<p>In this case the optimal choice is $(x^*, y^*) = (3, 1)$. Here is the picture :</p>

<p><a href="https://i.sstatic.net/EqzLW.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/EqzLW.png" alt="enter image description here"></a></p>

CC BY-SA 4.0
2018-09-10T13:44:57.593Z
2018-09-10T13:44:57.593Z
Amit
<p>The indifference curve is the set all optimal sets of consumption.</p>

<p>The indifference curve derives from the utility function, which itself is a 3 variables equation (both x and y explain u)</p>

<p>Mathmatically , once you have the budget constraint you need to use it with the derivative of the utility function to find the optimum *under * the specific budget constraint</p>

<p>Your utility function cannot be derived once, but needed to be derived thrice, and "sewed" on the mininum places</p>

CC BY-SA 4.0
2018-09-10T12:39:36.650Z
Budget constraint can be obtained from the given values of Px, Py and M. The constraint would be: 1x + 2y = 5
Kong
CC BY-SA 4.0
2018-09-10T12:55:19.027Z
right... I'll edit my answer
Guy Louzon
CC BY-SA 4.0
2018-09-10T12:28:08.750Z
2018-09-10T13:12:18.627Z
2018-09-10T13:12:18.627Z
Guy Louzon
<p>Suppose u(x,y)=min{x+y,4(x)^1/2,4(y)^1/2} , Px=1, Py=2, M=5 . Here, Px, Py and M are the price of x, price of y, and the Income. </p>

<p>Give an example of the optimal consumption bundle of x and y for this consumer.</p>

<p>I know to plot the Indifference Curve given a value of Utility,however how could I know what is the maximum utility that can be obtained in this case? </p>

<microeconomics>
Finding Optimal Consumption Bundle
Kong
# Finding Optimal Consumption Bundle

(Asked by: username_0 on 2018-09-10)

Suppose u(x,y)=min{x+y,4(x)^1/2,4(y)^1/2} , Px=1, Py=2, M=5 . Here, Px, Py and M are the price of x, price of y, and the Income.

Give an example of the optimal consumption bundle of x and y for this consumer.

I know to plot the Indifference Curve given a value of Utility,however how could I know what is the maximum utility that can be obtained in this case?

**Tags:** microeconomics

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## 2 answers

### Answer by username_1 on 2018-09-10. Score: 3

In this case the optimal choice is $(x^\*, y^\*) = (3, 1)$. Here is the picture :

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


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### Answer by username_2 on 2018-09-10. Score: 0

The indifference curve is the set all optimal sets of consumption.

The indifference curve derives from the utility function, which itself is a 3 variables equation (both x and y explain u)

Mathmatically , once you have the budget constraint you need to use it with the derivative of the utility function to find the optimum \*under \* the specific budget constraint

Your utility function cannot be derived once, but needed to be derived thrice, and "sewed" on the mininum places

> **Comments:**
> **username_0**: Budget constraint can be obtained from the given values of Px, Py and M. The constraint would be: 1x + 2y = 5  
> **username_2**: right... I'll edit my answer  

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