The Keynesian Cross is “[a] simple model of income determination, based on the ideas in Keynes’s General Theory, which shows how changes in spending can have a multiplied effect on aggregate income.” (Mankiw, 2010) Well, it might be a nice simple model with neatly placed lines, however, this only measures a closed economy and wrongly assumes spending provides economic stimulus and spending decreases economic stimulus. “It takes fiscal policy and planned investment as exogenous and then shows that there is one level of national income at which actual expenditure equals planned expenditure.” (Mankiw, 2010) Income here is determined by expenditure. Planned investment (I), is exogenous in this model, therefore, 
. Government policies, such as tax and spending are also fixed in the equation below.
Notation:
PE = C (Y-T) + I + G = Planned expenditure
Y = real GDP = Actual expenditure
Both equations are equal PE = Y in equilibrium. Where any difference is classed as unplanned inventory investment. Note the C (Y – T) in the planned expenditure equation is just the consumption function. Here are the drawn graphs:
Here, the government increase in spending is represented in the government purchases multiplier, in which the increase in income resulting from a $1 increase in G. To Solve for the increase in Y :
While, the tax increase is represented in the tax multiplier, in which the decrease in income resulting from a $1 increase in T. To solve for the increase in T:
Alternatively, if government spending and taxation are both increased, the government purchases multiplier and the tax multiplier both cancel each other out, as long as one is not larger than the other. As government purchases exceed taxes there is a government deficit that increases income, or where taxes exceed government purchases there is a government surplus that decreases income, in this model. This excuses in the Keynesian doctrine that budget deficits are good as spending is more productive than saving, see my article on a similar argument that is put across, Central Banks Interest for Resolving Unemployment. There is also further reading by the Mises Institute, see this article on the Self-Defeat of the Keynesian Cross.
Reference List
Mankiw, N. G. (2010). Macroeconomics, (7th Int. ed.). United States: Worth Publishers, Harvard University.
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Copyright © 2016 Zoë-Marie Beesley
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