What is autonomous investment
We now have the tools together to construct a first, albeit still quite simple, ex-ante model of our model economy with which we can the next section will even be able to carry out simulation calculations. Our macroeconomy currently consists only of the goods market. We also assume "autonomous investment". As with Save and with Here, too, consumption signals that the adjective "autonomous" means that we regard investments as an exogenous quantity. We initially assume that the companies have already made their investment decisions and in the period Iaut want to invest and don't let anything dissuade you from it.
Our model thus consists of three equations: the consumption function, the "investment function" and the income identity. The consumption function and the investment function are Behavior equations, as they describe decisions - i.e. behavior - of economic subjects. The investment function is currently doing this in a rudimentary way: companies invest I.aut, Basta. The Income identity is a Definition equation the national accounts.
 C = Caut + cY
 I = Iaut
 Y = C + I
All three equations can be found in Figure 1, which for the sake of clarity continues the previous numerical example. The We have already discussed the consumption function in detail. Since the investments are now also shown in the diagram, the symbol I has been added to the ordinate. The autonomous investments are assumed to be 100. The investment function is parallel to the abscissa, since the investments are independent of the level of income.
The equilibrium in autonomous investments: The demand for consumer and capital goods corresponds to the supply of goods for equilibrium income Y *.
Equation  describes the model equilibrium. Perhaps this would be a little clearer if the variables had not been identified as planned sizes in . The convenient omission of indices is (unfortunately?) Common among economists. The extensive notation is
[3a] Yplanned = Cplanned + Iplanned (or: AS = AD)
Strictly speaking,  is no longer the definition equation from the national accounts, which must always be fulfilled, but a shortened form of the Equilibrium condition [3a]. When it is fulfilled, the economy is in equilibrium, but when it is
[3b] Yplanned > Cplanned + Iplanned ,
is the supply of goods greater than the demand, and if so
the supply remains behind the demand.
To that Equilibrium income To determine analytically, the consumption and investment functions are inserted into the equilibrium condition:
 Y = Caut + cY + Iaut
 Y-cY = Caut + Iaut
 (1-c) Y = Caut + Iaut
 (Equilibrium income)
The equilibrium income Y * depends solely on the model parameters of autonomous consumption, autonomous investments and the marginal consumption rate. The level of overall economic production is therefore determined solely by (consumption and investment) demand. The three parameters can be assumed to be known. The marginal consumption rate and autonomous consumption can be determined via the Determine the estimate of the consumption function. The national accounts can be used for the amount of autonomous investments. The equilibrium income can therefore be determined - at least in principle. Of course, this rudimentary model is not suitable for a practical simulation or forecast calculation.
For the graphical solution, consumption and investments must be added to the total demand C + I shown in green. This function is obtained by shifting the consumption function upwards by the amount of investment (here always 100), i.e. adding the function values of both functions for each income. The equilibrium condition [3a] (AS = AD) corresponds to the 45 ° line in the diagram. The left side of this equation (Yplanned) we read off the abscissa, the right side (Cplanned + Iplanned) on the ordinate.
The figure shows that aggregate supply and aggregate demand match with an income of 800. The visual impression can be confirmed by inserting the parameter values into the analytical solution :
The macroeconomic supply of goods corresponds to the demand if the planned savings match the planned investment volume. [Mouse-sensitive graphics: To graphically determine the balance, savings and investment functions are sufficient.]
Determination of the equilibrium via I = S
From our considerations on the economic cycle, we know that in the overall economic equilibrium of the goods market, "saving equals investing" applies. For this reason, the savings function has been added to Figure 2 compared to Figure 1, and we find, with the close inspection method, to confirm that saving and investing match, as expected, for equilibrium income.
Analytically we could have determined the equilibrium as follows:
 S = I (actually it would be better: Splanned = I.planned)
 paut + sY = Iaut
 sY = -Saut + Iaut
The coloring makes it clear that the equations  and  basically do not differ, since the variables of the same color are related to each other to match.
Equation 9 enables the experienced user to quickly determine the equilibrium income graphically. In a prepared income-expenditure diagram (see mouse-sensitive Fig. 2), two lines are sufficient. The first line is the savings function, the second the investment function. The intersection shows the equilibrium income.
Stability of equilibrium
Since the model is not created dynamically *, you can only guess at the adjustment processes. This is done in Figure 3.
The goods market equilibrium is stable because production is expanded when there is excess demand and decreased when there is excess supply.
In the red shaded area, aggregate demand (C + I) exceeds production (Y). If the companies have free capacity, they will expand their production. This means that production is shifting in the direction of the red arrow, i.e. in the direction of equilibrium income.
An excess supply can be observed in the purple shaded area. The companies do not get rid of their goods and therefore limit production. Here, too, we observe a movement in the right direction with the purple arrow. So we can have hope that the equilibrium is stable.
Inflation and deflation gap
Since there is a gap between supply and demand in the shaded areas, one speaks of an inflationary or deflationary gap based on the microeconomic price theory. Excess demand in a market leads to the Walrasian price adjustment hypothesis to price increases, excess supply to price decreases. Corresponding reactions are assumed for the price level. If there are general gaps in demand, then the price reductions in the individual markets will be reflected in a falling price level. If, on the other hand, there is a shortage of supply in the majority of markets, the rising prices across the board will pull the price level upwards.
These statements are based on plausibility considerations. So far, the model has not taken into account the price level in any way, but on the contrary goes from one fixed price level.
The underemployment balance
Of particular interest is the deflationary gap, which is related to the one described above The basic position of the Keynesian theory - one could also formulate: with the Keynesian creed - corresponds. The deflationary gap is characterized by underemployment.
"Equilibrium in underemployment": The deflationary gap justifies underemployment with a lack of demand.
To do this, we consider Figure 4 and make use of the idea that we are not looking at income on the abscissa, but indirectly also incomeEmployment, as higher income goes hand in hand with higher employment. Now assume that full employment with an income of YVB= 1200 would prevail.
The companies would plan to produce at this level if they expected that they could sell it. With an income of 1200, the aggregate demand AD is only 1100, since households 1000 ask for consumption and companies 100 for investment purposes. The companies will be the Demand gap (= deflationary gap) in the amount of 100 do not want to produce permanently in stock. So they will reduce their production. Employment is falling, income is falling. Only when production has fallen to 800 does the supply of goods face an equally high demand. The goods market is in equilibrium, but there is unemployment - the famous "Equilibrium in underemployment". Summarized:
The cause of unemployment is the demand gap.
The term Equilibrium in underemployment is actually a contradiction in terms. Underemployment means that the labor market is imbalanced. In addition, the capacities of the companies are underutilized.
balance more in
What should be expressed, however, should be clear: The goods market is in a stable situation. There will be no impulses from him, as the companies see no reason to increase their production. If production is not increased, income will not increase either. But that would be necessary to induce additional demand. One - apparently? - hopeless situation:
Companies do not produce because there is a lack of demand, and households do not ask because there is a lack of income.
... and there is a lack of income because not enough is being produced. So that there is no wrong impression - the model by no means excludes full and overemployment situations. If fewer people wanted to work at the prevailing wages, so that the full employment income would be Y * (in the numerical example 800), both the goods and labor markets would be in equilibrium. If the labor supply were to be even lower, the economy would find itself in an inflationary gap, a situation of boom with a shortage of labor.
And the self-healing powers of the markets?
Let's look a little beyond the edge of the model. It will Price level fall and in this way additional demand arises if there is unemployment due to deficit demand?
Proponents of this model would argue that there is no way out. The goods market is in equilibrium at Y *. Why should the price level fall? There is no reason for this, because the companies sell their production at the prevailing prices.
Yes, but what about them Wages? If there is unemployment, entrepreneurs would have to seize the opportunity and recruit workers at lower wages - suppose that the unions allow it.
The Keynesians will counter that falling wages would not lead to more employment. In their view, the level of wages is not the cause of unemployment. The cause is the lack of demand, which is unlikely to increase due to falling wages. * The opposite is to be feared. Reinforced by psychological effects, falling wages would lead to even greater reluctance to consume. Citizens buy new cars when incomes rise, not when they fall.
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