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")

Expert Answers
gsenviro eNotes educator| Certified Educator

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.

deix | Student

Would U(x,y) = 1.25y + 0.5x also satisfy the condition?

balajia | Student

it is 0.6x+y=1.

It satisfies the condition that for one bag of chips and 400ml of salsa the utility is one.