The Neoclassical Growth Model and Steady States

THE NEOCLASSICAL GROWTH THEORY: This focuses on capital accumulation, and how it is affected by savings

One important function in the neoclassical growth theory is the AGGREGATE PRODUCTION FUNCTION. This function shows the relationship between total real output and total inputs (sort of like a "macro" version of the production function for individual firms we saw in microeconomics)

REMEMBER from the last leccture? There are three main determinants of economic growth: labour, capital, and technology. Well, with the aggregate production function, we say that output is technology times a function of labour and capital

Y = A x F(N,K) where A = total factor productivity (disembodied technology), N = Labour and Human Capital, and K = capital (both quantity and quality)

Now what happens if we divide through by N?

Well, we get

y = A x F(k) where y is the amount of GDP produced per worker, and k is the amount of physical capital available for each worker

Also, potential output is also representable here

Y* = A x F(Nfe, Kfc) where Nfe is full employment, and Kfc is full capacity. In other words, potential output is technology times a function of labour at its full employment level, and physical capital at its full- capacity level

Some important things to remember:
We assume in the long run that income is at its potential level (that there is no output gap)
L is labour quantity, H is labour quality, and N includes both the quality and quantity of labour.
K includes both the quality and quantity of physical capital
We omit land as a factor input for the sake of simplicity in this model
Technology includes entrepreneurship and savviness

PROPERTIES OF THE NEOCLASSICAL AGGREGATE PRODUCTION CURVE

1: In the short run, there are diminishing returns to scale: as more of a variable factor is added to a given amount of fixed factor, the additional output generated by the added factor (the "return") will get increasingly smaller and smaller: they will diminish... ceteris paribus (they will diminish if all other things are held constant) after a certain point (they will not begin to diminish immediately)
But, this is only true of the short run when one factor is increased, and all other factors are held constant!

2: In the long run, there are constant returns to scale: When all factors increase the same amount, output will also increase by that amount (so if I double the amount of workers and also the amount of sewing machines, my sweat shop should double its output of shitty sneakers!)

3: Technology is nuetral: A affects the productivity of K and N equally, so although technology is present, it will not disproportionately impact any one factor.

Image Plz! y = f(k)

4: Steady state equilibrium: Here, the per-capita capital (k) and the per capita output (y) remain constant over time, so /\y = /\k = 0

If the population is growing at n, then income and capital must also grow at the same rate in order to remain in a steady state equilibrium. In other words, in order to be in a stead state equilibrium, the percentage change in output must equal the percentage change in capital, which must = the percentage change in the workforce.

y* and k* are the steady state values (they don't change over time)

Investment required to provide capital for new workers and to replace machines that have worn out (depreciation) is just equal to the national savings in a steady state equilibrium, so New Capital + Replacement Capital = Investment = Savings

If savings is greater than investment, than capital per worker will increase, and thus output per worker will also increase

If savings is just equal to investment, then the capital per worker will be k* and thus output per worker will be y*

When savings is equal to required investment, the economy is in a steady state equilibrium, each worker will have access to k*, and will produce y*

MORE ON THE STEADY STATE

To maintain k at a constant rate, investment depends on both population growth and the depreciation rate. Some of investment will have to go to the new workers

WE ASSUME that the population growth rate is constant: thus, to keep capital per worker constant, you must grow capital by nk (the population growth rate times the amount of capital per worker)
WE ASSUME that the rate of depreciation is constant: thus to keep capital per worker constant, you must grow capital by dk as well (the depreciation rate times the amount of capital per worker)

The level of investment required to fund all of this capital growth to maintain a constant capital-worker ratio can be represented by
I = (n + d)k

THE SAVINGS FUNCTION
Here, we assume that we have a frugal economy (there is no government or international trade)
We also assume that the marginal propensity to save is constant
So:
S/N = sy = sf(k)
in other words, per capita savings are a function of per-capita output, which in turn, is a function of the labour-capital ratio

PUTTING IT ALL TOGETHER:
The net change in the capital-labour ratio is equal to the excess of actual savings over required investment
/\k = to per-capita savings - the capital-labour ratio multiplied by (the population growth rate + the rate of depreciation)

In a steady state, /\k = o, so per-capita savings must be equal to per-capita required investment
sy* = (n + d)k*

Image plz

If we graph the production function, the savings function, and the required investment function with money on the Y axis and the capital labour ratio on the X axis, the savings function and the required investment function will eventually intersect: this point is the steady state equilibrium, E
at E, actual investment is just equal to required investment
the capital-labour ratio k* and standard of living y* are constant
At capital labour ratios lower than k*, savings will be greater than required investment, so the capital labour ratio and the standard of living will both increase.

Macroeconomic Timespans

Macroeconomic Time Spans: Changes can have different effects over the long run than they do in the short run! This is just going to be a brief comparison exercise between the long run and the short run.

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IN THE SHORT RUN:
-Changes in national income are a function of factor utilization rate: for an example, the rate of employment. When more people are employed, more factors are being utilized, so national income increases
-National income is demand-induced: aggregate demand determines what the national income is going to be. The higher demand is, the higher the factor utilization rate will have to be in order to sate demand.
-Actual GDP, or Y determines national income: this means that there can be recessionary or inflationary output gaps
-Fiscal and monetary policy can affect both aggregate demand and actual national income
-Policies focus on shifting aggregate demand
-Gapbusting is the political objective
-Policies affect utilization rates
-Policies are focused on stabilizing real GDP at it's potential

IN THE LONG RUN
-Changes in national income are a function of both the supply of factors (ie: the size of the labour force), and factor productivity (ie: how productive and useful, on average, each worker is). The larger the workforce, and the more productive that workforce is, the higher national income will be
-National income is supply-induced: even if demand increases, wages will simply adjust and price will change, but producers will still produce the same amount in the long run UNLESS their production capabilities change. The supply and productivity of factors affects supply, and therefore, can change production in the long run.
-Potential GDP (Y* or Yfe) is a better determinant of what the national income will be. While understanding that output gaps do occur thanks to the business cycle, it is long run aggregate supply which basically determines what GDP will be
-Fiscal and monetary policy have a neutral effect (or even a negative effect: if expansionary policies increase consumption at the expense of savings, then there will be a smaller "pot" for investors to borrow from, so investment will be lower in the long run, causing a lower long run GDP)
-Policies are aimed at affecting potential GDP
-Technological change is key
-Policies attempt to affect factor supply and productivity
-Growth is the political goal

Cool?

Cool! =D

Honestly, just read the chapter for this one: it's short, and it makes more sense than the class notes...

Supply Shocks and Other Important Things!

SUPPLY SHOCKS: These also correct themselves in the long-run, but unlike demand shocks, these do not cause any net changes in the price level.

NEGATIVE SUPPLY SHOCK
-Let's say that the cost of oil rises: this shifts AS to the left, which decreases overall economic output and increases the price level.
-There is now a recessionary gap in the economy, and this will cause unemployment to rise
-As unemployment rises, firms can get away with paying their workers less, so wages fall
-Because wages are a cost, production costs fall, and this shifts aggregate supply to the right, back to equilibrium
-Ultimately, the economy is right back where it started at: there is NO NET CHANGE

POSITIVE SUPPLY SHOCK
-Let's say that a new technology emerges which lowers the price of electricity: this shifts AS to the right, which increases overall economic output and decreases the price level
-There is now an inflationary gap in the economy, and this will cause unemployment to fall below its natural level
-As unemployment falls wages rise (overtime and worker retention)
-Because wages are a cost, production costs rise, and this shifts aggregate supply to the left, back to equilibrium
-Ultimately, the economy is right back where it started at: there is NO NET CHANGE

BUT, just because the economy is the same, this doesn't mean that wealth doesn't shift. In the event of a negative supply shock wealth tends to shift from the workers to the capital owners (so workers are paid less, and company owners make more money)

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SHOCKS AND THE BUSINESS CYCLE

Positive supply and demand shocks cause GDP to rise above it's potential level for a period of time, and then to fall back to potential (because inflationary gaps cause decreased unemployment, higher wages, and increased factor prices)

THESE SHOCKS ARE RANDOM...

SO:

The economy's adjustment system accounts for these random shocks, and basicaly incorporates them into business cycles (short term fluctuations of the economy)

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LONG RUN AGGREGATE SUPPLY: This is the relationship between price and GDP after changes in input prices have been taken into account. LRAS is the result of automatic adjustments which bring GDP back to its potential level. LRAS is also called classical aggregate supply, because classical economists assumed that the economy has an automatic tendency to return to Y*

LRAS, graphically, is a vertical line at Y*, because the amount of goods produced at the normal utilization rate is Y*

The only thing which this can be used to demonstrate is price changes: as long as factor prices rise by the same proportion as output prices, then Y*remains constant

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SHIFTING Y*