In: Economics
The following equations describe an economy. (Think of C, I, G, etc., as being measured in billions and I as a percentage; a 5 percent interest rate implies I=5).
C = 0.8 (1 – t) Y
t = 0.30
I = 1000 – 50 i
G= 500
L = 0.25Y – 65 i
M/P = 700
AD = C + I + G + NX
AD = 0.8 (1 – t) Y + 1000 – 50i + 500
AD = 0.8 (1 – 0.3) Y + 1500 – 50i
At equilibrium AD = Y so
Y= 0.8 (1 – 0.3) Y + 1500-50i
Y- [0.8 (1 - .3) Y]=1500 – 50i
Y[1 – (0.8(1 - .3))] = 1500 – 50i
Y= [1/ (1- (0.8 (1- 0.3))] x (1500- 50i)
Y= 2.27(1500 – 50i)
Y= 3405 – 113.5i
M-bar/P-bar = L
700= .25Y – 65i
0.25Y = 700 +65i
Y= 4(700 + 65i)
Y= 2800 + 260i
3405 – 113.5i = 2800 + 260i
3405 – 2800 = 113.5i + 260i
605= 373.5i
i= 1.62
Y= 2800 + 260(1.62)
Y= 3221.2