Q2.1 Suppose consumers consumes two goods, X and Y. The prices of both products are Pr and P, respectively. (35 points) a) Janice has a utility function given by the expression: U = 4X0Y05, P, =10, P, = 10, Janice's income being 200. Please write out Janice's budget constaint, and solve the optimal consumption bundle of X and Y, and the corresponding utility at this point. b) When Pr decreases to 2.5, while Py remains 10 and income still is 200, please solve the new optimal consumption bundle and the corresponding utility level. c) For the previous changes from a) to b), or when Pr drops from 10 to 2.5, what is the total effect of price change on X consumption. And please solve the corresponding substitution effect and income effect on X consumption. d) Derive the demand function of X. What is the price elasticity of demand for good X? Are X and Y independent goods, subsitutions or complements? e) If Jack has a utility function given as U =2X + Y, P, =10, P, =10, assuming that he also has a total income of 200. What is the optimal consumption bundle for him? What is the MRS (# of Y he is willing to give up in order to increase one more unit consumption of X) at this optimal consumption point? f) Does Janice or Jack have strong preferences of X at their optimal consumption points? Why