In the Solow growth model, what determines the steady-state level of capital per worker and why do we converge to it?

• A. Increasing returns to capital lead to a stable steady state; the steady-state capital per worker depends on saving rate, population growth, and depreciation.
• B. Constant returns to scale; determined by technology alone.
• C. Random shocks; determined by foreign investment only.
• D. Increasing returns to capital lead to a continually rising steady state.

Answer: (B)

The key idea is how the economy settles at a stable level of capital per worker when technology is fixed. In the Solow model, with constant returns to scale, the capital per worker changes according to investment minus depreciation and the need to equip a growing workforce: Δk = s f(k) − (n + δ) k. The steady state happens where Δk = 0, so s f(k*) = (n + δ) k*. This shows what fixes the steady-state: the saving rate, the population growth rate, the depreciation rate, and the shape of the production function (which technology helps determine). Technology matters because it shapes how much output you get from a given amount of capital, but it does not, by itself, pin down the steady-state level of capital per worker; you also need saving behavior and the flow of new workers and depreciation.

Convergence to that level occurs because of diminishing returns to capital. If capital per worker is below k*, investment per worker exceeds what’s needed to cover depreciation and to equip new workers, so capital per worker rises. If it’s above k*, investment falls short of those needs, so capital per worker falls. This dynamic pulls the economy toward the steady-state level.

So, the best description is that the steady-state level of capital per worker is determined by saving, population growth, depreciation, and the production function (technology shapes it), not by technology alone. The option stating constant returns to scale determined by technology alone is not correct.