<p>Let <span class="math-container">$x_i(p,m)$</span> be the demand for good <span class="math-container">$i$</span>. If there is no money illusion, this function is homogeneous of degree zero: <span class="math-container">$\forall t &gt; 0$</span>
<span class="math-container">$$
x_i(tp, tm) = x_i(p,m)
$$</span>
Next use Euler's theorem for homogeneous functions. You will find that you can write the income elasticity as minus the sum of all price elasticities.</p>

CC BY-SA 4.0
2024-02-28T17:48:39.390Z
Thank you! Now I understand. Could you help me this question? https://economics.stackexchange.com/questions/57790/which-of-the-two-lotteries-will-a-risk-averse-consumer-choose
Jonathen
CC BY-SA 4.0
2024-02-28T18:42:33.350Z
I am more concerned on this question: https://economics.stackexchange.com/questions/57776/which-of-these-two-lotteries-a-consumer-with-von-neumann-morgenstern-preference
Jonathen
CC BY-SA 4.0
2024-02-28T17:22:33.940Z
2024-02-28T17:22:33.940Z
tdm
<p>True, false or uncertain: If there is no money illusion, once all price elasticity is known, the income elasticity of commodity demand can be calculated.</p>
<p>My answer is false. I don't think it's possible to get the income elasticity from the price elasticity. But obviously my answer doesn't use the condition that &quot;there is no money illusion&quot;.</p>
<p>So maybe I am wrong.</p>

<microeconomics>
True or False: If there is no money illusion, once all price elasticity is known, the income elasticity of commodity demand can be calculated
Jonathen
# True or False: If there is no money illusion, once all price elasticity is known, the income elasticity of commodity demand can be calculated

(Asked by: username_0 on 2024-02-27)

True, false or uncertain: If there is no money illusion, once all price elasticity is known, the income elasticity of commodity demand can be calculated.

My answer is false. I don't think it's possible to get the income elasticity from the price elasticity. But obviously my answer doesn't use the condition that "there is no money illusion".

So maybe I am wrong.

**Tags:** microeconomics


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## 1 answers

### Answer by username_1 on 2024-02-28. Score: 1 | Accepted answer

Let $x\_i(p,m)$ be the demand for good $i$. If there is no money illusion, this function is homogeneous of degree zero: $\forall t > 0$
$$
x\_i(tp, tm) = x\_i(p,m)
$$
Next use Euler's theorem for homogeneous functions. You will find that you can write the income elasticity as minus the sum of all price elasticities.

> **Comments:**
> **username_0**: Thank you! Now I understand. Could you help me this question? https://economics.stackexchange.com/questions/57790/which-of-the-two-lotteries-will-a-risk-averse-consumer-choose  
> **username_0**: I am more concerned on this question: https://economics.stackexchange.com/questions/57776/which-of-these-two-lotteries-a-consumer-with-von-neumann-morgenstern-preference  

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