# Finding Optimal Consumption Bundle

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?

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

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

• Budget constraint can be obtained from the given values of Px, Py and M. The constraint would be: 1x + 2y = 5
– Kong
Commented Sep 10, 2018 at 12:39
• right... I'll edit my answer Commented Sep 10, 2018 at 12:55