PART 4: Very long question (1 question; 35 points): 1. Consider the Solow model. Let the resource constraint be given by Yt = Ct + It, where Yt = KALf is production at time t, Ct is consumption, , is investment, K, is capital, and Le is labor. Let the capital accumulation equation be given by AKt+1 = It - dkt, where d is the rate of capital depreciation. Suppose that investment is equal to It = sYt, where s is the percentage of outputsthat is invested. Suppose that labor is exogenous and equal to L (that is, Lt = L in every period). (a) Let the steady state value for capital be denoted by K*. Solve for the steady state value of capital as a function of the exogenous parameters. Show every step of all calculations. (b) Let the steady state value for consumption be denoted by C*. Derive the steady state value of consumption as a function of the exogenous parameters. Show every step of all calculations. (c) Draw the Solow diagram. That is, make a graph where you plot investment, depreciation, and output (with the capital stock on the horizontal axis). Highlight the steady state value for capital in the graph. Show graphically what the value for consumption is when capital is equal to its steady state value. (d) Now draw a new Solow diagram where you show what happens to output and capital if the savings rate permanently decreases. Comment on the results. (e) Draw a graph where you show what happens to the growth rate of output over time as output converges from the original steady state to the new steady state in part (d). Comment on the results