Please include explanation of the work :)

(The question 2 reference):

2. Consider a consumer (Abby), whose preferences are described by utility (, ) = 102

a) Solve the utility maximization problem to find the ordinary demand functions and the indirectutility function. How much of the budget is spent on each good?b) Solve the expenditure minimization problem to find the compensated demand functions( , , ) and ( , , ). c) Show that the elasticities-based Slutsky equation holds for good x, in both the own-price and the cross-price formulations:, =, ,, =, ,where is the share of the budget spent on x, and is the share spent on y.

(2 problems, 4 points each -> 8 points total) 1. Recall Abby from question 2 in Problem Set 5, whose utility function was U(x, y) = 10x/y. (You can use the solutions from that problem set, if useful.) Suppose she has income / = 500 and is facing prices Py = 10 and Py = 80 a) How much of each good does Abby consume at these initial prices? What if the price of good x increases to P = 30? Draw an optimal choice x-y diagram showing the initial and final budget line and the chosen consumption bundles. b) If it is discovered that the reason for the increase in the price of good x was illegal collusion by the producers in that market, Abby might be entitled to compensation. Discuss and calculate the different ways this amount might be computed Naive method (assuming no substitution) Compensating variation Equivalent variation Consumer surplus (you don't have to find the numerical value for this case - but show clearly how you would do so)