Consider the following growth model and answer the questions below. (1H S=I (2) S=5sY 00, Fy >0,F 0 Endogenous (6): I, S, , K, L Predetermined (3): K, L Initial Conditions (3): K, L Exogenous (5): n, s, Compared to the model presented in class, this model adds depreciation. The variable & is the ratg at which capital depreciates. For example, = .15 implies 15 percent of the existing capital stock will wear out over the next year. (The first three questions below are worth most of the credit for this take-home portion of the final. You should be able to answer them by following the steps we took in class for the simpler model.) 1. Using the definitions k = % andy = %, show that equations (1)-(5) reduce to the following two intensive form equations. y =fk) k'=sy[n+6lk 2. Show in a diagram how an increase in the rate of depreciation affects the steady state levels for k and y. rate of population growth n. 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