Economic growth and economic development 113

Introduction to Modern Economic Growth Exercise 2.8 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 and Assume that capital is owned by capitalists and labor is supplied by a different set of agents, the workers Following a suggestion by Kaldor, suppose that capitalists save a fraction sK of their income, while workers consume all of their income (1) Define and characterize the steady-state equilibrium of this economy and study its stability (2) What is the relationship between the steady-state capital-labor ratio in this ∗ defined above? economy k∗ and the golden rule capital stock kgold Exercise 2.9 Consider the Solow growth model with constant saving rate s and depreciation rate of capital equal to δ Assume that population is constant and the aggregate production function is given by the constant returns to scale production function F [AK (t) K (t) , AL (t) L (t)] where A˙ L (t) /AL (t) = gL > and A˙ K (t) /AK (t) = gK > (1) Suppose that F is Cobb-Douglas Determine the steady-state growth rate and the adjustment of the economy to the steady state (2) Suppose that F is not Cobb-Douglas Prove that there does not exist a steady state Explain why this is (3) For the case in which F is not Cobb-Douglas, determine what happens to the capital-labor ratio and output per capita as t → ∞ Exercise 2.10 Consider the Solow model with non-competitive labor markets In particular, suppose that there is no population growth and no technological progress and output is given by F (K, L) The saving rate is equal to s and the depreciation rate is given by δ (1) First suppose that there is a minimum wage w, ¯ such that workers are not allowed to be paid less than w ¯ If labor demand at this wage falls short of L, employment is equal to the amount of labor demanded by firms, Ld Assume that w ¯ > f (k∗ ) − k∗ f (k∗ ), where k ∗ is the steady-state capital- labor ratio of the basic Solow model given by f (k∗ ) /k∗ = δ/s Characterize 99