I need help with this

Problem 3. Trade Consider an exchange economy in which there are only two agents, Alice and Bob, and two goods, 1 and 2. Denote with (ml ,w2) e R2 and (101 ,w2 3) e R2 the initial endowments of Alice and Bob, respectively. The preferences of the two agents are described by the real-valued utility functions A A A _ A A u ($1,332):2 m1+332, and B B B u (3:1,m2) 2:331 +2 23'29, defined on R1. (a) Compute the demand functions of Alice and Bob (Note: Assume that the budget constraint holds with equality, that the solution is interior and that the second order conditions are satised. Moreover, assume that prices are strictly positive). (b) Now assume that Alice is endowed with 2 units of good 1 and no good 2, i.e., (triing): (2,0), and that Bob is endowed with no good 1 and 2 units of good 2, i.e., (1051023): (0 2). Compute the competitive equilib- rium price and allocation. To do so, formulate the market-clearing con- ditions. These may look complicated. To solve them, remember that: (a) by Walras' law, it is enough to restrict attention to one of them,- (b) you can choose one good (either one) to be the numeraire and set its price equal to 1. (c) Compare the utility of each of Alice and Bob at the competitive equi- librium to that which they would receive if they did not trade with one another. Comment your nding (one line)