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Please help as I am not able to solve either parts.

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  • $\begingroup$ Where do you have problems in a)? Can you get dY/dG? $\endgroup$ – FooBar Mar 20 '15 at 11:02
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Since I don't know where exactly you have the problems, I 'm just providing a rough solution scheme here. Note that it's quite long ago that I did this stuff, so I may be outright wrong - don't follow without verifying that the following actually makes sense.

a)

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.

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