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Determination of GDP in the cross model

Main result

In the cross model, GDP is determined as the solution to the equation YD(Y) = Y

We may illustrate the determination of Y graphically:

Determination of GDP in cross model.

Fig, 11.3: Determination of GDP in cross model.

All points on the 45-degree line has the same x- and /-coordinates. Since we have Y on the x-axis, and YD on the /-axis, YD = Y for all points on the 45-degree line. The AD curve shows the aggregate demand YD as a function of Y. There is only one level of Y where aggregate demand is equal to Y, the point where AD cuts the 45-degree line. This level is called the equilibrium level of GDP and it is denoted by Y*. Formally, Y* is defined implicitly by YD(Y*) = Y*.

Justification

Note that we have not said anything about the aggregate supply so far. In order to justify why GDP is determined solely by aggregate demand we have to explain why aggregate supply YS plays no role and why YS always will be exactly equal to YD (which is required for the goods market to be in equilibrium).

We can explain why YS = Y* by analyzing what would happen if firms did not supply this quantity.

1. Imagine that the firms supplied and also produced a larger quantity so that Y > Y*.

2. From the diagram above, YD < Y and firms cannot sell everything they produce.

3. Unplanned stock investments will increase by Y - YD when companies are forced to put unsold products in stock.

4. Firms will then want to lower their supply. The reduction will continue until

Y = Y*.

5. If, on the other hand, they supply and produce too little, Y < Y* and then Yd > Y. Stocks will now be reduced and firms will want to increase the supply.

Note that the Keynesian model always assumes quantity adjustment to get back to equilibrium. There are no price adjustments in the Keynesian model.

Say’s Law

Also note how the entire outcome of the cross model depends on the elimination of Say’s Law. With Say’s Law, aggregate demand would always be equal to aggregate supply and the cross model would be incorrect.

Keynes’s argument as to why Say’s Law does not apply can be illustrated in the cross model. According to Say’s law, supply creates its own demand. When supply increases, income increases and a higher income creates an equally large increase in demand. Households and firms are stimulated to a higher demand by cuts in the real interest rates. Higher aggregate supply will lower the real interest rate and consumption and investment will increase. According to Say’s Law, r will fall to the level where the total increase in C and I is exactly as large as the increase in aggregate supply.

According to Keynes and cross model, this will not happen. When Y increases, C will increase but not as much as Y (and I will not change at all). Aggregate demand will not increase as much as aggregate supply and Say’s Law will fail.

Reversed Say’s Law

In the cross model, supply must instead follow demand. The cross model not only rejects Say’s Law, it turns it completely upside down. In the cross model "demand creates its own supply".

Just as Say’s Law is criticized by many economists, there is criticism of this reversed form of Say’s Law. In this reversed form, firms passively produce exactly what the consumers want. If there is an increase in demand, firms will just produce this additional quantity. The motivation for this behaviour by the firms is further analyzed when we describe the labor market in the cross model.

Determination of other variables

Once Y is determined, almost all of the other variables are determined because they are either exogenous or they depend on Y. From Y we can determine C by the consumption function, Im from the import function and NT from the net tax function.

Determination of C, Im and NT.

Fig. 11.4: Determination of C, Im and NT.

When these variables are determined, we can determine net exports, household savings, government savings and rest of the world savings. All macro variables except L and U are thus determined.

 
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