<p>One example of the utility function that can give <span class="math-container">$y=x^2$</span> as income consumption curve is <span class="math-container">$u(x,y)=\min(x^2,y)$</span>
<a href="https://i.sstatic.net/fYpnm.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/fYpnm.png" alt="enter image description here" /></a></p>

CC BY-SA 4.0
2023-11-06T17:35:25.607Z
2023-11-12T18:35:51.533Z
2023-11-12T18:35:51.533Z
Amit
<p>From the Engel's Law we know that as income increases the share of income spent of foods decreases and the share of income spent on luxury goods increases. I wanted to represent this using Consumer Theory Models. Namely, I wanted to obtain an income consumption curve that was exponential, that is, as income increases the amount of the luxury good increases at a faster rate than income, and the amount of the necessity good increases at a slower rate than income. Like in the following Image.</p>
<p><a href="https://i.sstatic.net/cpuql.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/cpuql.png" alt="enter image description here" /></a></p>
<p>I want to reach this departing from the equation Marginal Utility of X/Marginal Utility of Y = Price of x/Price of y. However I haven't been able to find a mathematical example of an Utility Function that after taking the derivatives would allow me to reach an income consumption curve like for example y=x^2. Can you provide a practical example? Thank you.</p>

<microeconomics><consumer-theory>
Exponential Income Consumption Curve
João Maria
# Exponential Income Consumption Curve

(Asked by: username_0 on 2023-11-06)

From the Engel's Law we know that as income increases the share of income spent of foods decreases and the share of income spent on luxury goods increases. I wanted to represent this using Consumer Theory Models. Namely, I wanted to obtain an income consumption curve that was exponential, that is, as income increases the amount of the luxury good increases at a faster rate than income, and the amount of the necessity good increases at a slower rate than income. Like in the following Image.

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

I want to reach this departing from the equation Marginal Utility of X/Marginal Utility of Y = Price of x/Price of y. However I haven't been able to find a mathematical example of an Utility Function that after taking the derivatives would allow me to reach an income consumption curve like for example y=x^2. Can you provide a practical example? Thank you.

**Tags:** microeconomics, consumer-theory

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## 1 answers

### Answer by username_1 on 2023-11-06. Score: 2

One example of the utility function that can give $y=x^2$ as income consumption curve is $u(x,y)=\min(x^2,y)$
[![enter image description here](https://i.sstatic.net/fYpnm.png)](https://i.sstatic.net/fYpnm.png)


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