Best buds, Sohail and Jimmy are binge watching The Price is Right when the covid lockdown starts. They are essentially marooned in Jimmy's apartment (think of this as a deserted island). Although they are unable to produce anything, they are very fortunate and each of them has a supply of cookies () and Mountain Dew () . Sohail has 6 cookies and 3 bottles of Mountain Dew, while Jimmy has 3 cookies and 6 bottles of Mountain Dew. Although they like the same products, they have different preferences over them; Sohail's utility function is (, ) = 2 and Jimmy's utility function is (, ) = 42 . The lockdown friends decide to engage in trade.

a. [6] Without normalizing prices, find their demand functions for each good.

b. [2] Write the excess demand function for cookies

c. [6] Normalizing the price of Mountain Dew, find the equilibrium price of cookies () that clears the two markets. How many cookies and how much Mountain Dew does each of them consume in the competitive equilibrium?

d. [4] Are they each better off after engaging in trade than they would have been consuming their endowments? Show your calculations.