Consider the Solow model. Let the resource constraint be given by Y} = C; + It, where Y; = Kf'Lf" is production at time t, C; is consumption, It is investment, K; is capital, L; is labor, d is productivity, and a is capital's share of income. Let the capital accumulation equation be given by AK 1+1 = It th, where cl is the rate of capital depreciation. Suppose that investment is equal to It = 5K, where s is the percentage of output that is invested. Suppose that labor is exogenous and equal to 15 (that is, L; = L in every period). Let a = 0.2. (a) Let the steady state value for capital be denoted by K\". Derive 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 output be denoted by Y'. Derive the steady state value of output as a function of the exogenous parameters. Show every step of all calculations. (c) 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. (d) Draw the Solow diagram. Highlight the steady state value for capital in the graph. Show graphi- cally what the value for consumption is when capital is equal to its steady state value. (e) Now draw a new Solow diagram where you show what happens to output, capital, and consump- tion if the depreciation rate, d, permanently declines. Comment on the results. (f) Draw a graph with time on the horizontal axis and the growth rate of consumption on the vertical axis. Show what happens to the growth rate of consumption over time following the permanent reduction in the depreciation rate, d, in part f). Comment on the result. (g) Use your answers to part a) and part b) to Show what happens to the steady state output to capital ratio, ;, , following a permanent increase in productivity, A. Comment on the results