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