# Proving government expenditure crowds out private consumption [closed]

## closed as off-topic by Giskard, BKay, Bayesian, Herr K., Adam BaileyMar 6 '17 at 22:25

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question does not meet the standards for homework questions as spelled out in the relevant meta posts. For more information, see our policy on homework question and the general FAQ." – Giskard, BKay, Bayesian, Herr K., Adam Bailey

• 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.