Keynes famously proposed that in the short run, an economy's income is determined by the spending plans of households, businesses and the government. The more people want to spend, the more goods and services firms can sell. Thhe more firms can sell, the more they will choose to produce and the more workers they will hire. Keynes believed that the problem during recessions is insufficient spending, which leads firms to reduce their output.

To model this insight, we begin by drawing a distinction between actual and planned expenditure. Actual expenditure is the amount households, firms and the government spend on goods and services, and equals the economy's GDP. Planned expenditure is the amount households, firms and the government would like to spend on goods and services.

Why would actual expenditure ever differ from planned expenditure? If firms sell less of their product than they planned, their stock of inventories rises. Conversely, if firms sell more than planned, their stock of inventories falls. In both cases, firms engage in unplanned inventory investment because their sales do not meet their expectations. Because unplanned inventory investment conts as investment spending by firms, it is counted in actual expenditure (GDP) but not in planned expenditure. Hence, actual expenditure can be above or below planned expenditure.

We now consider what determines planned expenditure. Assuming that the economy is closed (net exports are zero), we write planned expenditure PEPE as the sum of consumption CC, planned investment II and government purchases GG:

PE=C+I+GPE = C + I + G

We add the consumption function:

C=C(YT)C = C(Y - T)

This equation states that consumption depends on disposable income, which is total income YY minus taxes TT. For now, we take planned investment, the level of government purchases and taxes as exogenously fixed:

I=II = \overline{I}
G=GG = \overline{G}
T=TT = \overline{T}

By combining these five equations, we obtain:

PE=C(YT)+I+GPE = C(Y - \overline{T}) + \overline{I} + \overline{G}

Planned expenditure is a function of income YY, as well as planned investment I\overline{I} and the fiscal policy variables G\overline{G} and T\overline{T}

The slope of the planned expenditure function is the marginal propensity to consume, MPCMPC. It shows how much planned expenditure increases when income rises by $1. We can explore how the Keynesian cross changes as a result of a change in the MPCMPC: