# Proving government expenditure crowds out private consumption [closed]

• Where do you have problems in a)? Can you get dY/dG? – FooBar Mar 20 '15 at 11:02

Since $Y = F(L)$ is increasing in $L$, the sign of $dY/dG$ is equal to the sign $dL/dG$. Through the government's budget constraint, any change in $G$ must be reflected in an increase in $M$ and/or an increase in $PT$.
Set up $\max_{C,L} U$ subject to the household's budget constraint, and then replace in the FOC $M - \bar M$ with $PG - PT$ , to get the dependence of $L$ on $G$. As soon as you have $L(G)$, you can compute $Y(G)$ as $F(L(G))$.
The next step then is just to look at the derivative of $d F(L(G))/dG$. Once you have $L(G)$, computing $C(G)$ is analogous.