11-13 Flashcards
Why do we care about growth?
It is indicative of standard of living which is reflected in the variable output per person
Why might it be difficult to compare standard of living across countries?
They have different currencies and then the prices for basic goods also differs. It isnt as simple as just using the exchange rates as they fluctuate.
What do we use to enable us to compare standard of living across countries?
Purchasing power parity. Constructed using a common set of prices for all countries
Malthusian trap
whereby a country is unable to increase its output per person
Emerging economies
Economics with high growth rates but low output per person
Aggregate production function
a specification of the relation between aggregate output and the inputs in production
What does K represent in the aggregate production function?
the sum of all the machines, plants and office buildings in the economy
What does N represent in the aggregate production function?
labour - the number of workers in the economy
What determines how much of each input is used?
state of technology
Returns to sale assumption of the production function
when the scale of operations in doubled (for example) the output will also double
What happen if only one of the inputs is increased?
The output will increase but by not as much as what the input was increased by keeping the other constant.
decreasing returns to capital
or
decreasing returns to labour
How do we tune turn the production function into one stating the output per worker?
Dividing it by N
Therefore
Y/N = F(K/N, 1)
What does the output of per worker state
the amount of output per worker is depends on the amount of capital per worker.
Relation between output per worker and capital per worker is represented by an upwards sloping curve with Y/N on the y axis and K/N on the x
What does the increase in the state of technology cause the output per worker curve?
Causes it to shift upwards
What are two sources of growth?
capital accumulation and technological progress
Why can capital accumulation not sustain an economy by itself
due to decreasing returns to capital, sustaining a steady increase in output per worker will require larger and larger increases in the level of capital per worker. At some point the economy will be unwilling or unable to save and invest enough to further increase capital so output per worker will stop growing.
savings rate
proportion of income that is saved
A higher savings rate can…
sustain a higher level of output
Two relations, at the centre of determination of output in the long run, between capital and output
the amount of capital determines the amount of ouptut being produced
the amount of output determines the amount of saving and, in turn, the amount of capital accumulated over time..
What assumptions do we initially make when considering the relation between capital per worker and output per worker?
- The size of the population, the participation rate and the unemployment rate are all constant therefore implying N is constant
- There is no technological progress
With these two assumptions the relation of output and capital per work from the production side can be written as:
Yt/N = f(Kt/n)
Known as production side
In a closed economy what is investment equal to?
Saving - the sum of the private and public saving But initially will be assumed that public saving is = 0.
What do we get when we combine the two relations of investment and saving and saving and income?
It = sYt
Investment is proportional to output: higher output implies higher saving and thus higher investment
What assumption do we make about capital
it depreciates year on year at rate δ. That is from one year to the next a proportion δ of the capital stock breaks down and becomes useless. The proportion of (1-δ) remains intact for the following year.
What is the evolution of the capital stock given by?
Kt+1 = (1-δ)Kt +It
What is the relation we can then obtain from the initial capital stock relation?
Replace investment with I=sYt and diving through by N
Kt+1/N = (1-δ)K/N +SYt/N
What is the second relation we can form between output and capital per worker?
Kt+1/N - Kt/N = sYt/N - δKt/N
The change in the capital stock per worker is equal to the saving per worker minu depreciation
Known as the saving side
What do we get when we put the production side and saving side together?
Kt+1/N - Kt/N = sf(Kt/N) - δ(Kt/n)
Relation describes what happens to capital per worker
Investment per worker
The level of capital per worker this year determines the output per worker this year. Given the savings rate, output per worker determines the amount of savings per worker and thus the investment per worker
Depreciation per worker
The capital stock per worker determines the depreciation per worker
If investment exceed depreciation per worker
the change in capital per worker is positive: capital per worker increases (and then vice versa if investment per worker is less than depreciation per worker)
What does depreciation per worker look like on a graph?
With output per worker on y and capital per worker on x
it is looks like a straight line
What happens when the economy reaches the point at which investment = depreciation?
Capital per worker and output per worker will remain constant at these equilibrium levels
The steady state
the state in which output per worker and capital per worker are no longer changing
The steady state value of capital of worker is such that….
the amount of savings per worker is sufficient to cover depreciation per worker
The effect of the savings rate on long run growth rate of output per worker..
It has no effect. The economy eventually converges to a constant level of output per worker in other words in the long run the growth rate is zero no matter what the savings rate. In order to sustain a constant positive growth rate in the long run more and more of the out put will have to be dedicated to capital accumulation. At some point the fraction would be greater than 1 which is impossible
The saving rate determines what in the long run
The level of output per worker. If there is a higher savings rate there will be a higher steady state of capital per worker and therefore higher level of output per worker
A higher savings rate will….
lead to a higher growth of output per worker for some time, but not forever. As output per worker increases to its new higher level in response to the increase in the savings rate, the economy will go through a period of positive growth.
How can a government affect the savings rate?
The can vary public saving. A budget surplus leads to higher overall saving.
Use of taxes to affect private spending. Tax breaks mean more to save thus increasing private saving.
What will be the consumption per worker if the savings rate is zero?
The capital is zero, therefore output is zero and so is consumption
What will be the consumption per worker if the savings rate is 1?
The level of capital and output per worker will be very high but because people save all their income consumption is still equal to zero
Golden rule level of consumption
The level of capital associated with the value of the savings rate that yields the highest level of consumption in steady state
How can we find the effect of an increase in the savings rate on steady state output?
Initially state with the production function. Divide through by N. Replace f(Kt/N) by the found capital per worker Put into the evolution of capital per worker over time relation. In the steady state the change is zero so s…=δ…
rearrange to get steady state capital per worker = to….
Consumption per worker is considered…
What is left after enough is put aside to maintain a constant level of capital. Therefore:
C/N = Y/N - δK/N
Consumption per worker in terms of savings rate and depreciation
C/N = s/δ - δ(s/δ)^2 = s(1-s)/δ
Human capital
set of skills workers in the economy have
More skilled workers can…
do more complex tasks more easily without unexpected complications which leads to higher output per worker
An increase in how much society “saves” in the form of human capital increases…
the steady state human capital per worker which leads to an increase in output per worker
models of endogenous growth
models that generate steady growth even without technlogy
Conclusions from endogenous growth models:
- Output per worker depends on the level of both physical and human capital per worker - increasing either the savings rate or the amount spent on education and training can lead to high levels of output.
- won’t a higher level of human capital lead to a greater tech progress
state of technology variable
a variable which tells us how much an output can be produced from given amounts of capital and labour at anytime
Extended production function
Y=F(K,N,A)
Which will be restricted to
Y = F(K,AN)
What effect does an increase in the technology progress have on labour?
It reduces the amount of workers needed to produce a given amount of output
For a given number of labourers what effect does tech progress have on output?
Increases the amount of output
Effective labour
AN
growth rate of effective labour
gA+gN
Amount of investment required to maintain a given level of capital per effective worker
I=δK+(gA+gN)K
or
I= (δ+gA+gN)K
the δ is needed to keep the capital stock constant. The additional amount is needed to keep up with the growth of effective labour
The steady state value of capital per effective worker
sf(Kt/AtNt)=(δ+gA+gN)Kt/AtNt
Slope of the required investment line
(δ+gA+gN)
Conclusion from capital and output per effective worker
In steady state, the growth rate of output equals the rate of population growth plus the rate of technological progress. By implication, the growth rate of output is independent of the savings rate
When an economy is in a steady state, what rate goes output per worker grow at?
gA - rate of growth of technological progress
Balanced growth path
another name for the steady state, due to the fact that capital, output and effective labour all grow at the rate gA+gN
Rate of growth of capital per effective labour
0
Rate of growth of output per effective labour
0
Rate of growth of capital per worker
gA
Rate of growth of labour
gN
What effect does an increase in the savings rate have?
Shifts the investment relation up (graphically). This causes the steady state level of capital per effective worker to be increased leading to an increase in the output per effective worker also. The economy converges to the new steady state
Determinants of technological progress
research and development
fertility of the research process
appropriability of research - how much a firm would benefit from the research
