Consider the following growth model and answer the questions below. (1) (2) (3) (4) (5) (6) S=lr S=SY 0 0, PAL > 0, FKK 0 A' =gA g>0 Endogenous (6): I, S, Y, K', Ll, Al Predetermined (3): K, L, A Initial Conditions (3): Kg, L0, A0 Exogenous (S): n, g, s, 5 Compared to the model presented in class, this model adds technological improvement and depreciation. The variable A is the level of technology and the variable 6' is the rate at which capital depreciates. For example, 6 = .15 implies 15 percent of the existing capital stock will wear out over the next year. 1. 2. 3. Using the denitions 1: = 1% and y = i, show that equations (1)(6) reduce to the two intensive form equations. y=f(k) k':sy[n+g+6]k Show in a diagram how an increase in the rate of depreciation affects the steady state levels for k and y. You should see that the rate of population growth It impacts the steady state levels for k and y in a way Slmartg the depreciation rate 6 . Thinking about this, comment using only words (no diagrams or equations) on how this model indicates a society could offset the damaging impacts of an increase in the rate of population growth by being proactive and seeking to change the rate at which its tools depreciate. Y Show that, if the economy is in a steady state where y = Z is constant, then the rate of growth of the per capita output level E is equal to the rate of growth in the level of technology A