Economics
The Multiplier-Accelerator Model of Business Cycle Fluctuations
Quick fact
Paul Samuelson, the first American Nobel laureate in economics, formalized this model in 1939, showing how the interaction of the multiplier and accelerator alone—without any external shocks—could produce alternating booms and busts.
Why this is interesting
Have you ever wondered why economies don't grow smoothly but instead lurch between booms and busts? What if a single new factory could set off a chain reaction that eventually triggers a recession?
Read the full explanation
Understanding The Multiplier-Accelerator Model of Business Cycle Fluctuations
The multiplier-accelerator model is like a swinging pendulum: a small push can make the whole system move back and forth. Let's start with two pieces of intuition. First, the multiplier: when a business invests in a new factory, workers earn income, they spend part of that income, which becomes income for others, who spend again. So an initial investment gets multiplied into much larger total income, following a geometric progression. Second, the accelerator: when income rises, businesses become more optimistic and invest even more to keep up with demand. So higher income leads to higher investment. The model puts these two together: investment drives income (multiplier), and income drives investment (accelerator). But because spending and income take time to adjust (there are lags), the feedback isn't immediate. So you get a delayed reaction, like when you push a child on a swing—each push comes a bit later, and the swing builds up, then slows down, then reverses. In the economy, a rise in investment boosts income, which next period boosts consumption, which boosts investment again, but the effects weaken or overshoot, leading to cycles.
A deeper explanation
The mechanism is a classic second-order linear difference equation. Let income be Yt, consumption Ct, and investment It. The multiplier says Ct = cY{t-1} (where c is the marginal propensity to consume). The accelerator says It = v(Y{t-1} - Y{t-2}), where v is the accelerator coefficient representing how much investment responds to changes in income. Total output is Yt = Ct + It + Gt (government spending). If we set Gt constant, we get: Yt = cY{t-1} + v(Y{t-1} - Y{t-2}) + G. This equation's behavior depends on c and v. For certain values, the economy converges smoothly to a new equilibrium; for others, it oscillates with damped, sustained, or even explosive cycles. The lags are the key: consumption is based on last period's income, and investment on the change in income from the previous to the last period. These lags create a time lag between cause and effect, which produces the cyclical pattern. This model brilliantly shows that internal economic forces alone, without external shocks (like technological breakthroughs or policy changes), can generate business cycles. It was a foundational step in endogenizing business cycles, influencing later real business cycle theory and New Keynesian models, and it remains a powerful teaching tool for understanding dynamic systems in economics.