Question

Problem 3. Consider the Solow model where the production function is Cobb-Douglas and takes this form, Y = Ka (LE)1-a, where 0 < α < 1. The savings rate s s, the depreciation rate isỗ, and the growth rate of E is g and the growth rate of L is n. Denote y E and LE 1. The economy is at the steady state. Report the steady-state growth rates of y, k, Y, K, L' K' ?, an 2. Assume that the market of labor is perfectly competitive. The economy is at the steady state. Express as a function of E and the parameters (i.e., α, s, δ,n, g). What is the steady-state growth rate of real wage, (Hint: Recall that MPL) 3. The savings rate in the country increases from s to s'. What happens to the growth rate of the level of capital stock, K after s increase? [It is sufficient to give qualitative description.] What is the growth rate of the level of capital, K in the long run? Now assume that the savings rate din't change, however, the country experiences a disaster, and therefore losses one-fourth of its capital stock 4. Express Y, K, ^, Y, and K as function of the steady state level of capital per effective worker, k* and E, L, a 5. What is the growth rate of the total output before the disaster? Is the growth rate of the total output after the disaster is larger or smaller than before? Why?