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