Questions: AK Model and Linear Production Functions

Question 1

In the AK model, a government policy permanently raises the national savings rate. What is the long-run effect on the growth rate of output per worker?

• A. No effect on the growth rate — savings rates only affect the level of income, not the long-run growth rate
• B. A temporary increase in the growth rate until the economy converges to a new steady state
• C. A permanent increase in the growth rate, because higher savings translates directly into faster capital accumulation indefinitely
• D. A permanent decrease in the growth rate, because higher savings crowds out consumption and reduces aggregate demand

Answer: (C)

In the AK model, the growth rate equals sA − δ, so a permanent increase in s raises the growth rate permanently. This is the sharpest contrast with the Solow model (option A), where saving affects only the *level* of income in the long run — the growth rate returns to zero (or the exogenous technology growth rate). The AK model breaks this result by eliminating diminishing returns, so each saved unit of output generates the same return as the last, sustaining constant growth indefinitely.

Question 2

Which of the following is the minimum theoretical ingredient required for endogenous sustained growth in the AK framework?

• A. Exogenous technological progress that increases productivity over time
• B. Constant or non-diminishing returns to the accumulable factor (capital)
• C. A sufficiently high initial capital stock that crosses a threshold
• D. Government intervention to correct market failures in R&D

Answer: (B)

The AK insight is purely structural: as long as the marginal product of capital does not fall toward zero as capital accumulates, growth can be self-sustaining. Exogenous technological progress (option A) is exactly what the model dispenses with — it shows you don't need it if returns are constant. The other options add mechanisms not required by the basic logic. The AK model demonstrates the minimum condition: no diminishing returns to K.

Question 3

In the AK model, countries with permanently different savings rates will have permanently different growth rates.

• T. True
• F. False

Answer: True

With growth rate = sA − δ, any permanent difference in s (savings rate) or A (productivity) translates into a permanent difference in growth rates. This implies no convergence between rich and poor countries — a sharp contrast with the Solow model, where all countries converge to the same steady-state growth rate regardless of initial conditions or savings rates. Whether this prediction matches the data is debated, but it follows directly from the model's structure.

Question 4

The AK model predicts that poor countries will eventually catch up to rich ones because continued capital accumulation will eventually face diminishing returns.

• T. True
• F. False

Answer: False

The AK model specifically assumes away diminishing returns — the production function Y = AK is linear in K, so the marginal product of capital is the constant A at all levels of K. There is no convergence mechanism. Poorer countries grow at exactly the same rate as richer ones if they share the same s and A, and countries with lower s or A grow more slowly forever. The convergence prediction belongs to the Solow model, not the AK model.

Question 5

Why does the Solow model predict that long-run growth per worker eventually stops (absent exogenous technology), while the AK model does not?

Model answer: The Solow model has a diminishing marginal product of capital: each additional unit of capital adds less output than the last. As capital accumulates, the extra output from saving falls until it just covers depreciation — at that point, net investment is zero and growth stops. The AK model assumes the marginal product of capital is constant (equal to A), so no matter how much capital accumulates, each additional unit still generates the same additional output. Investment never stops being productive enough to outpace depreciation, so growth continues indefinitely at rate sA − δ.

This is the core intuition of endogenous growth theory. The Solow model's diminishing returns create a gravitational pull back to zero growth. The AK model's linearity breaks that pull. Economically, the constant A can be justified by interpreting K broadly to include human capital, knowledge, and institutional capacity — factors that may not exhibit diminishing returns at the aggregate level even if physical capital alone does.