<p>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 - <em>don't follow without verifying that the following actually makes sense</em>.</p>

<h2>a)</h2>

<p>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 $PT$. </p>

<p>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 $F(L(G))$.</p>

<p>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. </p>

CC BY-SA 3.0
2015-03-20T12:49:16.930Z
2015-03-20T12:49:16.930Z
FooBar
<p><img src="https://i.sstatic.net/Xo97I.png" alt="enter image description here"></p>

<p>Please help as I am not able to solve either parts.</p>

CC BY-SA 3.0
2015-03-20T11:02:59.897Z
Where do you have problems in a)? Can you get dY/dG?
FooBar
<microeconomics>
Proving government expenditure crowds out private consumption
saubhik
# Proving government expenditure crowds out private consumption

(Asked by: username_0 on 2015-03-20)

![enter image description here](https://i.sstatic.net/Xo97I.png)

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

**Tags:** microeconomics

> **Comments:**
> **username_1**: Where do you have problems in a)? Can you get dY/dG?  

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## 1 answers

### Answer by username_1 on 2015-03-20. Score: 1

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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