Intermediate MicroeconomicsHomework Set 2: Preferences and UtilityDue: Wednesday, February 8th at 2 pm via NYU Classes websiteExercise1Consider the following utility functions on the choice setX={(x1, x2) :x1, x2≥0}:(1)u(x1, x2) =x1+ 2x2,(2)u(x1, x2) = 2x0.251x0.752,(3)u(x1, x2) =-12x21-x2,(4)u(x1, x2) = min{x1,2x2},(5)u(x1, x2) = max{x1,2x2}.For each of (1) to (5), sketch two indi↵erence curves of the utility function. (Please usedi↵erent graphs for each utility.)Exercise2Consider the following utility functions on the choice setX={(x1, x2) :x1, x2>0}:(1)u1(x1, x2) =x21x22,(2)u2(x1, x2) =x1+x2,(3)u3(x1, x2) = logx1+ logx2,(4)u4(x1, x2) =x31+ 3x21x2+ 3x1x22+x33,(5)u5(x1, x2) =x1x2.How many distinct preference relations do these utility functions represent?Whichutilities represent the same preferences?Exercise3Consider a two-period economy with a single commodity (say leisure):x1is the con-sumption of leisure in period 1, andx2is the consumption of leisure in period 2. WhenPeter evaluates consumption streams, he cares only about the best time in his life. Onthe other hand, Christine only cares about the worst time in her life. Provide utilityrepresentation for their preferences.Exercise41