1.An economy is described by the following equations:

C=15500+0.5(Y-T) - 50000r,

I^p=10000-20000r,

G=8000,

X= 1300,

M=1800,

T=T=8000,

Y^*=50000

(a)Find a numerical equation relating planned aggregate expenditure to output and to the real interest rate (Given PAE=C+I^p+G+NX)(7 marks)

(b)What should the Reserve Bank set the real interest rate to eliminate output gap if any? (8 marks)