Q: Suppose a country has a production function $$y = k$$^{1/2}$$, a depreciation rate $$\delta = 0.1$$, and a population growth rate n = 0.02$. What is the break-even investment per worker when k = 16$?

Break-even investment $$= (0.1 + 0.02) \times 16 = 1.92$$

Question 1

According to the Solow-Swan model, which of the following equations represents the law of motion for capital per worker in a closed economy with no population growth?

Accepted Answer

$$\Delta k = s f(k) - \delta k$$

Question 2

Suppose a country increases its saving rate. According to the Solow-Swan model, what is the predicted long-run effect on output per worker and the growth rate of output per worker?

Accepted Answer

Output per worker increases, but the long-run growth rate of output per worker remains unchanged.

Question 3

In the Solow model, what is the steady-state condition for capital per worker $$k^*$$?

Accepted Answer

$$s f(k^*) = \delta k^*$$

Question 4

If a country’s population growth rate increases, what does the Solow-Swan model predict will happen to the steady-state level of capital per worker and output per worker?

Accepted Answer

Both capital per worker and output per worker will decrease.

Question 5

Which of the following best describes the 'Golden Rule' level of capital in the Solow model?

Accepted Answer

The steady-state capital stock that maximizes consumption per worker.

Question 6

Given the per-worker production function $$y = k$$^{1/2}$$, a saving rate s = 0.3$, and a depreciation rate $$\delta = 0.1$$, what is the steady-state value of k$?

Accepted Answer

$$k^* = 9$$

Question 7

In the Solow model with population growth, what is the formula for break-even investment per worker?

Accepted Answer

$$(\delta + n)k$$

Question 8

Suppose an economy is initially below the Golden Rule level of capital. If the saving rate is increased to reach the Golden Rule, what happens to consumption per worker in the short run and in the long run?

Accepted Answer

Consumption per worker falls in the short run but rises in the long run.

Question 9

Which of the following conditions characterizes the Golden Rule steady state in the Solow model with population growth?

Accepted Answer

$$MPK = \delta + n$$

Question 10

If a country is above the Golden Rule level of capital, what policy should it pursue to maximize consumption per worker, and what is the effect on current and future generations?

Accepted Answer

Reduce the saving rate, which increases consumption for both current and future generations.

Question 11

Which of the following is a key prediction of the Solow-Swan model regarding the relationship between saving rates and long-run living standards?

Accepted Answer

Countries with higher saving rates will have higher levels of capital and income per worker in the long run.

Question 12

Consider the per-worker production function $$y = k$$^{1/3}$$, a saving rate s = 0.3$, and a depreciation rate $$\delta = 0.12$$. What is the steady-state value of k$?

Accepted Answer

$$k^* = 2.25$$

Question 13

Which of the following statements about the Malthusian model is correct?

Accepted Answer

It predicts that population growth will outstrip the Earth’s ability to produce food, leading to poverty.

Question 14

According to the Kremerian model, how does population growth affect economic growth?

Accepted Answer

Population growth can promote economic growth by increasing the number of innovators.

Question 15

Suppose a country has a production function $$y = k$$^{1/2}$$, a depreciation rate $$\delta = 0.1$$, and a population growth rate n = 0.02$. What is the break-even investment per worker when k = 16$?

Accepted Answer

Break-even investment $$= (0.1 + 0.02) 	imes 16 = 1.92$$

Question 16

Which of the following is NOT an assumption of the basic Solow-Swan model as presented in the lecture?

Accepted Answer

There is government spending and net exports.

Question 17

If the marginal product of capital (MPK) at the steady state is less than $$\delta + n$$, what does this imply about the steady-state capital stock relative to the Golden Rule level?

Accepted Answer

The steady-state capital stock is above the Golden Rule level.

Question 18

Which of the following best explains why economic growth is important, as discussed in the lecture?

Accepted Answer

Even small increases in the long-run growth rate can lead to large improvements in living standards over time.

Question 19

In the Solow model, what happens to the steady-state level of output per worker if the depreciation rate increases, holding all else constant?

Accepted Answer

The steady-state output per worker decreases.

Macroeconomic Theory I: Growth I – Capital & Population (Solow Model and Golden Rule)

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