1. (a) if the utility of a consumer is given by U= min(x1, 3x2) where P1=2 and P2=4 and budget m=$100, find the utility-maximizing bundle for the consumer. Draw a diagram to relate to your working.
(b) If technology available to a firm allows it to produce output y by y=x1^(1/3)*x2^(1/3) and price of output per unit in a competitive market is $20, where cost of input x1 is $9 and cost of input x2 is $3 per unit, find out the profit-maximizing output level along with optimal amounts of inputs x1 and x2 in the long run.
