Question 1

In the Solow model without technological progress, the capital accumulation equation is given by $$ \Delta k = s f(k) - (\delta + n)k . $$What does the term $$ (\delta + n)k $$ represent?

Accepted Answer

The amount of capital lost due to depreciation and population growth

Question 2

Suppose the production function in the Solow model is Cobb-Douglas: $$ Y = K$$^{\alpha}$$ L$$^{1-\alpha}$$ . If $$the savings rate increases, what is the long-run effect on output per worker?

Accepted Answer

Output per worker increases permanently

Question 3

In the Solow model, what happens to capital per worker $$k if$$ $$s f(k) \u003c (\delta + n)k$$?

Accepted Answer

Capital per worker decreases

Question 4

Given the steady-state condition in the Solow model $$ s f(k^*) = (\delta + n)k^* $$, what happens if the depreciation rate $$\delta$$ increases, holding all else constant?

Accepted Answer

Steady-state capital per worker $$k^*$$ decreases

Question 5

If the population growth rate $$n$$ rises in the Solow model, what is the effect on steady-state output per worker $$y^*$$?

Accepted Answer

Steady-state output per worker decreases

Question 6

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

Accepted Answer

The level of capital that maximizes consumption per worker

Question 7

Suppose a country is at its steady-state in the Solow model. If the savings rate $$s$$ increases, what is the immediate effect on the growth rate of capital per worker $$g_k$$?

Accepted Answer

The growth rate of capital per worker becomes positive

Question 8

Given the Cobb-Douglas production function $$ y = k$$^{\alpha}$$ $$, what is the marginal product of capital (MPK)?

Accepted Answer

$$ MPK = \alpha k$$^{\alpha-1}$$ $$

Question 9

In the Solow model, which of the following will NOT affect the steady-state level of output per worker?

Accepted Answer

The initial level of capital per worker

Question 10

If a country is below its steady-state capital per worker $$k^*$$, what will happen over time according to the Solow model?

Accepted Answer

Capital per worker will increase toward $$k^*$$

Question 11

Suppose the savings rate is $$s$$, the depreciation rate is $$\delta$$, and the population growth rate is $$n. $$What is the steady-state capital per worker $$k^* in $$the Solow model with Cobb-Douglas production $$y = k$$^{\alpha}$$?

Accepted Answer

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

Question 12

Which of the following statements about the Solow model is TRUE?

Accepted Answer

A higher population growth rate leads to a lower steady-state output per worker

Question 13

If the marginal product of capital (MPK) is less than the sum of the depreciation rate and population growth rate, what should a country do to maximize steady-state consumption per worker?

Accepted Answer

Decrease the savings rate

Question 14

In the Solow model, what is the effect of a permanent increase in the savings rate on the long-run growth rate of output per worker?

Accepted Answer

It has no effect on the long-run growth rate of output per worker

Question 15

Which of the following best explains why the Solow model predicts convergence in output per worker across countries, assuming similar savings rates, depreciation, and population growth?

Accepted Answer

Countries with lower initial capital per worker grow faster due to diminishing returns to capital

Question 16

Suppose a country has a Cobb-Douglas production function $$Y = K$$^{0.3}$$L^{0.7}$$, a savings rate $$s = 0.2$$, depreciation rate $$\delta = 0.05$$, and population growth rate $$n = 0.01. $$What is the steady-state capital per worker $$k^*$?

Accepted Answer

$$ k^* = \left( \frac{0.2}{0.05 + 0.01} \$$right)^{\frac{1}$${1-0.3}} $$

Question 17

If the steady-state output per worker is $$y^* = (\frac{s}{\delta + n}$$)^{\frac{\alpha}$${1-\alpha}}$$, what happens to $$y^* if $$the savings rate $$s$$ doubles?

Accepted Answer

$$y^*$$ increases, but by less than double

Question 18

Which of the following is a key assumption of the Solow model without technological progress?

Accepted Answer

Constant returns to scale in the production function

Question 19

In the Solow model, what is the main reason that actual investment per worker is not linear in capital per worker?

Accepted Answer

Because the production function is not linear in capital per worker

Solow Model – Notes Part 1: The Solow Growth Model without Technological Change

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