Hi, please help below question about economics, thanks in advance.

1) Repeat the previous question, but this time assume that Every unit of Good 1 consumed above 50 units costs, half the cost of a unit of consumption consumed up to 50 units, which one is correct?

a. The Extreme Value Theorem ensures that the utility maximization problem has a well-defined solution for all (p; y) 0.

b. For every (p; y) 0, there must be a unique utility maximizing choice.

c. Part (b) but only if preferences are also strictly convex and locally non-satiated.

d. Since the budget sets are not convex, Extreme Value Theorem does not apply here.

2)

The following is a Slutsky Matrix for some rational consumer in a three good economy at some given (and fixed) (p, u): -10 a S = C -4 d 3 e You may assume that the Hicksian Demand of each good with respect to its own price is strictly decreasing. Using the properties of the Slutsky Matrix we may conclude that a. b= a and d = e. b. f