Questions: Solow Growth Model

Question 1

A country permanently increases its savings rate. According to the Solow model, what is the long-run effect on per-capita GDP growth?

• A. The long-run growth rate rises permanently
• B. The long-run growth rate falls, because less is consumed
• C. The long-run growth rate is unchanged, but the level of per-capita GDP rises to a new, higher steady state
• D. The long-run growth rate is unchanged and so is the level of per-capita GDP

Answer: (C)

In the Solow model, the steady-state growth rate of per-capita output is pinned by the rate of technological progress (g) alone — it is independent of the savings rate. A higher savings rate raises capital per worker, which raises the level of per-capita GDP, but due to diminishing returns to capital the economy eventually settles at a new (higher) steady-state level where investment again exactly covers depreciation and workforce growth. The growth rate itself reverts to g.

Question 2

The Solow model predicts that, holding technology constant, a higher savings rate permanently raises the long-run growth rate of per-capita GDP.

• T. True
• F. False

Answer: False

This is the most common misconception about the Solow model. A higher savings rate raises the steady-state *level* of capital and income per worker, but because of diminishing returns to capital, each additional unit of capital contributes less output. The growth rate during the transition to the new steady state temporarily exceeds g, but in the long run growth reverts to the exogenous rate of technological progress. Savings rate affects level, not the long-run growth rate.

Question 3

Why can capital accumulation alone — without technological progress — not sustain indefinite growth in per-capita income?

Model answer: Because of diminishing returns to capital: each additional unit of capital adds less and less to output. As capital per worker rises, new investment eventually only covers depreciation and workforce growth rather than raising output further. The economy reaches a steady state where per-capita income stops growing. Only technological progress, which shifts the production function upward, can permanently increase what each worker produces.

The production function in the Solow model satisfies the Inada conditions — marginal product of capital is large when capital is scarce and approaches zero as capital becomes abundant. This means there is a capital stock at which gross investment just covers (δ + n)k, leaving no net capital deepening. Technological progress (A growing) shifts this boundary outward continually, which is the only engine of sustained per-capita growth in the model.