Consider a modified version of the continuous-time Solow growth model where the aggregate production function is
where Z is land, available in fixed inelastic supply. Assume that α + β
(a) First suppose that there is no population growth. Find the steady-state capital-labor ratio in the steady-state output level. Prove that the steady state is unique and globally stable.
(b) Now suppose that there is population growth at the rate n, that is, L/L ? = n. What happens to the capital-labor ratio and output level as t → ∞? What happens to returns to land and the wage rate as t → ∞?
(c) Would you expect the population growth rate n or the saving rate s to change over time in this economy? If so, how?