# I have a utility function problem with perfect complement that I am having trouble solving. I have the following information:Max eats chips and...

I have a **utility function problem** with ** perfect complement** that I am having trouble solving.

I have the following information:

Max eats chips and salsa, and he cannot have one without the other.

For every bag of chips, he must have 400ml of salsa. When he consumes **400ml** of salsa and **one **bag of chips,** **his utility is **1**.

I'm using the current variables : x- number of chips (number of bags) y- amount of salsa (by liter)

What would be the utility function in this case?

U(x,y) = (formula) = 1?

Utility function will take the form:

u(v, c) = min{av, bv} **also written as**

u(x, y) = min{av, bv}

(p. 2, "**Perfect Complement: Katherine**")

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Using the example of "p2. Perfect Complement: Katerine",

we have to find the utility function f(x,y) =1

that satisfies the condition: U (x,y) = min (av, bv)

Given condition:

1 bag of chips & 400 ml of salsa

or, 1x & 0.4 y will lead to utility of 1.

Thus the utility function will be, U(x,y) = min (0.4x, 1y)

and any monotonic transformation of this will also satisfy the utility function.

Thus, the form, 125y+0.5x will also be a valid form, since x:y = 0.5:1.25 = 0.4:1

Hope this helps.