Outline:

1st Introduction to the problem

2nd The main representatives and opponents

3rd Starting point: Say's law

4th Keynes' criticism on the Say's law

5th A simple C-I model

6th Criticism on the purchasing power parity theory

7th The alternative S-I model

8th Supply and demand for money

9th The Hick's IS-LM model

10th Integration of the employment function

11th Criticism on Keynes' assumptions

7th The alternative S-I model

We will now continue our analysis of the Keynesian system and turn to the S-I model again. In our previous considerations, we assumed that the volume of investment was determined autonomously and therefore does not depend on economic variables such as the interest rate. We now want to cancel this assumption and assume expressis verbis that investment demand depends on the interest rate in such a way that interest rate reductions trigger an increase in investment demand.

True, we have seen that Keynes himself doubted whether interest rate reductions were capable of stimulating investment demand. Now, in the section on the criticism of Keynes, we will show that this assumption does not correspond to reality at all, that it can very well be expected that interest rate reductions will lead to an expansion in investment demand.

Therefore, in the further course of this analysis, we want to modify the Keynesian assumption on interest rate elasticity to the extent that we assume a certain interest rate elasticity. Here, we can indeed remain with the assumption that via interest rate reductions a certain increase in investment is achieved, but that this effect is not sufficient to achieve full employment via interest rate reductions alone, as it was assumed by neoclassical theory.

Thus, we now start from our S-I model, but initially we only draw the savings function in this diagram. We now add a new second quadrant to this graph. The first northeast quadrant informs us about the course of savings depending on national income, while the newly constructed second quadrant (as northwest quadrant) shows the dependence of investment demand on the respective interest rate. To do this, we plot the investment volume on the ordinate in the NW quadrant and the respective interest rate on the abscissa.

We assume a certain interest
rate i_{1}. At this interest rate, entrepreneurs are willing to make
the investment demand I_{1}. Equilibrium on the capital market
presupposes that savings also correspond to this investment demand. According
to the course of the savings function, this saving is achieved with an income E_{1}.
Let us now assume that this income is not sufficient to guarantee full
employment. Full employment would rather require an income of the amount E_{2}.
With this income, so much is saved that equilibrium on the capital market is
only reached with an investment volume I_{2}. However, to trigger this
investment demand, an interest rate i_{2} is required.

With the help of this graph, we
can thus show that the aim of full employment could also be achieved by
lowering the interest rate to i_{2}. Of course, the results of the
previous section remain valid. Full employment could also be achieved by
raising the I-curve (the curve of the creation of purchasing power), for
example by increasing deficit-financed government spending. In this case, the
I-curve would have to be shifted upwards by dI:

8th Supply and demand for money

In our previous considerations, we referred exclusively to the criticism by Keynes on the assumption that via interest rate reductions an increase in investment demand that is sufficient for full employment could be achieved. Now Keynes had also criticised Say's theorem because he was of the opinion that in times of recession and depression not all savings would be invested on the capital market. These considerations led Keynes to develop his liquidity preference theory, to which we will turn now. To do this, we turn from the capital market to the money market.

According to Keynes, the demand for money depends on two motives. On the one hand, money is needed by private households and businesses to carry out the various transactions; Keynes calls this need for money the transaction motive. We must assume that the dates of daily income and expenditure do not syncronise. For example, an employee received his monthly salary on the first of the month and would spend this money over the course of the following days in such a way that he did not spend all his money until the end of the month. In this case, he has an average money supply, and the amount of this depends on the one hand on payment customs, and on the other hand on the amount of income. It is therefore assumed that the liquidity need due to this transaction motive increases with growing income.

According to Keynes, the amount of money held in cash by private economic agents also depends on the level of the interest rate. In this context, Keynes speaks of the speculative motive. We have already seen above that in times of recession and depression it can be quite worthwhile to hold money in cash temporarily and forego interest income, because in these times heavy price losses must be feared, which turn out to be higher than the already low interest income.

This demand for cash due to the speculative motive would depend on the level of the interest rate, whereby it can be assumed that the lower the interest rate is, the higher the demand for cash is due to this motive.

Now we can draw these two relations (transaction motive and speculation motive) in a new diagram, where we draw the demand for money, the liquidity preference L, as well as the supply of money M on the abscissa and the level of the interest rate on the ordinate.

If we assume a certain income
E_{1}, we get a negatively sloped curve of the demand for money L(E_{1}),
i.e. demand increases to the same extent as the interest rate decreases. Again,
it applies that we are only calculating with linear functions for the sake of
simplicity, it can be assumed that these graphs have a curved course in
reality.

If we now assume a higher
income E_{2}, the demand for money is higher due to the transaction
motive if interest rates remain the same. In this way, we obtain a whole set of
money demand curves, whereby these are shifted further to the right the higher
the respective income is.

We can now also draw a curve in this graph that reflects the money supply. Since we assume that the money supply is determined autonomously by the central bank, we can draw the money supply curve as a parallel to the ordinate. Equilibrium prevails on the money market where the money supply curve intersects one of the demand curves. If we assume a very specific level of income, there is only one clear intersection between money supply and money demand.

Our graph now shows how the level
of employment can be increased by means of monetary policy measures. We assume
an interest rate i_{1} and an income E_{1}.
At this income there is underemployment. At a constant interest rate, the
central bank could now bring about a new money market equilibrium at an income
E_{3} by increasing the supply of money.

To this new equilibrium corresponds in any case with a higher income also a higher employment. Thus, we now know three possibilities for increasing employment: Firstly, the state can increase employment by increasing deficit spending; secondly, by way of an interest rate reduction, an employment-increasing effect can be achieved automatically. Finally, it is possible to increase income and also employment by increasing the money supply. However, the last two possibilities are not independent of each other; an increase in the money supply generally leads to a reduction in the interest rate, while an increase in the key interest rate on the part of the central bank triggers a reduction in the demand for money.

9th The Hick's IS-LM model

Up to now we have examined the conditions on the capital markets and the money markets isolated from each other. This is certainly unsatisfactory, since in the Keynesian model both markets are controlled by the interest rate. One could perhaps still try to justify this isolated approach by distinguishing between a short-term money market interest rate and a long-term capital market interest rate. However, there are many substitution relations between these two markets, which have the consequence that changes in the interest rate on one market lead relatively quickly to similar changes in the interest rate on the other market. It is therefore necessary to merge both markets, which is indeed done in the IS-LM model developed by Hicks.

Let us first look at the relations on the capital market. In a two-quadrant model we have shown the course of savings depending on income and investment demand depending on the interest rate. We can now transfer these relationships into a new diagram in which the level of income is plotted on the abscissa and the respective interest rate on the ordinate. Rising interest rates correspond to falling incomes.

Next, we turn to the money market. If we assume a given constant money supply, it is possible to assign to each interest rate a certain income at which just the supply of money and the demand for money correspond. If the interest rate rises, equilibrium is only reached if income rises as well. This means that the LM curve, which connects all possible equilibrium points on the money market, has a rising course.

At the intersection of the IS curves and LM curves, we obtain a combination of interest level and income level at which both the money market and the capital market are in equilibrium.

Again, let us assume that at
this intersection there is underemployment, and that full employment was only
reached at an income of E_{2}.

Now, let us ask ourselves how a
full employment income could be realised. First of all, this graph shows that a
reduction in interest rates on i_{2} obviously leads automatically to
an increase in income on E_{2}, which is assumed to make full
employment possible.

However, an increase in income
and thus also an increase in employment could also be achieved by a shift of
the yellow IS curve upwards and thereby a market equilibrium would have been
achieved at a higher income. In this case the IS curve could be shifted upwards
by an increase in government spending (or generally by an increase in
purchasing power). Then, However, the interest rate would climb to i_{3}.

Thirdly, an increase in income and employment could however also be achieved by expanding the money supply and thus shifting the LM curve to the right. Let us illustrate these relations once again with the money market model.

This graph shows that with an increase in the money supply, the money market equilibrium is at ever higher incomes. This means that the same interest rate corresponds to an ever higher equilibrium income, in other words: via an increase in money, the equilibrium income can be increased, and interest rates fall.

In our considerations so far, fluctuations
in goods prices have not played a role. Keynes in fact assumed that goods
prices do not play a decisive role anyway, at least in an economic downturn.
That is why we did not need to distinguish between a nominal and a real view so
far. Of course, __real__ national income must rise if employment is to
increase. However, if one starts from the assumption that goods prices are
fixed anyway, the equilibrium approach can - without committing major errors -
also be applied to nominal variables.

However, in reality we must assume that the prices of goods rise even in times of economic slowdown; in the post-war period, for example, the phenomenon of stagflation was observed, whereby the decline in economic activity is accompanied by general price increases. It is therefore necessary that the decisive problem variables of the Keynesian model are expressed in real terms, the real variables can be calculated by deflating the nominal variables, thus dividing them by the price level. We therefore always speak of real national income, which in the Keynesian model is determined by the real investment sum as well as the demand for real consumer goods.

We can now introduce the price
level expressis verbis into
the model for the money market. Here also, we must ask about the real money
supply (M/P) as well as the real demand for money. An increase in the money
supply in this model can now take place in two ways. Either the central bank
autonomously increases the nominal money supply or there is a change in the
real money supply insofar as, with a constant nominal money supply, the price
level varies and with it the __real__ money supply. Reductions in the price
of goods would thus automatically lead to an increase in the real money supply.

Thus, if we consider the possibility of variations in goods prices in our IS-LM model, then equilibrium could also be achieved by decreasing goods prices.

To
be continued!