Consider the continuous-time Solow model without technological progress and with constant rate of population growth equal to n. Suppose that the production function satisfies Assumptions 1 and 2. Assume that capital is owned by capitalists and labor is supplied by a different set of agents, the workers. Following a suggestion by Kaldor (1957), suppose that capitalists save a fraction sK of their income, while workers consume all of their income.
(a) Define and characterize the steady-state equilibrium of this economy and study its stability.
(b) What is the relationship between the steady-state capital-labor ratio k∗ and the golden rule capital stock k∗gold defined in Section 2.2.3?