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

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closed as off-topic by Giskard, BKay, Bayesian, Herr K., Adam Bailey Mar 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

  • $\begingroup$ 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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