SEM 1 - LEC 4 - SOLOW GROWTH MODEL

Question 1

what does the slow model allow us to consider

Answer 1

The Solow model allows us to consider the accumulation of capital as a possible engine of long-run economic growth.

This accumulation of capital is endogenized in the Solow model → it is converted from an exogenous variable into an endogenous variable.

Question 2

what’s the resource constraint equation

Answer 2

Question 3

what’s the capital accumulation equation

Answer 3

Question 4

what do we assume with labour in the slow model

Answer 4

We assume that the amount of labour is given exogenously at the constant level L ̄.

Question 5

what’s the investment rate equation

Answer 5

Question 6

what is the real interest rate equal to in this economy, and what does this mean

Answer 6

The real interest rate in this economy is equal to the rental price of capital, which in turn is given by the marginal product of capital.

Question 7

what equation tells us that the change in capital stock is equal to investment less depreciation.

Answer 7

Question 8

what does the solow diagram look like

Answer 8

The Solow diagram plots the two terms, s ̄Y and d ̄K that govern the change in the capital stock in equation (6).
New investment (green line) depend on the production function and
can be written as:
This is the curved line that looks like the production function scaled
down by s ̄.
The second line shows the amount of capital that depreciates, d ̄K.
This is just a linear function of capital.

Question 9

how can the New investment (green line) depend on the production function and
can be written as in the slow diagram

Answer 9

Question 10

how does the slow diagram work..

Answer 10

At the starting level K ̄0, the amount of investment, s ̄Y, exceeds the amount of depreciation, d ̄K ̄0.

Net investment is positive and the capital stock increases.

This process continues until the economy reaches a capital level K∗.

At this point, the amount of investment undertaken is exactly equal to the amount of capital that wears out through depreciation.

Since the investment equals depreciation, the change in capital stock is zero, and the capital stock remains constant.

In the absence of any shocks, the capital stock will remain at K∗ forever, since each period’s investment is just enough to offset the depreciation that occurs during production.

This point is called steady state of the Solow model.

Question 11

what’s the transition dynamics of the economy

Answer 11

We call the behaviour away from the steady state the transition dynamics of the economy.

The economy will also converge to the steady state if we start with a level of capital that is larger than K∗.

When Kt > K∗, we have that the amount of capital that wears out in production exceeds the amount of investment.

Net investment is therefore negative and the capital stock declines.

This process continues until the economy settles down at K∗.

Question 12

what does the solow diagram look like with output

Answer 12

Question 13

how do you mathematically solve the solow model

Answer 13

A higher investment rate, s ̄, leads to a higher steady-state capital
stock.

The steady-state level of capital stock also increases if the underlying level of productivity, A ̄, is higher. If the economy is more productive, output will be larger and the larger output translates in a higher capital accumulation.

A higher depreciation rate, d ̄, reduces the capital stock.

A larger workforce, L ̄, produces more output, which leads to more investment and hence more capital in the steady state.

Question 14

what’s the steady state production equation

Answer 14

A higher investment rate, s ̄, and a higher productivity, A ̄, lead to a higher steady-state level of production, but faster depreciation, d ̄ lowers it.

Doubling labour leads in the long-run to a doubling of steady-state production.

Question 15

what the output per person in the steady state

Answer 15

A higher productivity level, A ̄, increases the long-run level of output per person in both cases.

Question 16

what’s the equation for s* which is the saving rate that maximizes per capita consumption.

Answer 16

Question 17

how do you show s* equals 1/3

Answer 17

Question 18

what’s the capital output ratio in steady state

Answer 18

Countries with high investment rates should have high capital-output ratios.

Question 19

how are differences in output per person explained

Answer 19

Differences in output per person are explained in part by differences in the investment rate, s ̄, and in part by differences in A ̄, assuming that the depreciation rate is the same in the rich and poor countries.

Question 20

what’s the steady state equation for output per person

Answer 20

Question 21

Why does the economy settle down to a steady state?

Answer 21

As we have seen at steady state: s ̄Y∗ = d ̄K∗.
The reason the economy settles down is that the sY ̄ curve exhibits diminishing returns

As we increase the capital stock, production increases and therefore investment increases.

However, the amount by which production and investment increase gets smaller as the capital stock grows.

In contrast, a constant fraction of capital stock depreciates every period, so the amount of depreciation increases.

Eventually, the amount of investment that 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 22

what are the implications of the steady state

Answer 22

Saving and investing in additional factories, machine tools and computers leads to economic growth in the medium term.

However, in the long run, the diminishing returns to capital accumulation cause the returns on investment to fall.

Eventually, depreciation and new investment offset each other, and the economy settles down to constant level of output per person.

Question 23

what does an increase in investment rate look like graphically

Answer 23

Assume an exogenous and permanent increase in the investment rate: for example, a change in tax regulations that encourages investment.

The economy begins at K∗, the steady state associated with the investment rate s ̄.

Then the investment rate increases to s ̄ , this causes the s ̄Y curve to rotate upward → the amount of investment increases for any given level of the capital stock.

The d ̄K does not shift since that expression does not involve s ̄. At the old investment rate, the economy was in steady state.

At the new investment rate, the amount of investment increases and exceeds the amount of depreciation.

This causes the capital stock to increase over time, until it reaches the new steady-state level K∗∗.

Question 24

what does an increase in investment rate look like including output and output over time

Answer 24

Panel (a): in addition to the depreciation curve, d ̄K, the old investment curve, s ̄Y , and the new investment curve, s ̄ Y , we have the production function that provides output, Y .

The increase in investment leads capital to accumulate over time.
The higher capital causes output to rise as well.
Output increases from its initial steady-state level Y ∗ to the new steady state Y ∗∗.

Panel (b): it shows the hypothetical behaviour of output over time, assuming that the increase in the investment rate occurs in the year 2020.

Output grows fastest immediately after the change in the investment rate.

Then over time, the growth rate of output falls, and the economy converges smoothly to its new steady state.

Question 25

what's the main messages of an increase in the investment rate

Answer 25

The increase in the investment rate causes the economy to grow over time, at least until the new steady state is reached. In the long run, both steady-state capital and steady-state production are higher. Since labour is constant, this means also that the level of output per person is permanently higher.

Question 26

what does an increase in depreciation rate look like graphically

Answer 26

Assume an exogenous and permanent increase in the depreciation rate: for example, a change in the climate that leads to more severe weather so that buildings and vehicles depreciate more quickly. We assume that the depreciation rate increases from d ̄ to some higher level d ̄′. In this case, the depreciation rate shows up in the d ̄K curve, not in the s ̄Y curve, so it is this curve that shifts. At any given level of capital, the amount of depreciation is now higher: thus, the depreciation curve rotates upward and to the left. At the original original depreciation rate, the amount of investment was just enough to offset the wear and tear of the capital stock. Now, since depreciation has increased, d ̄′K exceeds s ̄Y. This means that the change in the capital stock is negative: the capital stock declines. The capital stock continues to decline until the ′economy reaches the new, lower steady state K∗∗, where s ̄Yt = d ̄ Kt.

Question 27

what does an increase in depreciation rate look like graphically with output and output over time

Answer 27

Panel (a): in addition to the investment curve, s ̄Y , the old depreciation curve, d ̄K, and the new depreciation curve, d ̄′K, we have the production function that provides output, Y . The increase in depreciation rate leads to a decline in the capital stock. The decline in capital reduces output as well. Output decreases from its initial steady-state level Y ∗ to the new steady state Y ∗∗. Panel (b): it shows the hypothetical behaviour of output over time, assuming that the decrease in the depreciation rate occurs in the year 2020. Output declines rapidly at first and then gradually settles down at its new, lower steady-state level Y ∗∗.

Question 28

what's the main messages of an increase in the depreciation rate

Answer 28

the increase in the depreciation rate induces a slow down of the economy over time, at least until the new steady state is reached. In the long run, both steady-state capital and steady-state production are lower. Moreover, the level of output per person is permanently lower.

Question 29

what's the intuiton of the The principle of transition dynamics

Answer 29

the farther below its steady state an economy is, the faster the economy will grow; similarly, the farther above its steady state an economy is, the slower the economy will grow.

Question 30

what equation tells us that when Kt < K∗, the capital stock grows. Moreover, the growth rate is higher the greater the distance below the steady state.

Answer 30

Question 31

why are the poor countries countries of the world are typically poor

Answer 31

because, according to the Solow model, the determinants of their steady states (investment rates and total factor productivity levels) are substantially lower than in rich countries.