Samuelson-Hicks Business Cycle: Multiplier-Accelerator Model

This simulator runs Paul Samuelson's 1939 multiplier-accelerator model period by period and plots national output Yₜ as a live scrolling time series against its equilibrium level. Output next period is driven by two Keynesian mechanisms working together: the multiplier, in which this period's consumption tracks last period's income, and the accelerator, in which investment responds to how fast consumption is changing rather than its level. Because the resulting recurrence is a genuine second-order difference equation, the same three sliders — the marginal propensity to consume, the accelerator coefficient and government spending — reproduce every regime economists actually classify: cycles that die out, cycles that sustain themselves indefinitely, and cycles that explode, exactly as the model's characteristic roots predict. A one-period spending shock button lets you see a fiscal impulse ripple through the economy and either fade or amplify depending on where the accelerator sits.