Questions: Steady-State Growth and Balanced Growth Path

Question 1

Country A permanently raises its savings rate from 20% to 30% of GDP. According to the Solow model, what is the long-run effect on the growth rate of output per worker?

• A. The growth rate permanently increases, because higher saving means faster capital accumulation indefinitely
• B. The growth rate temporarily rises during the transition to the new steady state, but returns to the exogenous technology growth rate g in the long run
• C. The growth rate permanently falls, because higher saving reduces consumption and thus aggregate demand
• D. There is no effect at all — the savings rate has no influence on either growth or income levels

Answer: (B)

This is the Solow model's most important and counterintuitive prediction. A higher savings rate shifts the investment curve upward, raising k* and the level of output per worker — but not the long-run growth rate. During transition, the economy grows faster as it accumulates capital toward the new, higher k*. Once there, diminishing returns ensure that investment again exactly equals break-even investment, and growth returns to g. Only exogenous technological progress drives sustained per-capita growth. Students who answer A confuse a one-time level increase (moving to a higher k*) with a permanent change in the growth rate.

Question 2

An economy is currently below its steady-state capital stock k*. What causes it to grow faster than its long-run balanced growth path rate during this period?

• A. Higher saving — below-k* economies typically have higher savings rates, boosting investment
• B. Diminishing returns working in reverse — when capital is scarce, its marginal product is high, so investment yields disproportionately large output gains
• C. The exogenous technology growth rate g is higher when capital is scarce
• D. Higher depreciation below k* reduces break-even investment, freeing resources for growth

Answer: (B)

The convergence mechanism is entirely due to the concavity of the production function. When k is low (below k*), the marginal product of capital is high — each unit of new capital adds a lot to output. Investment exceeds break-even, so k rises. As k approaches k*, diminishing returns reduce the marginal product until it exactly equals break-even investment. This is why conditional convergence — poorer countries growing faster than richer ones with similar fundamentals — is a testable prediction of the Solow model, and why it follows from diminishing returns rather than any change in savings behavior.

Question 3

In the Solow model, a permanently higher savings rate raises the long-run steady-state level of output per worker but does not permanently raise the growth rate of output per worker.

• T. True
• F. False

Answer: True

This is the central result of neoclassical growth theory. The savings rate determines k* (and thus the level of output per effective worker at steady state) but not the growth rate along the balanced growth path. Once the economy reaches k*, the growth rate of output per worker is g — the exogenous rate of technological progress — regardless of the savings rate. Policy can affect whether an economy is richer or poorer in steady state, but only technological progress can sustain permanently rising living standards.

Question 4

An economy that has accumulated more capital than k* (its steady-state capital stock) will continue to grow faster than the balanced growth path rate as it adjusts.

• T. True
• F. False

Answer: False

When k > k*, break-even investment (δ + n + g)k exceeds actual investment s·f(k) because diminishing returns have made capital less productive. The capital stock per effective worker is *falling*, not rising — the economy is decumulating capital back toward k*. Growth in output per worker is therefore *below* the balanced growth path rate, not above it. The steady state is a two-sided attractor: economies below k* grow faster than g (converging upward), and economies above k* grow slower than g (converging downward).

Question 5

Why does the Solow model predict that only technological progress can sustain long-run growth in output per worker, while a permanently higher savings rate cannot?

Model answer: The answer lies in diminishing returns to capital. As the capital stock per effective worker rises, each additional unit of capital produces less additional output. Eventually, the output gain from new investment exactly equals the break-even investment needed to maintain the capital stock (replacing depreciation and equipping new workers and new-technology-efficiency units). From that point, additional saving cannot raise growth — it only maintains the capital stock at k*. Technological progress, by contrast, shifts the production function upward continuously, meaning each unit of capital at any stock level now produces more output than before. This prevents the marginal product from falling to break-even permanently, sustaining growth in output per worker indefinitely at rate g.

Students who say 'diminishing returns' without explaining why technological progress escapes them are only halfway there. The key is that technological progress shifts the production function itself — it's not capital deepening but capital-augmenting efficiency growth, which changes the level at which diminishing returns bite.