<p>Is there any reason not to make <span class="math-container">$P_0 = 1$</span>?</p>
<p>In microeconomics (which your problem seems to be about, rather than macro) consumer's demand is homogeneous of degree zero in prices &amp; income. That is if all parameters measured in money change by the same ratio (say they are all multiplied by 10) consumer decisions are unchanged. The root of this is that what usually matters is the price ratio between two goods. But
<span class="math-container">$$
\frac{p_1}{p_2} = \frac{r \cdot p_1}{r \cdot p_2}
$$</span>
for all <span class="math-container">$r &gt; 0$</span>, so any proportional price change does not change the price ratio between two goods.</p>
<p>As a result of this, we are usually left with a degree of freedom when solving these models. To do away with it and simplify equations it is best to just arbitrarily select a good and appoint it numeraire.</p>
<p>In macroeconomics you have similar issues if you assume the <a href="https://en.wikipedia.org/wiki/Neutrality_of_money" rel="nofollow noreferrer">neutrality of money</a>.</p>

CC BY-SA 4.0
2023-08-28T03:53:48.117Z
Is this the same for more involved macro models? The price of one good is numeraire at the beginning of time? Is this good a state variable then?
EndLoop
CC BY-SA 4.0
2023-08-28T04:40:18.447Z
I have no clue.
Giskard
CC BY-SA 4.0
2023-08-28T06:06:11.663Z
Perhaps I should formulate a question and pose it in the forum to be specific.
EndLoop
CC BY-SA 4.0
2016-12-22T18:22:10.590Z
2021-03-14T09:38:31.767Z
2021-03-14T09:38:31.767Z
Giskard
<p>Often in macro pure exchange economy models (sequential trading), authors make the initial period good price $P_0=1$ asserting this set-up is to make the consumption at period $0$ the numeraire.</p>

<p>But I don't see any detailed explanation or justification for doing this.</p>

<p>Just to add some background story:<br>
The usual set-up is that agents are endowed with some units of goods, say oranges. So the unit of their consumptions is oranges. $P_t$ often the price, at $t=0$, of an orange consumption promised for delivery in period $t$. Why make $P_0=1$?</p>

<macroeconomics>
Why Need a Numeraire Good in Dynamic Analysis
Frank Swanton
# Why Need a Numeraire Good in Dynamic Analysis

(Asked by: username_0 on 2016-12-22)

Often in macro pure exchange economy models (sequential trading), authors make the initial period good price $P\_0=1$ asserting this set-up is to make the consumption at period $0$ the numeraire.

But I don't see any detailed explanation or justification for doing this.

Just to add some background story:  
The usual set-up is that agents are endowed with some units of goods, say oranges. So the unit of their consumptions is oranges. $P\_t$ often the price, at $t=0$, of an orange consumption promised for delivery in period $t$. Why make $P\_0=1$?

**Tags:** macroeconomics


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## 1 answers

### Answer by username_1 on 2016-12-22. Score: 4 | Accepted answer

Is there any reason not to make $P\_0 = 1$?

In microeconomics (which your problem seems to be about, rather than macro) consumer's demand is homogeneous of degree zero in prices & income. That is if all parameters measured in money change by the same ratio (say they are all multiplied by 10) consumer decisions are unchanged. The root of this is that what usually matters is the price ratio between two goods. But
$$
\frac{p\_1}{p\_2} = \frac{r \cdot p\_1}{r \cdot p\_2}
$$
for all $r > 0$, so any proportional price change does not change the price ratio between two goods.

As a result of this, we are usually left with a degree of freedom when solving these models. To do away with it and simplify equations it is best to just arbitrarily select a good and appoint it numeraire.

In macroeconomics you have similar issues if you assume the [neutrality of money](https://en.wikipedia.org/wiki/Neutrality_of_money).

> **Comments:**
> **username_2**: Is this the same for more involved macro models? The price of one good is numeraire at the beginning of time? Is this good a state variable then?  
> **username_1**: I have no clue.  
> **username_2**: Perhaps I should formulate a question and pose it in the forum to be specific.  

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