<p>In determining competitive equilibrium in general equilibrium models, you can normalise any one of the strictly positive prices to unity. This is irrespective of whether the preferences are homothetic or not. The reason is because the price-allocation pair <span class="math-container">$(p^*,x^*)$</span> is a competitive equilibrium if and only if the price-allocation pair <span class="math-container">$(\lambda p^*, x^*)$</span> is a competitive equilibrium for all <span class="math-container">$\lambda &gt; 0$</span>. Please note that wage is a price of labor and can be normalised to one if it is non-zero.</p>

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2024-09-17T06:37:23.543Z
2024-09-17T06:37:23.543Z
Amit
<p>In an <span class="math-container">$n$</span>-good model with prices <span class="math-container">$p_i \in \{ p_1,...,p_n \}$</span> can you normalize one price to unity if the underlying preferences are non-homothetic? Or is this price normalization property only a function of homothetic preferences?</p>
<p>I have seen that one way to get around this might instead be to normalise the wage rate, <span class="math-container">$w$</span>, to unity in a general equilibrium model. If price normalization fails for the goods, can it be done with the factors instead?</p>

<preferences><general-equilibrium>
Normalizing one price with non-homothetic utility
Debreu
# Normalizing one price with non-homothetic utility

(Asked by: username_0 on 2024-09-17)

In an $n$-good model with prices $p\_i \in \{ p\_1,...,p\_n \}$ can you normalize one price to unity if the underlying preferences are non-homothetic? Or is this price normalization property only a function of homothetic preferences?

I have seen that one way to get around this might instead be to normalise the wage rate, $w$, to unity in a general equilibrium model. If price normalization fails for the goods, can it be done with the factors instead?

**Tags:** preferences, general-equilibrium

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## 1 answers

### Answer by username_1 on 2024-09-17. Score: 2 | Accepted answer

In determining competitive equilibrium in general equilibrium models, you can normalise any one of the strictly positive prices to unity. This is irrespective of whether the preferences are homothetic or not. The reason is because the price-allocation pair $(p^\*,x^\*)$ is a competitive equilibrium if and only if the price-allocation pair $(\lambda p^\*, x^\*)$ is a competitive equilibrium for all $\lambda > 0$. Please note that wage is a price of labor and can be normalised to one if it is non-zero.


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