Solow Model with Productivity Growth In this question, we consider the Solow model with productivity growth. Suppose that production function takes Cobb-Douglas form with growth of labor productivity :  =  ^ () ^1 . Capital accumulates according to +1 = (1  ) +  . Investment is equalized to aggregate saving at the equilibrium:  =  In what follows, we assume that productivity grows at the constant rate of , and labor grows at the constant rate of : +1  = 1 + , +1  = 1 + n

 

(d) () Drive the output per unit of effective labor, , at the balanced growth path with the parameters.

(e) () Suppose that we are at the balanced growth path. Express the growth rate of the economy ( ) with the parameters. See how the productivity growth rate affects the growth rate of the economy.

(f) () Drive the saving rate such that maximizes consumption per unit of effective labor at the balanced-growth path: = , . Express as a function of the parameters.