Question 1

Suppose an economy's production function is given by $Y = Af(K, N)$. If both capital ($K$) and labor ($N$) are doubled, and output ($Y$) also doubles, what type of returns to scale does this production function exhibit?

Accepted Answer

Constant returns to scale

Question 2

The Cobb-Douglas production function for the U.S. is often written as $Y = A(k^{0.3}N^{0.7})$. What does the exponent 0.3 represent in this context?

Accepted Answer

The share of output attributable to capital

Question 3

If a country increases its saving rate, according to the Solow growth model, what is the long-run effect on output per worker?

Accepted Answer

It will increase the level of output per worker, but not the long-run growth rate

Question 4

Given the Cobb-Douglas production function $Y = AK^{0}N^{ 70}$, what is the marginal product of capital ($MPK$)?

Accepted Answer

$MPK = 0.3Y/K$

Question 5

Which of the following best explains why the Solow model predicts convergence among wealthy nations but not globally?

Accepted Answer

Differences in technology and institutions are more pronounced globally

Question 6

In the Solow model, what happens to the capital stock per worker ($k$) if investment per worker equals depreciation per worker?

Accepted Answer

Capital stock per worker remains constant (steady state)

Question 7

Suppose a country has underdeveloped financial institutions and low domestic savings. Which type of foreign investment is most likely to provide stable, long-term capital for economic growth?

Accepted Answer

Foreign direct investment

Question 8

If the production function is $Y = AK^{ 30}N^{ 70}$ and both $K$ and $N$ grow at 2% per year, what is the approximate growth rate of output ($Y$), assuming $A$ is constant?

Accepted Answer

0.3(2%) + 0.7(2%) = 2% per year

Question 9

Which of the following is NOT a limitation of the Solow growth model?

Accepted Answer

It explains endogenous technological progress

Question 10

If the marginal product of labor ($MPL$) in a Cobb-Douglas production function is $MPL = 0.7Y/N$, what does this imply about the distribution of income in the economy?

Accepted Answer

Labor receives 70% of total income

Question 11

A country experiences a sustained increase in its standard of living over several decades. According to the Solow model, what is the most likely explanation for this?

Accepted Answer

Continuous growth in total factor productivity ($A$)

Question 12

Which scenario best illustrates diminishing returns to capital in the Solow model?

Accepted Answer

Adding more capital increases output, but each additional unit of capital adds less to output than the previous unit

Question 13

If a country has a Cobb-Douglas production function and the sum of the exponents on $K$ and $N$ is less than 1, what type of returns to scale does the production function exhibit?

Accepted Answer

Decreasing returns to scale

Question 14

In growth accounting, why is the natural logarithm of the production function used?

Accepted Answer

It makes the function additive and allows growth rates to be interpreted as derivatives

Question 15

Suppose a country’s output per worker is $y = Ak^{0.3}$. If $A$ increases by 5% and $k$ increases by 10%, what is the approximate percentage increase in output per worker?

Accepted Answer

5% + 0.3(10%) = 8%

Question 16

Which of the following factors is NOT directly included in the Solow model’s production function?

Accepted Answer

Government spending

Question 17

If a country’s capital-labor ratio ($K/N$) increases, what happens to the marginal product of capital ($MPK$) in a Cobb-Douglas production function?

Accepted Answer

$MPK$ decreases

Question 18

Which of the following best describes the role of institutions in explaining differences in output per worker across countries?

Accepted Answer

Strong institutions promote higher productivity and sustained growth

Question 19

In the Solow model, what is the effect of an increase in total factor productivity ($A$) on the steady-state level of output per worker?

Accepted Answer

It increases the steady-state level of output per worker

Question 20

Which of the following is a plausible reason why capital might flow from poor to wealthy nations, contrary to the predictions of the Solow model?

Accepted Answer

Wealthy nations have better institutions and lower risk

Long Run Economic Growth: Production Functions, Returns to Scale, and the Solow Model

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