SEM 1 - LEC 4 - SOLOW GROWTH MODEL Flashcards
what does the slow model allow us to consider
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.
what’s the resource constraint equation
what’s the capital accumulation equation
what do we assume with labour in the slow model
We assume that the amount of labour is given exogenously at the constant level L ̄.
what’s the investment rate equation
what is the real interest rate equal to in this economy, and what does this mean
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.
what equation tells us that the change in capital stock is equal to investment less depreciation.
what does the solow diagram look like
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.
how can the New investment (green line) depend on the production function and
can be written as in the slow diagram
how does the slow diagram work..
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.
what’s the transition dynamics of the economy
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∗.
what does the solow diagram look like with output
how do you mathematically solve the solow model
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.
what’s the steady state production equation
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.
what the output per person in the steady state
A higher productivity level, A ̄, increases the long-run level of output per person in both cases.
what’s the equation for s* which is the saving rate that maximizes per capita consumption.
how do you show s* equals 1/3
what’s the capital output ratio in steady state
Countries with high investment rates should have high capital-output ratios.
what’s the steady state equation for output per person
what are the implications of the steady state
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.
what does an increase in investment rate look like graphically
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∗∗.
what does an increase in investment rate look like including output and output over time
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.
what does an increase in depreciation rate look like graphically
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.
what does an increase in depreciation rate look like graphically with output and output over time
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 ∗∗.
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.
