The Solow growth model with a Cobb-Douglas production function In this question, you will study the Solow growth model with a Cobb-Douglas production function

The Solow growth model with a Cobb-Douglas production function In this question, you will study the Solow growth model with a Cobb-Douglas production function. Consider the following model of economic growth: Kt+1 = (1 - 8)K, +1 (1) Y = AKN (2) S = sy (3) It = St (4) A = A for allt (5) N = N for allt (6) 1/(1-a) (a) Is the production function (2) characterized by constant returns to scale? Explain. (b) Transform the production function (2) into a relation between output per worker, y, and capital per worker, kt (c) Show that ke+1 = (1 - 3)k4 + sAk! (d) Show that the steady-state level of capital per worker, k", is given by (e) Give an expression for output per worker in the steady state, y", and consumption per worker in the steady state, c'. For c", assume that T = 0. (6) Explain what happens to the steady state output, Y", and output per worker y", doubles. when N