Question 1

Describe the relationship between the production function,the investment function,and the capital-labour ratio.

Accepted Answer

Financial markets operate to ensure that the level of savings equals the level of investment.For simplicity,we assume that the economy saves a constant fraction,s,of real GDP per worker,y.So,investment per worker,i,equals sy.As the capital-labour ratio increases,real GDP per worker also increases,which causes investment per worker to increase.Due to diminishing marginal returns,increasing the capital-labour ratio causes smaller and smaller increases in real GDP per worker,so the production function becomes flatter.Because investment per worker equals the saving rate multiplied by real GDP per worker,sy,the increase in investment also gets smaller and smaller as the capital-labour ratio increases.

Question 2

An increase in the level of total factor productivity will lead to

Accepted Answer

An increase in total factor productivity means that the same amount of inputs (capital and labor) can produce more output. This leads to an increase in real GDP per worker as production becomes more efficient. However, it does not necessarily lead to changes in investment, depreciation, or the break-even investment line.

Question 3

In the Solow growth model,a change in the capital-labour ratio is equal to

Accepted Answer

In the Solow growth model, the change in the capital-labour ratio is equal to the difference between investment and depreciation. Investment represents the amount of output that is saved and used to create new capital, while depreciation represents the amount of capital that is lost due to wear and tear or obsolescence. Therefore, the change in the capital-labour ratio is equal to the net increase or decrease in the amount of capital available per unit of labour, which is captured by the difference between investment and depreciation.

Question 4

As the capital-labour ratio increases,real GDP per worker ________,and investment per worker ________.

Accepted Answer

When the capital-labor ratio increases, it means there is more capital available per worker, which increases productivity and output per worker, leading to an increase in real GDP per worker. At the same time, with an increase in capital available, investment per worker also increases. Therefore, as capital-labor ratio increases, real GDP per worker and investment per worker both increase.

Question 5

An economy accumulates capital when

Accepted Answer

Capital accumulation refers to an increase in the stock of physical capital in an economy. This can be achieved by increasing the capital-labor ratio, which means that there is a higher amount of capital goods per unit of labor input. Therefore, option A is the correct choice. Option B is incorrect because an increase in the number of workers does not necessarily lead to an increase in the capital stock. Option C is incorrect because an increase in GDP per capita does not necessarily imply an increase in the capital stock either. Option D is incorrect because a decline in labor productivity indicates a decrease in efficiency and would not lead to capital accumulation.

Question 6

By comparing ________ and ________,we will be able to determine what happens with capital stock over time.

Accepted Answer

Investment represents the addition of new capital stock, while depreciation represents the decrease in value of existing capital stock over time. By comparing the two, we can determine the net change in the capital stock over time. Options A and B do not take into account the effect of depreciation, which is crucial in determining changes in capital stock. Option D only considers the effect of consumption, which is not sufficient for understanding changes in capital stock. Therefore, option C is the best choice for comparing investment and depreciation.

Question 7

In the Solow growth model,the steady state occurs when

Accepted Answer

In the Solow growth model, the steady state is reached when investment equals depreciation, meaning the amount of capital being added is equal to the amount being lost, resulting in no net change in the capital stock.

Question 8

Suppose y = k¹/²,total factor productivity is constant and equal to 1,s = 0.40,and d = 0.10.When the economy reaches the steady state,the capital-labour ratio is ________ of capital per worker.

Accepted Answer

The answer of Suppose y = k¹/²,total factor productivity is...

Question 9

As the capital-labour ratio increases,investment per worker

Accepted Answer

There is a diminishing marginal productivity of capital, which means that as more capital is added to the production process per worker, the marginal product of capital decreases. Therefore, the increase in investment per worker will increase at a decreasing rate.

Question 10

Suppose y = k¹/²,total factor productivity is constant and equal to 1,s = 0.40,and d = 0.10.When the economy reaches the steady state,consumption per worker is ________.

Accepted Answer

In the steady state, consumption per worker is given by c = (1 - s) * y. Here, y = k¹/² and in the steady state, s * y = d * k. Solving for k gives k = (s/d)². Substituting s = 0.40 and d = 0.10, we find k = 16. Therefore, y = 16¹/² = 4. Thus, c = (1 - 0.40) * 4 = 2.40.

Question 11

To analyze the Solow growth model,we make the simplifying assumption that

Accepted Answer

The Solow growth model assumes a constant ratio of workers to the population to simplify the analysis of economic growth dynamics.

Question 12

Suppose y = k¹/²,total factor productivity is constant and equal to 1,s = 0.40,and d = 0.10.When the economy reaches the steady state,real GDP per worker is ________.

Accepted Answer

The answer of Suppose y = k¹/²,total factor productivity is...

Question 13

In the Solow growth model,if the level of investment is greater than depreciation at the initial capital-labour ratio,then △k is ________,and the capital-labour ratio ________ toward the steady-state capital-labour ratio.

Accepted Answer

If the level of investment is greater than depreciation at the initial capital-labor ratio, then the net investment (i.e., investment minus depreciation) is positive, which means that the capital stock will increase (i.e., △k>0). As a result, the capital-labor ratio will also increase as there are more units of capital per unit of labor, moving toward the steady-state capital-labor ratio. This is consistent with choice A.

Question 14

In the Solow growth model,if the level of investment is less than depreciation at the initial capital-labour ratio,then △k is ________ and the capital-labour ratio ________ toward the steady-state capital-labour ratio.

Accepted Answer

If investment is less than depreciation, the change in capital per worker (△k) is negative, causing the capital-labour ratio to decrease towards the steady-state.

Question 15

Suppose k = y¹/²,total factor productivity is constant and equal to 1,s = 0.40,and d = 0.10.When the economy reaches the steady state,investment per worker is ________.

Accepted Answer

In the steady state, investment per worker (i) is given by: 
i = s*y
Using the Cobb-Douglas production function y = k^(1/2) and substituting d and TFP = 1: 
i = 0.40*(k^(1/2)) = 0.40*(y^(1/4)) 
Substituting k = y^(1/2) yields: 
i = 0.40*(y^(1/4))*(y^(1/4)) = 0.40*y^(1/2) 
Because we are in the steady state, investment per worker equals depreciation per worker: 
i = d*y 
Substituting d = 0.10 and solving for y: 
0.40*y^(1/2) = 0.10*y 
y = 6.4 
Finally, substituting y back into our expression for investment per worker: 
i = 0.40*y^(1/2) = 1.6

Question 16

Keeping total factor productivity constant,as the capital-labour ratio increases,labour productivity

Accepted Answer

As the capital-labor ratio increases, the marginal productivity of labor decreases. This is because an increase in capital per worker eventually leads to diminishing returns to capital, which reduces the marginal productivity of labor. Therefore, as the ratio increases, labor productivity increases at a decreasing rate.

Question 17

Assume the capital-labour ratio remains constant.If investment increases at a constant rate,real GDP per worker will increase ________,and if total factor productivity increases at a constant rate,real GDP per worker will increase ________.

Accepted Answer

The answer of Assume the capital-labour ratio remains constant.If investment...

Question 18

In the steady state in the Solow growth model,the economy is in equilibrium with the capital-labour ratio and real GDP per worker ________,and with capital,labour,and real GDP ________.

Accepted Answer

In the steady state of the Solow growth model, the capital-labour ratio and real GDP per worker are constant, while capital, labour, and real GDP grow at the rate of population growth.

Question 19

The rate at which the capital stock declines due to either capital goods becoming worn out by use or becoming obsolete is called the

Accepted Answer

The rate at which the capital stock declines due to wear and tear or obsolescence is known as the depreciation rate. Therefore, option C is the correct answer. Choice A (amortization rate) typically refers to the process of paying off a loan over time, while option B (terminal rate) and D (steady-state rate) are not relevant to the concept of capital depreciation.

Question 20

The critical determinant of real GDP per capita is

Accepted Answer

GDP per capita is a measure of productivity, which is defined as output per unit of input. Therefore, the critical determinant of real GDP per capita is labour productivity (i.e. how much output can be produced with a given amount of input, specifically labour). While the size of the labour force, population, and working-age population can all impact GDP, they do not have as direct an effect on real GDP per capita as labour productivity.

Quiz 8: Long-Run Economic Growth