In: Economics
Given the following economy:
Y = C(Y - T) + I(r) + G
C(Y - T) = a + b(Y - T)
I(r) = c - dr
M/P = L(r,Y)
L(r,Y) = eY - fr
i. Solve for Y as a function of r, the exogenous variables G and T, and the model's parameters a, b, c, and d.
ii. Solve for r as a function of Y, M, P, and the parameters e and f.
iii. Derive the aggregate demand curve. This solves for Y as a function of P, the exogenous variables M, G, and T; and the model's parameters. This expression should not contain r.
Hint: For part iii. substitute result from ii. into result from i.