A short‑run macroeconomic model in which equilibrium national income (output) is determined by the intersection of planned aggregate expenditure and actual output, with changes in autonomous spending producing multiplied changes in equilibrium income through induced consumption.

Principle

An exogenous change in autonomous spending (investment, government spending, or net exports) shifts planned expenditure and, multiplied by the marginal propensity to consume (MPC), yields a larger change in equilibrium income (the fiscal multiplier) while prices and capacity are held fixed.

Demonstration

Situation: Government increases autonomous spending by a fixed amount. Recognition: Planned aggregate expenditure schedule shifts upward. Action: Firms produce more to meet higher demand; households increase consumption in proportion to MPC. Consequence: Equilibrium output rises by the initial spending times the multiplier (1/(1−MPC)), assuming fixed prices and idle capacity.

Misapplication

Using the model to predict long‑run growth or applying the multiplier without checking for binding capacity, price adjustments, open‑economy leakages, or time‑dependent behavioral responses; the error is treating a short‑run, fixed‑price accounting framework as a full specification of long‑run determination.

Consequence

Within its assumptions, the model implies fiscal policy can change short‑run output and employment, informing policy design, forecasting and the interpretation of demand shocks; it does not by itself determine inflation, long‑run growth, or supply constraints.

Reversal

When prices are flexible, the economy is near full employment, capital is fixed, or in open economies with large import leakages, the multiplier is reduced and fiscal stimulus may crowd out private expenditure or raise prices rather than output.

Boundary

Clearly within: closed, short‑run economy with fixed prices and unused capacity. Boundary case: small open economy where part of increased demand is met by imports. Clearly outside: long‑run growth analysis where capital accumulation, productivity and supply‑side factors determine output.

Semantic Tension

Tension with classical/supply‑side views that emphasize flexible prices and output determined by factors of production; operationally the tension is whether demand management can change real output given supply constraints.

Synthesis

The Keynesian Cross is a diagnostic bookkeeping device that makes explicit how demand changes propagate through induced consumption to affect short‑run output under fixed‑price assumptions; its policy relevance depends on whether those short‑run assumptions hold.