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, show the step of your working.
b)At the optimal choice, how mamy units of X1 will be combined with each unit of X2? Show your working.
a) 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.
Partial derivative of U with respect to X1:
∂U/∂X1 = a
Partial derivative of U with respect to X2:
∂U/∂X2 = a
Therefore, the consumer demand functions for X1 and X2 are:
X1 = a
X2 = a
b) At the optimal choice, the consumer will combine one unit of X1 with one unit of X2. This can be seen by setting the partial derivatives of the utility function equal to zero.
∂U/∂X1 = 0
∂U/∂X2 = 0
Therefore, X1 = X2 = a, which implies that one unit of X1 will be combined with one unit of X2.