<p>Your claim that:</p>
<blockquote>
<p>if <span class="math-container">$(Y-T-C)=S$</span> is true then <span class="math-container">$(T-G)=0$</span>, in equilibrium</p>
</blockquote>
<p>is not correct claim. There is no reason why <span class="math-container">$T-G=0$</span> in equilibrium. For example, plausible equilibrium values for <span class="math-container">$Y$</span>, <span class="math-container">$T$</span>, <span class="math-container">$G$</span> and <span class="math-container">$C$</span> would be 1000, 100, 50 and 800 respectively giving us:</p>
<p><span class="math-container">$1000 - 100 -800=100$</span></p>
<p>Next AD could be given by <span class="math-container">$Y=C+I+G$</span> where <span class="math-container">$1000= 800 +150 +50$</span> (recall that <span class="math-container">$I=S+T-G$</span>).</p>
<p>So there is absolutely nothing in this formulas requiring balanced budget.</p>
<blockquote>
<p>When the government has a balanced budget, G=T. So there are no transfer payments, and revenues = spending, for the government.</p>
</blockquote>
<p>Again something that is not true. First, government spending <span class="math-container">$G$</span> does not represent transfers. It represents spending on goods and services. For example, government purchasing aircraft carrier or highway or something like that.</p>
<p>Transfer are included in <span class="math-container">$T$</span> since transfers are negative taxes. If government taxes you 100 and transfers 50 to you in form of some subsidies then in the model above T would be 50. If government taxes you 50 and gives you 100 in subsidies T above would be -50.</p>
<p>Note government can both engage in transfers and run balanced budget. The simple model you are playing with works with aggregates. However, the total consumption is actually sum of a consumption of all individuals. Hence actually;</p>
<p><span class="math-container">$$C(Y-T)= \sum_{i=1}^n C_i(Y_i-T_i)$$</span></p>
<p>where <span class="math-container">$C_i$</span> is consumption of person <span class="math-container">$i$</span> (<span class="math-container">$n$</span> is total number of people in the country), <span class="math-container">$Y_i$</span> is income of person <span class="math-container">$i$</span> and <span class="math-container">$T_i$</span> net tax of person <span class="math-container">$i$</span>. For some people <span class="math-container">$T_i$</span> will be negative which means government is subsidizing those people, for others <span class="math-container">$T_i$</span> will be positive meaning those people pay on net money to the government so government can subsidize others.</p>
<p>Consequently there is absolutely no reason to believe that government cannot have balanced budget and make transfer payments. Government can even run surpluses and still have transfers to the poor.</p>
<blockquote>
<p>At equilibrium, do we have G=T?</p>
</blockquote>
<p>Not necessarily.</p>
<blockquote>
<p>If not, then we wouldn't want an equilibrium for the loanable funds market?</p>
</blockquote>
<p>You are not even modeling loanable funds market.  <span class="math-container">$Y-T-C=S$</span> is not equilibrium condition for loanable funds market, this is just definition of <em>private</em> saving in the economy. The equilibrium condition for loanable funds market is given by:</p>
<p><span class="math-container">$$\frac{M}{P} = L(i,Y)$$</span></p>
<p>Where <span class="math-container">$M/P$</span> is real money supply (or you can re-interpret it as real supply of loanable funds) and <span class="math-container">$L(i,Y)$</span> is money demand, or demand for loanable funds.</p>

CC BY-SA 4.0
2022-09-09T15:06:44.330Z
2022-09-09T15:06:44.330Z
1muflon1
<h2>Equilibrium in the market of loanable funds</h2>
<p>We have: S=(Y-T-C)+(T-G)=I</p>
<p>So,</p>
<ul>
<li>(Y-T-C)=S?</li>
<li>If that's true, then (T-G)=0, in equilibrium.</li>
</ul>
<p>So the government doesn't have savings, since all taxes are spent on government purchases?</p>
<p>When the government has a balanced budget, G=T. So there are no transfer payments, and revenues = spending, for the government.</p>
<p>What about transfer payments? How does the government give money to those in need?</p>
<p>If it didn't, we wouldn't want a balanced budget. Therefore, we want the government to gain more than it spends (G excludes payment transfers, since G=Taxes-Payment transfers).
So we want a budget surplus, meaning G&gt;T.</p>
<p>At equilibrium, do we have G=T? If not, then we wouldn't want an equilibrium for the loanable funds market? Or are the G and T comparisons irrelevant in the matter?</p>
<p>Thank you.</p>

<macroeconomics><mathematical-economics><economic-growth>
Questions about the equation: S=(Y-T-C)+(T-G)=I, in a situation of Equilibrium, in the market of loanable funds
student
# Questions about the equation: S=(Y-T-C)+(T-G)=I, in a situation of Equilibrium, in the market of loanable funds

(Asked by: username_0 on 2022-09-09)

## Equilibrium in the market of loanable funds

We have: S=(Y-T-C)+(T-G)=I

So,

* (Y-T-C)=S?
* If that's true, then (T-G)=0, in equilibrium.

So the government doesn't have savings, since all taxes are spent on government purchases?

When the government has a balanced budget, G=T. So there are no transfer payments, and revenues = spending, for the government.

What about transfer payments? How does the government give money to those in need?

If it didn't, we wouldn't want a balanced budget. Therefore, we want the government to gain more than it spends (G excludes payment transfers, since G=Taxes-Payment transfers).
So we want a budget surplus, meaning G>T.

At equilibrium, do we have G=T? If not, then we wouldn't want an equilibrium for the loanable funds market? Or are the G and T comparisons irrelevant in the matter?

Thank you.

**Tags:** macroeconomics, mathematical-economics, economic-growth

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## 1 answers

### Answer by username_1 on 2022-09-09. Score: 0

Your claim that:

> if $(Y-T-C)=S$ is true then $(T-G)=0$, in equilibrium

is not correct claim. There is no reason why $T-G=0$ in equilibrium. For example, plausible equilibrium values for $Y$, $T$, $G$ and $C$ would be 1000, 100, 50 and 800 respectively giving us:

$1000 - 100 -800=100$

Next AD could be given by $Y=C+I+G$ where $1000= 800 +150 +50$ (recall that $I=S+T-G$).

So there is absolutely nothing in this formulas requiring balanced budget.

> When the government has a balanced budget, G=T. So there are no transfer payments, and revenues = spending, for the government.

Again something that is not true. First, government spending $G$ does not represent transfers. It represents spending on goods and services. For example, government purchasing aircraft carrier or highway or something like that.

Transfer are included in $T$ since transfers are negative taxes. If government taxes you 100 and transfers 50 to you in form of some subsidies then in the model above T would be 50. If government taxes you 50 and gives you 100 in subsidies T above would be -50.

Note government can both engage in transfers and run balanced budget. The simple model you are playing with works with aggregates. However, the total consumption is actually sum of a consumption of all individuals. Hence actually;

$$C(Y-T)= \sum\_{i=1}^n C\_i(Y\_i-T\_i)$$

where $C\_i$ is consumption of person $i$ ($n$ is total number of people in the country), $Y\_i$ is income of person $i$ and $T\_i$ net tax of person $i$. For some people $T\_i$ will be negative which means government is subsidizing those people, for others $T\_i$ will be positive meaning those people pay on net money to the government so government can subsidize others.

Consequently there is absolutely no reason to believe that government cannot have balanced budget and make transfer payments. Government can even run surpluses and still have transfers to the poor.

> At equilibrium, do we have G=T?

Not necessarily.

> If not, then we wouldn't want an equilibrium for the loanable funds market?

You are not even modeling loanable funds market. $Y-T-C=S$ is not equilibrium condition for loanable funds market, this is just definition of *private* saving in the economy. The equilibrium condition for loanable funds market is given by:

$$\frac{M}{P} = L(i,Y)$$

Where $M/P$ is real money supply (or you can re-interpret it as real supply of loanable funds) and $L(i,Y)$ is money demand, or demand for loanable funds.


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