Chapter 3

Question 1

What explains long run growth in the Solow model?

Answer 1

Capital, which is no longer exogenous (no longer a fixed number and can be accumulated). Capital increases therefore production increases

Question 2

How can output be used?

The resource constraint

Answer 2

Output can be used for consumption or investment (creating new capital)

Question 3

The production function

Answer 3

• Variables are time subscripted
• 1/3 capital exponent
• No government
• Closed economy therefore no net exports

Question 4

Capital accumulation

Answer 4

• Investment creates new capital
• Depreciation is capital that has worn off and is longer usable (7-10%)
• Creating enough new capital to compensate for depreciated capital means the capital stock should be increasing.
• Capital accumulation allows for an increase in production
• Change in capital is shown by the amount of capital in the next year minus the capital in the current year

Question 5

What is labour denoted as?

Answer 5

Constant in order to isolate the main mechanisim

Question 6

Investment equation

Answer 6

• Y_t is the output of the economy/ gross investment in the economy
• Fixed proportion of s is different for every year

Question 7

Saving

Answer 7

• Income left after consumption is just saving therefore savings is equal to investment
• Each unit of saving is equal to a unit of investment therefore they are equal.
• Unit of saving can be used as unit of investment and this investment is used to attain a unit of capital.

Return on savings = price at which the unit of capital can be rented

Real interest rate = rental prices of capital= marginal product of capital

Question 8

Simple diagram

Answer 8

• Depreciated capital at time t is linear (dK_t) where the gradient is depreciation
• Invested capital will follow the graph of a production function (sYt). Follows the assumption in which there is a diminishing returns. Slope becomes smaller as capital increases because it is diminshing (more capital added gains less returns)
• Net investment is the difference between sYt - dK_t, which is the vertical difference between investment and depreciation

Question 9

Economy where investment is greater than depreciation

Answer 9

• At the level k₀, the investment curve is higher than the depreciation which means that the investment in the economy in this period is more than the capital that has been depreciated. This implies the capital stock will be higher. Gains are higher than the ones that have been destroyed. Then there is a movement to k₁. Vertical line between green and orange line shows the change in capital (the increase that will come) from the current period to the next one. Investment > Depreciation so higher capital in the next period.
• In the k₁ period, the vertical difference between the orange and green line is different. Orange line is sloped at a decreasing rate and therefore the growth of investment becomes smaller and smaller. Whilst the green curve remains linear
  *

Question 10

Economy where depreciation is greater than investment

Answer 10

•Capital will decrease by the difference between the orange and the green line

Question 11

Steady state

Answer 11

• Economy is going to tend towards a point in the economy where there is an intersection between these two points (called transition period)
• Intersection is called the steady state and capital doesn’t grow but it is constant (K*). Economy will always reach that point and once we reach that point capital doesn’t grow any more
• The capital stock will stay at this value of capital forever.
• Investment = depreciation

Growth stops and the following factors are constant

• output,
• Capital,
• output per person, and
• consumption per person

Question 12

Transition dynamics

Answer 12

• Transition dynamics take the economy from its initial level of capital to the steady state (k^*).
• Point where capital does not grow anymore
• There is growth but it slows down until we reach the steady state

Question 13

Conclusion of the Solow model

Answer 13

• Growth through capital accumulation, but will stop at a point
• Growth very high but will slow down, due to diminishing returns of investment
• No long run growth
• In the steady state, investment = depreciation
• Capital accumulation is not the engine of long run growth
• When depreciation is greater than investment, there is negative growth and the output tends to a little change
• Higher productivity has additional effects in the Solow model by leading the economy to accumulate more capital.

Question 14

Solow diagram with output

Answer 14

• Diminishing capital means the growth process stops at some point.
• Assumed that population was constant
• Future capital stock depends on current capital stock.
• Whenever the green curve is above the blue, there will be an increase in stock and there is an increase in output
• When the blue curve is above the green curve, there will be a decrease in stock and there is a decrease in output
• Changes in capital reflected in changes in output and growth until we reach the steady state
• Capital will increase/ decrease by the difference between the green and blue line

Question 15

Solving the steady state mathematically

Answer 15

• Alpha is assumed to be 1/3
• •At the steady state, there is no growth
• Exponent of productivity is rgeater than the productivity model

Question 16

What increases capital/ positively related to?

Answer 16

• Labour
• Investment proportion
• TFP

Question 17

What decreases capital?

Answer 17

Depreciation rate

Question 18

What changes the steady state?

Answer 18

• Changing S, A or D changes the steady state
• Increasing s, means higher saving rate therefore less consumption means more goes towards investment therefore steady state increases
• Increases A (TFP) means increases the level of capital in the steady state
• Increasing d means a decrease in the level of capital in the steady state, as more capital is lost due to depreciation
• Living standards is related to output per worker

Question 19

Solow with per worker axis

Answer 19

• Divide equation by labour force in order to find change in capital per worker is the investment per worker minus depreciation
• Because of constant returns to scale, we get an f(k) function
• Steady state is where investment per worker is equal to depreciation per worker
• f(k) is the production function which has been divded by labour to find the per worker

Question 20

Capital to output ratio

Answer 20

• Capital output ratio should be equal to the ratio of the investment and depreciation rate
• Depreciation rate is said to be similar (7-10%), therefore we can assume it is more or less the same
• Saving/Investing rate is what differs amongst countries
• Countries with a higher s have a high capital output ratio

Question 21

What is the correlation between capital-output ratio and investment rate?

Answer 21

Positive relationship

Question 22

Solow model and TFP

Answer 22

TFP is more important, as the exponent is greater than in the production model, as it is now equal to 3/2

• In the Solow model, a higher productivity parameter raises output directly just as in the production model
• there is an additional effect in the Solow model. The higher productivity level leads the economy to accumulate more capital as well. This explains the larger exponent in the Solow framework.

Question 23

What is the steady state positively related to (Increase leads to a higher steady state)?

Answer 23

• Investment level
• Size of workforce
• Productivity of workforce

Question 24

What is the steady state neagtively related to?

Answer 24

Depreciation rate

Question 25

What is the equation for the change in capital per worker?

Answer 25

Question 26

Why is the interest rate equal to marginal product of capital?

Answer 26

• Interest rate is the amount a person can earn through saving on unit of output
• We now see that the unit of saving gets used as a unit of investment, and a unit of investment becomes a unit of capital. Therefore, the return on saving is equal to the price at which the unit of capital can be rented.

Question 27

How does the Solow model expalin differences in GDP per capita?

Answer 27

• Using investment
• Growth comes from capital accumulation

Question 28

Why is a steady state reached?

Answer 28

• Investment has a diminishing returns. As capital stock rises, the addition of one unit adds less and therefore the rise in investment is smaller. we increase the capital stock, production rises and therefore investment rises. But the amount by which production and investment rise gets smaller as the capital stock grows, a fact embedded in our production function: Y = A̅K^1/3L̅^2/3
• The fact that production exhibits diminishing returns to capital accumulation means that each addition to the capital stock increases production—and therefore investment—by less and less. But it increases depreciation by the same amount, d̅.
• Eventually, the amount of investment the economy generates is equal to the amount of capital that depreciates. Net investment is zero, and the economy stabilizes at the steady state.

Question 29

Can growth in the labour force lead to overall economic growth?

Answer 29

• It can be in the aggregate
• It cannnot in the output per person
  
  • GDP and population grow at the same rate
  • GDP per capita is not growing

Question 30

When depreciation is greater than investment?

K_t>K^*

Answer 30

• Net investment is negative therefore capital stock declines and the economy returns to the steady state

Question 31

What are the endogenous variables in the model (have the potential to shift the curve)?

Answer 31

• Labour force
• Productivity
• Investment rate
• Depreciation rate

Question 32

What happens when there is an increase in:

• Investment level
• Size of workforce
• Productivity of workforce

Question 33

What does it mean that the Solow model endogenizes the process of capital accumulation?

Answer 33

Explains where capital stock comes from

Question 34

What happens in the long run?

Answer 34

Economy reaches Y^* and K^*

^{eventually growth stops as the capital stock and production converge to constant levels.}

Question 35

What are the weaknesses of the Solow model?

Answer 35

• Economic growth shows no signs of disappearing, but in the Solow model, this is exactly what happens, as in the long run, the diminishing returns to capital accumulation cause the return to these investments to fall.
• Important factor of TFP is missing
• Doesn’t explain why there are different investmetn and productivity rates

Question 36

What happens when there is an increase in the investmetn rate?

Answer 36

• Investment curve moves upwards
• Depreciation curve remains unchanged
• The capital stock increases by transition dynamics to reach the new steady state.
• This happens because investment exceeds depreciation.
• The new steady state is located to the right.
• Investment exceeds depreciation.
• S is an investment rate and it can go from 0-100%. It will probably not reach 100% as consumption is essential.
• The rise in investment leads capital to accumulate over time. This higher capital causes output to rise as well. Output increases from its initial steady state level
• Y* to the new steady state Y**.
• In an attempt to reach the new steady state, an economy will grow that corresponds with the new capital level but it levels off due to diminishing returns on capital. Initially growth is fast because we are far away from the steady state but it slows down

Question 37

What happens when there is a rise in the depreciation rate?

Answer 37

• The depreciation curve rotates upward.
• The investment curve remains unchanged.
• The capital stock declines by transition dynamics until it reaches the new steady state.This happens because depreciation exceeds investment.
• The new steady state is located to the left.
• The decline in capital reduces output.
• Output declines rapidly at first, and then gradually settles down at its new, lower steady state level Y**.

Question 38

What are the principles of transition dynamics?

Answer 38

• If an economy is below steady state:
  
  • It will grow.
• If an economy is above steady state:
  
  • Its growth rate will be negative.
• When graphing this, a ratio scale is used: Output changes more rapidly if we are further from the steady state.
• The farther below its steady state an economy is (in percentage terms), the faster the economy will grow. The closer to its steady state, the slower the economy will grow. This allows us to understand why economies grow at different rates.
• As the steady state is approached, growth shrinks to zero.
• Economies seem to recover quickly after war

Question 39

According to the Solow model, why are countries poor?

Answer 39

They have parameters that yield lower steady states (investment rate, labour force and TFP)

countries that are poor in 1960 would be far below their steady state, while countries that are rich would be closer to (or even above) their steady state. The principle of transition dynamics predicts that the poorest countries should grow quickly while the richest should grow slowly. This is exactly what the negative slope between GDP per capita in 1960 and per capita growth

Question 40

Strengths of the Solow model:

Answer 40

• It provides a theory that determines how rich a country is in the long run.
  
  • Long run = steady state
• •The principle of transition dynamics allows for an understanding of differences in growth rates across countries.
  
  • A country further from the steady state will grow faster.