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PART 4: Very Long Questions (1 Questions; 35 Points l5 Points for Each Part 1. Consider the Solow model. Let the resource constraint be given by Y) = C,- + I),- where Y; = AKfLi'\" is production .at time t, C; is consumption, It is investment, K, is capital, L, is labor, and fl is productivity. Let the capital accumulation equa~ tion be given by Kt+1 K, = i} (1K),- where d is the rate of capital depreciation Suppose that investment is equal to I, = SIG, where s is the percentage of output that is invested. Suppose that labor is exogenous and equal to E (that is, L; = Z in ' every period). (a) Let the steady state value for capital be denoted by K". Solve for the steady I state value of capital as a function of the exogenous parameters. (Show everya- _ step of all calculations) (b) Let the steady state value for output be denoted by I\". Solve for the steady state value of output as a function of the exogenous parameters. (Show every step of all calculations) (c) Solve for the steady state value of the capital-output ratio, C", as a function of the exogenous parameters. (Show every step of all calculations) ' (d) Use your answers to part (a) and part (b) to solve for the steady state output to capital ratio, % (Show every step of all calculations). Now assume that productivity increases permanently from A to A'. Comment on how thetratio % changes due to the change in productivity. (e) Draw the Solow diagram. That is, make a graph where you plot investment, depreciation, and output (with the capital stock on the horizontal axis). High- light 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. (f) Draw the Solow diagram. That is, make a graph where you plot investment, depreciation, and output (with the capital stock on the horizontal axis). High ' light the steady state value for capital in the graph. Show graphically what the values for investment and depreciation are when capital is equal to its steady state value. (g) Now draw a new Solow diagram where you show what happens to output, capital, and consumption if the depreciation rate, d, permanently declines to 5", here of > d', permanently declines (Hint: change in depreciation rate changes the slope of the depreciation line). Comment on the results