Let Yo = 20K N-a and Y4 = 21K4N1-4. Subscripts 0 and 1 denote the current and future periods respectively. Let d is the depreciation rate; I is the investment; Wo is the wage rate in period 0; wi is the wage rate in period 1; To is the profit in period 0; Ti is the profit in period 1; V is the present value of the profits; and r is the real interest rate. (a) Derive the optimal investment schedule (Hint: Net MPKj is equal to real interest rate). Show all steps and provide explanations for the key equations. (b) Now assume Nj=1; a=0.3; 22=1; and d=0.05. Draw a graph that shows the relationship between I and r. Provide a brief explanation. (Hint: Set K1=1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. Each K, calculate the corresponding I and r. It might be easier if you do it on Excel. Do NOT submit your Excel file. Copy your graph onto your text file). Let Yo = 20K N-a and Y4 = 21K4N1-4. Subscripts 0 and 1 denote the current and future periods respectively. Let d is the depreciation rate; I is the investment; Wo is the wage rate in period 0; wi is the wage rate in period 1; To is the profit in period 0; Ti is the profit in period 1; V is the present value of the profits; and r is the real interest rate. (a) Derive the optimal investment schedule (Hint: Net MPKj is equal to real interest rate). Show all steps and provide explanations for the key equations. (b) Now assume Nj=1; a=0.3; 22=1; and d=0.05. Draw a graph that shows the relationship between I and r. Provide a brief explanation. (Hint: Set K1=1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. Each K, calculate the corresponding I and r. It might be easier if you do it on Excel. Do NOT submit your Excel file. Copy your graph onto your text file)