If an Individual Should Subtract the Present Value of Future $$\begin{array} { l } I = I \\\mathrm { G } = G \\\mathrm {~T} = T \\\mathrm { Y } = C + I + G\end{array}$$

If an individual should subtract the present value of future tax obligations due to the government deficit from his or her disposable income, this situation suggests that, in aggregate analysis, the government deficit should be subtracted from disposable income. That is, instead of
C = a + b(Y - T), we should use: C = a + b((Y - T - (G - T)), or = a + b(Y - G).

a. Using this consumption function and the further relations:
$$\begin{array} { l } I = I \\\mathrm { G } = G \\\mathrm {~T} = T \\\mathrm { Y } = C + I + G\end{array}$$
write the equilibrium equation determining $Y$ as a function of $a , I , G$ , and $T$ .
b. If $b$ equals $0.5$ , what are the numerical values of the multipliers for $l , G$ , and $T$ , respectively?