Please read the following instructions:

.  Please try to answer all questions.  Your assignment will be graded based on effort rather than accuracy.

.  Please write down your full name on your assignment.  Initials are not sufficient to tell who you are.

.  If you discuss with your classmates to finish the assignment, please list their names on your assignment. You should still hand in your own version of assignment.

.  The due date is February 20th before the class starts. Email submission is not accepted. .  The solutions of this assignment will be posted one week after Midterm 1.

1.  At p = (3, 4), the consumer’s Walrasian demand is x = (4, 3). At p′ = (8, 6), the consumer’s Walrasian demand is x′ = (3, 4). Does the consumer’s preferences satisfy WARP? Why or why not?

2.  Jeremy has a monthly income of $60.  He spends his money making telephone calls (good x, measured in minutes) at a price of px  and on other composite good y, whose price has been normalized to one, meaning py  = $1.  His mobile phone company offers him two plans:  plan A, in which he pays no monthly fee and makes calls for $0.50 per minute, or plan B, in which he pays a $20 monthly fee and benefits from cheaper phone calls at $0.20 per minute.

(a)  Depict Jeremy’s budget constraint under each of the two plans, with the number of phone calls (good x) in the horizontal axis and the composite good (good y) in the vertical axis.

(b)  If Jeremy mentioned that plan A is better for him, what is the set of consumption bundles he may purchase if his behavior is consistent with WARP?

3.  Consider the CES utility function

u (x1, x2) = [x1(p) + x2(p)] 1/p

where p < 0. The prices and wealth are p 1, p2, w.

(a) Write down the Lagrangian function and Kuhn-Tucker conditions of UMP.

(b)  Find the Walrasian demands of this consumer, x1 (p, w) and x2 (p, w).  (Please argue the existence of interior and/or corner solutions.)

(c) What are the Walrasian demands when p → 0?  Could it remind you of any preference or utility function?

4.  Consider a consumer faces the prices (p 1, p2) and wealth w. For the following utility functions, please write down the Walrasian demands, and indirect utility functions.   Please argue the existence of interior and/or corner solutions.

(a) u (x1, x2) = max{x1, x2}