A government permanently subsidizes investment, raising the economy's savings rate. In the AK model, what is the long-run effect on the growth rate of output?
AThe growth rate temporarily rises during a transition period, then returns to its original level
BThe growth rate permanently rises, because the savings rate directly determines the growth rate
COnly the level of output rises; the long-run growth rate is determined by technology, not savings
DThe growth rate falls, because more investment means less consumption and lower welfare
In the AK model, the long-run growth rate is g = sA − δ, so a permanent rise in s produces a permanent rise in g. This is the fundamental departure from Solow: in Solow, higher savings raises the level of output per worker but not the long-run growth rate (which depends only on exogenous technology). Option C describes the Solow result — the most common wrong answer here — and confuses the two models.
Question 2 Multiple Choice
Why does the AK model produce no steady state, unlike the Solow model?
ABecause the AK model ignores depreciation, so capital always grows
BBecause constant returns to capital mean each additional unit of capital generates the same output as the last, so saving never 'runs out of steam'
CBecause total factor productivity A grows over time, continuously shifting the production function upward
DBecause the AK model assumes an infinite labor supply that keeps the marginal product of capital constant
In Solow, the economy converges to a steady state because of diminishing returns: each additional unit of capital adds less output, so eventually new saving just covers depreciation. In the AK model, the marginal product of capital is constant at A regardless of the capital stock — there are no diminishing returns to the broadly defined K. So the gap between new capital formation and depreciation never closes, and the economy grows without bound. A is wrong because AK models include depreciation (δ) — it's the constant MPK, not the absence of δ, that removes the steady state.
Question 3 True / False
In the AK model, a permanently higher savings rate leads to permanently faster long-run output growth.
TTrue
FFalse
Answer: True
Yes — this is the defining property of the AK model. The growth rate g = sA − δ is directly proportional to the savings rate s. This contrasts sharply with the Solow model, where a higher savings rate shifts the economy to a higher output level but leaves the long-run growth rate unchanged (determined by exogenous technology). Policy that raises investment rates has permanent growth effects in the AK framework.
Question 4 True / False
The AK model assumes diminishing marginal returns to capital, just like the Solow model, but incorporates knowledge externalities that offset them at the aggregate level.
TTrue
FFalse
Answer: False
The AK model assumes *constant* marginal returns to a broad capital aggregate — this is its defining assumption, and the source of both its power and its fragility. The 'broad K' interpretation (including human capital, knowledge, infrastructure) is the justification for why returns might not diminish, but the model itself simply assumes Y = AK with no externalities needed. Models that explicitly model knowledge externalities (Romer 1986) provide microfoundations for constant returns, but the AK model takes constant returns as a primitive assumption.
Question 5 Short Answer
Why does the AK model predict that policy (e.g., tax incentives for investment) has permanent growth effects, while the Solow model predicts only temporary level effects?
Think about your answer, then reveal below.
Model answer: In Solow, diminishing returns to capital mean that each unit of investment adds less output as the capital stock grows, so higher savings eventually just replaces depreciation at a higher but stable level — a steady state. In AK, constant returns mean every additional unit of capital generates the same output increment regardless of how much capital already exists, so the economy never 'settles down.' A higher savings rate translates directly into a permanently higher growth rate, making policy interventions that raise investment have lasting consequences.
The key is the presence or absence of diminishing returns. Solow's diminishing returns create a convergence force that eventually offsets the savings advantage. AK's constant returns eliminate this force. Students often conflate 'higher output' with 'higher growth' — the Solow model does raise output with higher savings, but only to a new steady-state level; the growth rate along the steady-state path remains at the exogenous rate of technological progress.