please explain and show work. Thank you!

Problem 2 Elsa consumes ice cream (good 1) and and chocolate (good 2). Denote by (221,32) E X her con- sumption bundle consisting of :31 units of ice cream and :32 units of chocolate. Let 301 be price of ice cream and 192 be the price of chocolate. Elsa's preferences are represented by: 11.0171, 2:2) = sh. 1. (10 points) Calculate Elsa's marginal utility for both ice cream and chocolate. Calculate the MRS. Does Elsa have a diminishing MRS? 2. (10 points) Write down Elsa's utility maximization problem. Calculate Elsa's optimal con- sumption bundle (mi, :33) in terms of m, p2 and m. What fraction of income does Elsa spend on chocolate? 3. (10 points) Let p1 = 2, p2 = 1 and m = 30. Write the equation for the budget line and nd the slope. Also determine the optimal consumption bundle (23:55:) for Elsa. 4. (10 points) Are ice cream and chocolate normal goods? Explain Why. 5. (10 points) Are ice cream and chocolate substitutes or complements? Explain Why