Economic growth and economic development 114

Introduction to Modern Economic Growth the dynamic equilibrium path of this economy starting withsome amount of physical capital K (0) > (2) Next consider a different form of labor market imperfection, whereby workers receive a fraction β > of output in each firm as their wage income Characterize a dynamic equilibrium path in this case [Hint: recall that the saving rate is still equal to s] Exercise 2.11 Consider the discrete-time Solow growth model with constant population growth at the rate n, no technological change, constant depreciation rate of δ and a constant saving rate s Assume that the per capita production function is given by the following continuous but non-neoclassical function: f (k) = Ak + b, where A, b > (1) Explain why this production function is non-neoclassical (i.e., why does it violate Assumptions and above?) (2) Show that if A−n−δ = 1, then for any k (0) 6= b/2, the economy settles into an asymptotic cycle and continuously fluctuates between k (0) and b−k (0) (3) Now consider a more general continuous production function f (k) that does not satisfy Assumptions and 2, such that there exist k1 , k2 ∈ R+ with k1 6= k2 and k2 = f (k1 ) − (n + δ) k1 k1 = f (k2 ) − (n + δ) k2 Show that when such (k1 , k2 ) exist, there may also exist a stable steady state (4) Prove that such cycles are not possible in the continuous-time Solow growth model for any (possibly non-neoclassical) continuous production function f (k) [Hint: consider the equivalent of Figure 2.9 above] (5) What does the result in parts and imply for the approximations of discrete time by continuous time suggested in Section 2.4? (6) In light of your answer to part 6, what you think of the cycles in parts and 3? 100