Consider an economy with two people, Bunter and Quelch and two goods: coee and milk.

Bunter's utility over these goods is given by

uB(xBc

; xB

m) = (xBc

)

1

2 (xB

m)

1

2 :

Here xBc

denotes the amount of coee consumed by Bunter and xB

m is the amount of milk consumed

by him. Bunter is endowed with 3 units of coee and 4 units of milk.

Quelch, on the other hand, has a utility function given by:

uQ(xQc

; xQ

m) = xQc

:

Here xQc

is the amount of coee consumed by Quelch and xQ

m is the amount of milk consumed by

him. Quelch is endowed with 2 units of coee and 1 unit of milk.

Throughout this problem, treat milk as the numeraire, and set pm = 1.

Question 3 (9 points) Consider an economy with two people, Bunter and Quelch and two goods: coffee and milk. Bunter's utility over these goods is given by u (IB, IB) = (18)1(15) 1. I denotes the amount of coffee consumed by Bunter and I is the amount of milk consumed by him. Bunter is endowed with 3 units of coffee and 4 units of milk. Quelch, on the other hand, has a utility function given by: u (12, 14) =19. Here ro is the amount of coffee consumed by Quelch and To, is the amount of milk consumed by him. Quelch is endowed with 2 units of coffee and 1 unit of milk. Throughout this problem, treat milk as the numeraire, and set pm = 1. 1. Is the allocation where Bunter and Quelch each consume their own endowments, Pareto optimal? [1 points] Circle One: Yes No Justification: 2. Find Bunter's utility maximizing demands for coffee and milk as a function of the unit price of coffee, Pc- [2 points] Optimal quantity of coffee consumed by Bunter is:. Optimal quantity of milk consumed by Bunter is:. Justification: 3. Find Quelch's utility maximizing demands for coffee and milk as function of the unit price of coffee, Pc- [2 points] Optimal quantity of coffee consumed by Quelch is: Optimal quantity of milk consumed by Quelch is:. Justification: 4. Bunter claims the following combination of prices and demands is a Walrasian Equilibrium: Pc = 1, Pm = 1, 19 = 3, 1 = 5, 19 = 2, 12 =0. Is he correct? [2 points] Circle One: Yes No Justification