Suppose a consumer drives utility from goods x1,x2, and x3 with corresponding prices p1,p2, and p3 according to the utility function.
U(x1,x2,x3) = log(x1-10) + log(x2) + log(x3)
q1) Now let the prices of p1 and p2 double, so that p4=p2=2, p1=4 and p3=1. what are the utility maximizing values for x1 and x2 now? Did a proportional increase in the prices p1 and p2 lead to proportional increase in the quantities x1 and x2?