Questions: Economic Growth and the Solow Model

Question 1

In the Solow model, what defines the steady-state level of capital per worker?

• A. The point where capital per worker grows at its maximum rate
• B. The point where investment per worker equals depreciation plus population growth, so capital per worker stops changing
• C. The point where technological progress is maximized
• D. The point where all countries have identical income per worker

Answer: (B)

At the steady state, new investment exactly replaces capital lost to depreciation and diluted by population growth (sf(k*) = (δ+n)k*), so capital per worker k* is constant. Below k*, investment exceeds break-even and k rises; above k*, break-even exceeds investment and k falls.

Question 2

According to the Solow model, a country can achieve sustained long-run growth in output per worker by continuously raising its savings rate.

• T. True
• F. False

Answer: False

A higher savings rate shifts the investment curve up, raising the steady-state level of k* and output per worker — but this is a one-time level effect. Once the new steady state is reached, growth stops again. Sustained growth in output per worker requires continuous improvement in total factor productivity (technology), not ever-higher savings, because of diminishing returns to capital.

Question 3

What does 'conditional convergence' mean in the Solow model, and why is the word 'conditional' essential?

Model answer: Conditional convergence means poor countries will grow faster than rich ones and eventually reach the same income per worker — but only if they share the same fundamentals (savings rate, population growth, technology). It is 'conditional' because countries with different fundamentals converge to different steady states, not to each other.

Countries below their own steady state have higher marginal products of capital and therefore grow faster. But if a poor country has a low savings rate or high population growth, its steady state is itself low — so convergence to a rich country's income level should not be expected. This distinction between unconditional and conditional convergence is empirically important: within similar country groups (e.g., OECD members), conditional convergence holds reasonably well.