Consumer utility function taker the following form. U(X1, X2)=min(aX1, X2) were X is a positive number.
a)find consumer demand fuction fo X1 and X2.
b)At the optimal choice, how mamy units of X1 will be combined with each unit of X2?
a) The consumer demand functions for X1 and X2 can be found by taking the partial derivatives of the utility function with respect to X1 and X2, respectively. This yields the following demand functions:
X1 = a/P1
X2 = a/P2
b) At the optimal choice, the consumer will combine one unit of X1 with one unit of X2. This is because the utility function is a minimum function, so the consumer will choose the combination of X1 and X2 that yields the lowest utility. Since the utility function is linear, the optimal combination is one unit of X1 with one unit of X2.