Home > Aggregate Demand, Macro > The Keynesian Cross

## The Keynesian Cross

You may have seen the Keynesian cross at A-level. This can be a fiddly one to understand at first. The idea behind this is there will be a level of planned expenditure in the economy which is the amount consumers (households), firms, and government plan to spend on goods and services. This is basically the demand for goods and services. When this planned expenditure is higher than firms producing goods expected, then will start depleting their inventory stocks of goods, and this will stimulate more production, they will start hiring more workers and produce more, so income will rise. When the planned expenditure is lower than the firms producing goods expected, then they start building up their inventory stocks with unsold goods, which will cause them to step back on production, lay workers off, and income will fall.

Either way, the goods market comes into equilibrium because firms producing goods will end up adjusting to the overall level of planned expenditure in the economy.

We can express this by expressing the closed economy Keynesian model of AD in terms of ‘demand’ which we will call Z.
$Z=a+b(Y-T)+I+G$. In this equation, C has been replaced by its components, a (autonomous consumpton), and b (marginal propensity to consume). The Keynesian Cross takes I and G and T to be exogenous, they are fixed amounts when you draw the line of planned expenditure (demand), if you change them you have to shift the whole line up or down.

The Keynesian Cross model has demand, Z on the vertical axis and income, Y on the horizontal axis, so the planned expenditure line will be upward sloping (Z increases as Y increases because when incomes are higher, consumers have more disposable income, and so demand more goods, hence Y appears in the equation above). As Y is multiplied by b, then b gives us the slope of the planned expenditure curve. Remember that b is the marginal propensity to consume, so we can say that the marginal propensity to consume will determine how steep the planned expenditure curve is.

The fixed components of the planned expenditure curve, a, T, I and G, determine the height of the curve (where it intercepts the vertical axis. If you increase a, I or G, then you push the curve up. If you increase T (taxation) then you push the curve down – because T has a minus sign in the equation so it affects Z negatively.

On the Keynesian Cross you will also always see the 45 degree line drawn in. This is because of the fact that the goods market always comes into equilibrium, like mentioned above, if planned expenditure (demand) is running ahead of firms’ production, then their existing inventory stocks get depleted and it encourages them to produce more as they know the demand is there to sell their goods. If demand is below firms’ production then they are just accumulating unsold stocks in their inventories, so they scale their production levels down. Eventually we have a situation where planned expenditure (demand) = actual production (output), so demand equals output (or income). So the 45 degree line is just because we have drawn Z on one axis and Y on the other, we know that in equilibrium Z=Y which will be somewhere on this 45 degree line. The actual point where it comes into equilibrium will be where the planned expenditure line crosses the 45 degree line.

Here we have an equilibrium at Y1, where the planned expenditure curve intersects the 45 degree line.

So the key points from the Keynesian Cross model are:

The marginal propensity to consume gives the slope of the planned expenditure curve

The planned expenditure curve shifts up if we increase autonomous consumption, investment or government spending, or if we decrease taxation. If this happens we get a higher level of income at equilibrium.

The planned expenditure curve shifts down if we decrease autonomous consumption, investment or government spending, or if we increase taxation. If this happens we get a lower level of income at equilibrium.