Keynesian Cross Model

The Keynesian Cross is the simplest model of demand-determined output. It takes the price level as fixed and asks which level of income makes planned expenditure equal to actual production.

The framework follows from Keynes' emphasis on effective demand, then became a standard teaching diagram through Samuelson's postwar textbook synthesis. It is not a complete macro model; it is a controlled goods-market experiment.

The model earns its place because it isolates the multiplier. A change in autonomous spending changes income, income changes consumption, and the feedback continues until leakages into saving, taxes, or imports stop the process.

The 45-degree line records accounting equality: every point on it has Y = E. The planned expenditure schedule records behavior: households consume part of income while investment and government purchases are held fixed.

Equilibrium sits where planned expenditure equals actual output. If planned expenditure exceeds output, firms see unintended inventory drawdowns and raise production. If planned expenditure falls short, inventories accumulate and firms cut production.

The marginal propensity to consume governs the slope of the spending line. The closer it is to one, the longer each dollar of new demand keeps circulating before leaking into saving.

Fiscal policy enters through autonomous expenditure. A government-purchase increase shifts the spending line up; the multiplier converts the direct purchase into a larger output effect as household income and consumption respond.

The model is most credible in slack conditions, when firms can raise output without immediately raising prices. Near capacity, the same demand impulse is more likely to produce inflation or crowding out.

For open economies, imports reduce the multiplier. A stimulus that leaks quickly into imported goods raises domestic income by less than the closed-economy cross suggests.