A firm maintains a capital-output ratio of 4. Last year output grew from $200M to $220M. This year output grows from $220M to $228M. What happens to the firm's gross investment this year compared to last year?
AIt stays the same — output is still growing, so investment continues at the same rate
BIt increases — the higher output level requires more total capital stock
CIt falls — slower output growth means less new capital is needed, even though output is still rising
DIt falls to zero — investment only occurs when output growth is accelerating
Last year: ΔY = $20M, so new investment = 4 × $20M = $80M. This year: ΔY = $8M, so new investment = 4 × $8M = $32M. Investment fell by 60% even though output is still growing — it just grew more slowly. The accelerator formula I = v·ΔY makes this mechanical: investment tracks the *change* in output, not the level. A deceleration (smaller positive ΔY) directly reduces investment even when output and output level are both rising.
Question 2 Multiple Choice
GDP growth slows from 4% to 2% — output is still rising, just less quickly. According to the accelerator principle, what happens to business investment in new capital?
AInvestment grows at 2% — it tracks the growth rate of output
BInvestment falls sharply — it depends on ΔY, so halving the growth rate roughly halves new capital spending needed above replacement
CInvestment is unaffected — the accelerator only responds to output actually falling, not slowing
DInvestment rises — firms rush to build capacity before the anticipated further slowdown
The accelerator predicts I ∝ ΔY. If output growth halves (same capital-output ratio), desired new capital roughly halves. Note this can mean a 50%+ fall in net investment even though the economy is still expanding. This is the amplification mechanism: modest output fluctuations translate into violent investment swings. Recessions often begin not with output falling but with growth slowing — and investment collapses in response, reducing aggregate demand further, which is the self-reinforcing cycle the multiplier-accelerator model captures.
Question 3 True / False
According to the accelerator principle, a firm will increase its investment whenever its output level is high relative to competitors.
TTrue
FFalse
Answer: False
The accelerator principle says investment depends on the *change* in output (ΔY), not the *level*. A firm with high but stable output already possesses the capital stock it needs to serve current demand; desired net investment is zero (only replacement for depreciation continues). New investment is triggered by rising output — when the firm needs to expand its capital stock to serve growing demand. A firm with high, stable output has no accelerator-driven incentive to invest more.
Question 4 True / False
The accelerator principle predicts that investment will be substantially more volatile over the business cycle than output itself.
TTrue
FFalse
Answer: True
Because investment I = v·ΔY depends on changes in output, and output changes are modest fractions of GDP, even small percentage swings in output produce large percentage swings in investment. In the numerical example from the Explainer, a 50% reduction in the output growth rate cut investment by 60%. Real-world data confirms this: GDP fluctuations of 2-4% accompany investment swings of 20-30%. Investment in machinery, equipment, and structures is consistently the most cyclically volatile major component of GDP.
Question 5 Short Answer
A factory's output holds perfectly flat for two consecutive years. According to the accelerator principle, what happens to its investment in new capacity, and why?
Think about your answer, then reveal below.
Model answer: Net investment in new capacity falls to zero. The accelerator formula gives I = v·ΔY = v·0 = 0 when output is flat. The factory already has the capital stock it needs to produce at its current level; since demand is not growing, no additional capacity is required. Only replacement investment (to offset depreciation on the existing capital stock) continues. This illustrates the principle's key implication: even a plateau — not a decline, just stable output — causes new investment to collapse. Firms add capital only when they expect to need more of it.
The policy implication is significant: policymakers who want to stimulate investment cannot simply keep output high; they must ensure output is rising. A stabilized economy at a high level generates no accelerator-driven investment. This is why recovery from recessions often requires sustained GDP growth — not just a return to pre-recession levels — to reignite capital spending.