Chapter 11 Flashcards
(18 cards)
What are the two relations between output and capital?
The amount of capital determines the amount of output being produced.
The amount of output being produced determines the amount of saving and, in turn, the amount of capital being accumulated (“collected”) over time.
What are the two steps to derive the effects of output on capital accumulation?
First, derive the relation between output and investment, second, derive the relation between investment and capital accumulation.
What is the relation between output and investment?
It = sYt
Describe what happens when investment per worker exceeds or is less than depreciation per worker.
- If investment per worker exceeds depreciation per worker, the change in capital per worker is positive: capital per worker increases.
- If investment per worker is less than depreciation per worker, the change in capital per worker is negative. Capital per worker decreases.
What represents change in capital per worker?
The change in capital per worker is represented by the difference in investment per worker and depreciation per worker. At point K0/N the difference is positive, so capital per worker increases.
Why does investment increase by less and less?
investment increases by less and less because the investment generates lower output, because of decreasing returns to capital, which in turn generates lower investment. Because investment is dependent on output since output generates income to workers, and part of that income goes to savings, which in this model is equal to investment
When is capital constant?
For some level of capital per worker K*/N, investments is just enough to cover depreciation, and capital per worker remains constant.
What happens if a country has suffered large capital losses during a war?
if a country has suffered larger capital losses than population losses due to a war, it will come out of the war with a low level of capital per worker: that is a point to the left of K*/N. The country will then experience large increases in both capital per worker and output per worker for some time.
What happens if a country has a very high level of capital?
If a country starts instead from a high level of capital per worker, from a point to the right of K/N - the depreciation will exceed investment and capital per worker and output per worker will decrease. The initial level of capital per worker is too high to be sustained, given the saving rate. This decrease in capital per worker will continue until the economy again reaches the point where investment equals depreciation and capital per worker is equal to K/N.
The economy always converges to this in the long run.
How does the saving rate affect the growth rate of output per worker?
The saving rate has no effect on the LR growth rate of output per worker, which is equal to zero.
In the LR, the growth rate of output is = 0, no matter what the saving rate is.
The saving rate determines the level of output per worker in the LR.
Other things being equal, countries with a higher savings rate will achieve higher output per worker in the LR.
An increase in the saving rate will lead to higher growth of output per worker for some time, but not forever.
This conclusion follows from the two propositions we just discussed. From the first, we know that an increase in the saving rate does not affect the LR growth rate of output per worker (which remains = 0). From the second, we know that an increase in the saving rate leads to an increase in the LR level of output per worker. It follows that, as output per worker increases to its new higher level in response to the increase in the saving rate, the economy will go through a period of positive growth. This period of growth will come to an end when the economy reaches its new steady state. (pg. 247)
How can government affect saving rate?
They can vary public saving: given private saving, positive public saving - a budget surplus - leads to higher overall saving (and vice versa)
They can use taxes to affect private saving: for example give tax breaks to people who save, making it more attractive to save and thus increase private saving.
What saving rate should government aim for?
Shift focus from output to consumption. Because what matters to people is not output but consumption.
Increase in saving must initially come from decrease in consumption.
A change in the saving rate this year has no effect on capital this year, and consequently no effect on output and income this year. So an increase in saving comes initially with an equal decrease in consumption.
governments face a trade-off: an increase in the saving rate leads to lower consumption for some time but higher consumption later.
How close governments should come to the golden rule depends on how much they value the welfare of the current citizens. Because higher savings rate now will decrease the welfare for the people now, but increase the welfare for the people in the long run (next generation).
Does an increase in saving lead to an increase in consumption in the long run?
We know that an increase in saving leads to an increase in the level of output per worker. But output is not the same as consumption.
Saving rate of 0 and 1 both implies a consumption of 0, meaning that there must be some value of the saving rate between zero and one that maximises the steady-state level of consumption.
Increases in the saving rate below this value lead to a decrease in consumption initially, but lead to an increase in the LR
Increases in the saving rate beyond this value decrease consumption not only initially but also in the LR.
This happens because the increase in capital associated with the increase in the saving rate leads to only a small increase in output - an increase that is too small to cover the increased depreciation = the economy carries out too much capital.
The value of capital associated with the value of the saving rate that yields the highest level of consumption in steady state is the golden-rule level of capital.
What happens with consumption when saving rate is between 0 and golden rule level?
For s between 0 and sG a higher saving rate —> higher K/N —> higher Y/N —> higher C/N.
What is Golden rule level of capital?
The value of capital associated with the value of the saving rate that yields the highest level of consumption in steady state
What happens with consumption when S is larger that golden rule level?
For s larger than sG, increases in the saving rate still lead to higher values of capital per worker and output per worker; but they now lead to lower values of consumption per worker.
This is because the increase in output is more than offset by the increase in depreciation as a result of a larger capital stock. For s = 1, consumption per worker is equal to zero. Capital per worker and output per worker are high, but all of the output is used just to replace depreciation, leaving nothing for consumption.
How does an increase in the saving rate affect economic growth in the short-run?
Is this a good way of generating economic growth in the long-run?
In the short-run, the economy grows at positive rates.
Once the new steady state is reached, economic growth reverts back to zero.
In this simple model, if the economy is at its steady state, there is thus no way that it can achieve sustainable growth. It is not realistic to keep increasing the savings rate forever, and with decreasing marginal returns, such a policy would necessarily be less and less effective.
So while this simple model can explain convergence, it only has limited explanatory power for why industrialized countries grow.
We have learnt that countries with higher savings rates are richer. Can we conclude that higher savings rates are always better? Or what should be the optimal savings rate?
Ultimately, we do not care about investment, but about consumption. (Remember Microeconomics: consumption, not investment, is in the utility function.) The optimal savings rate is the rate at which steady state consumption is maximized.
