A consumer utility takes the following form, U(X1, X2)=min(aX1, X2) were "a" is a positive parameter.

The consumer demand function for X1 and X2 can be found by taking the partial derivatives of the utility function with respect to X1 and X2.

For X1:

∂U/∂X1 = a

For X2:

∂U/∂X2 = 1

Therefore, the consumer demand functions for X1 and X2 are:

X1 = a/P1

X2 = 1/P2