Consider the basic Solow growth model with a constant saving rate s, constant population growth at the rate n, and no technological change, and suppose that the aggregate production function takes the CES form in (2.38).
(a) Suppose that σ > 1. Show that in this case equilibrium behavior can be similar to that in Exercise 2.22 with sustained growth in the long run. Interpret this result.
(b) Now suppose that σ → 0, so that the production function becomes Leontief:
The model is then identical to the classical Harrod-Domar growth model developed by Roy Harrod and Evsey Domar (Harrod, 1939; Domar, 1946). Show that in this case there is typically no steady-state equilibrium with full employment and no idle capital. What happens to factor prices in these cases? Explain why this case is pathological, giving at least two reasons for why we may expect equilibria with idle capital or idle labor not to apply in practice.