Walrasian Demand Function

Flamed Diving

How do I find a Walrasian function for this type of utility function.

U(x1,x2) = min{x1,x2}

Or more generally, how do I interpret that (above) function?

EDIT: Ok, I just figured out that it is a Leontief preference function. However, the books I have offer little explanation as to what can be done with it.

Time Magazine

Generally, that function is to be interpreted as a pair of perfect compliments. You want two buns for every burger, additional buns are of no additional utility. And let's pretend you don't like burger on its own, as silly as that sounds, but that's the idea of the min{} function.

The indifference curves are typically L-shaped for minimum utility functions.

If the utility function is L-shaped it's non-continuous so obviously you can't differentiate it, so the MRS is a bit f*cked up. However if you assume rationality, you can assume the consumer will purchase bundles such that if u(x,y)=min{x,2y}, then x=2y. Why? If x were greater than 2y, his utility is only 2y but he is paying for that quantity of x that is greater than 2y. The same logic holds for x<2y.

When x=2y, you essentially have the MRS. You can sub this into your budget constraint (presumably (price of x)*(x) + (price of y)*(y) = income) and you have Walrasian quantities as a function of prices and income.

Flamed Diving

Flamed Diving wrote: »

How do I find a Walrasian function for this type of utility function.

U(x1,x2) = min{x1,x2}

Or more generally, how do I interpret that (above) function?

EDIT: Ok, I just figured out that it is a Leontief preference function. However, the books I have offer little explanation as to what can be done with it.

Trick is for any leontief-esque property - that x1 will equal x2 at the optimum. This allows you to solve it. PM me if you are still stuck

Edit: treat min as max min (you are still maxing utility)

If you want some fun:

u: min{x1, x2+x3}
u: min{x1, x2x3}

Flamed Diving

Thanks, I will give that a go.