Problem Set #2 (to be submitted online by 11:59 p.m. CDT Friday, October 1 st) 1 . A utility maximizing consumer has the following utility function: U(X, Y) = min [ 2X , Y ] a. Derive the consumer's optimal demands X*(Px,PY,I) and Y*(Px,PY,I), assuming he faces the standard, linear budget constraint: PxX + PYY =I. Show the optimum in a well-labeled graph. i. This consumer's optimal demand for X is: a. X* = 2* [I/ ( Px + PY) ] b . X* = 1/2 * [ I/ ( Px + PY) ] C. X* = I/ ( Px + 2*PY) ] d. X* = 1/ ( 2*Px + PY) ] This consumer's optimal demand for Y is: d. Y* = 4* [ I/ (Px + PY ) ] b. Y* = [I/ (Px + PY ) ] C. Y* = 2* [ I/ ( Px + 2*Py ) ] Y* = 2* [ I/ ( 2*Px + PY ) ] b. Derive an expression for this consumer's income consumption curve. Derive an expression for this consumer's price consumption curve for Px . Comment on their similarities or differences.Derive an expression for this consumer's income consumption curve. Derive an expression for this consumer's price consumption curve for Px . Comment on their similarities or differences. i. This consumer's income consumption cuwe is: a. Y\" = X* b. Y\" = 2X* c. Y\" = 1/2X* d. Y\" = 3f2 X* ii. This consumer's price consumption curve for Px is: a. Y* = X\" 1). Y\" = 2 X\" c. Y'\" = '/2X"' (1. Y" = 3!?! X* iii This consumer's price consumption curve for Px and their income consumption curve are , because any change in Px results in