The following set of equations describe an economy: C = 15,000+ 0.5(YT) - 50,000r IP = 10,000 25,000 G = 8,000 NX = = 2,000 T = 8,200 Y* = 46,800 a. Find a numerical equation relating planned aggregate expenditure to output and to the real interest rate. PAE= 30900 75000 r 0.5 Y b. At what value should the Fed set the real interest rate to eliminate any output gap? (Hint: Set output Yequal to the value of pote output given above in the equation you found in part a. Then solve for the real interest rate that also sets planned aggregate expenditure equal to potential output.) Instructions: Enter your response as a whole number. Real rate of interest: 13%