

y

. Once at this new steady state, growth in per-worker output ceases (or returns to the rate of technological progress,

g

, if included in the model, which is unchanged). Therefore, the long-run growth rate returns to its original rate. Choice A incorrectly states the long-run growth rate increases. Choice B is incorrect about the short-run effect. Choice D incorrectly states the short-run effect is a decrease; consumption growth might decrease initially, but output growth increases.

Question 17

In a Solow model where the population growth rate (n) permanently increases, what are the long-run consequences for the steady-state level of output per worker (y*) and the steady-state growth rate of total output (Y)?

y* decreases; growth rate of Y increases. (correct answer)
y* decreases; growth rate of Y decreases.
y* increases; growth rate of Y increases.
y* is unchanged; growth rate of Y increases.

Explanation: An increase in the population growth rate (n) means that more investment is required simply to keep the capital-per-worker ratio constant (the break-even investment line,

(\delta+n+g)k

, becomes steeper). With an unchanged saving rate, the economy will converge to a new, lower steady-state level of capital per worker (k*). A lower k* results in a lower level of output per worker (y*). The steady-state growth rate of total output is

n+g

. Since n has increased, the steady-state growth rate of total output will increase. Therefore, the level of output per worker falls, but the growth rate of the total economy speeds up.

Question 18

In a given year, an economy's real output grew by 3.5%, its capital stock grew by 4.0%, and its labor input grew by 1.0%. The capital share of income is 0.4. What was the growth rate of labor productivity (output per worker) during this year?

1.5%
1.3%
2.5% (correct answer)
3.5%

Explanation: The growth rate of labor productivity is defined as the growth rate of output minus the growth rate of labor. Given the data, the calculation is: Growth of labor productivity = Growth rate of real output - Growth rate of labor input = 3.5% - 1.0% = 2.5%. An alternative, more complex method is to first calculate the growth of total factor productivity (TFP),

g_A = g_Y - \alpha g_K - (1-\alpha)g_L = 3.5\% - 0.4(4\%) - 0.6(1\%) = 1.3\%

, and then use the productivity growth decomposition:

g_{Y/L} = g_A + \alpha g_{K/L} = 1.3\% + 0.4(4\% - 1\%) = 1.3\% + 1.2\% = 2.5\%

. Choice A is an arbitrary calculation. Choice B incorrectly identifies the growth rate of TFP as the growth rate of labor productivity. Choice D incorrectly uses the total output growth rate, failing to account for the growth in the labor force.

Question 19

In the decades following World War II, both Germany and Japan experienced significantly higher growth rates than the United States. This phenomenon is best explained by the fact that Germany and Japan:

had higher saving rates, leading to a permanently higher rate of long-run growth.
started with lower capital-labor ratios and were in a phase of transitional growth toward their steady states. (correct answer)
benefited from superior technological innovation, which increased their Total Factor Productivity growth rate.
maintained lower population growth rates, which increased the steady-state level of output.

Explanation: This is a classic example of convergence and transition dynamics. After WWII, much of the capital stock in Germany and Japan was destroyed, leaving them with very low capital-labor ratios. The United States, by contrast, had a large and intact capital stock. According to the Solow model, economies with low levels of capital per worker (far from their steady state) will experience rapid growth as they accumulate capital, due to the high marginal product of capital. The US, being closer to its steady state, grew more slowly. This 'catch-up' growth is a key prediction of the model. Choice A is incorrect because a higher saving rate does not lead to a permanently higher growth rate. Choice C is unlikely; they were primarily adopting existing technology, not innovating at a faster rate than the US. While choice D can affect the level of output, the primary reason for the dramatic difference in growth rates was their starting position relative to their steady state.

Question 20

Suppose a country's production technology is described by $Y = K + L$ . In this economy, there is no depreciation, no population growth, and no technological progress. If the saving rate is $s$ , what does this model predict about long-run growth in output per capita?

The economy will reach a steady state with zero growth, as in the standard Solow model.
The growth rate of output per capita will be positive and will depend on the saving rate $s$ . (correct answer)
The economy will exhibit explosive growth until all labor is replaced by capital.
The growth rate of output per capita will be positive but will not depend on the saving rate.

Explanation: This question describes a simple 'AK' model, a form of endogenous growth model. The production function is

Y=K+L

, so per worker it is

y = k+1

. The marginal product of capital (MPK) is

dY/dK = 1

, which is constant. It does not diminish as capital accumulates. The fundamental Solow equation is

\Delta k = sy - (\delta+n+g)k

. With the given parameters, this becomes

\Delta k = s(k+1) - 0 = sk+s

. The growth rate of capital per worker is

\Delta k / k = s + s/k

. As k becomes large, this growth rate approaches

s

. Since

y=k+1

, the growth rate of output per worker also approaches

s

. Because there are no diminishing returns to capital, a positive saving rate leads to perpetual growth, and the rate of that growth depends on the saving rate. This contrasts with the Solow model where diminishing returns cause growth to eventually cease.