Consider a two-person (persons 1 and 2), two good (goods x and y) exchange economy. Persons 1 and 2 have the following quasi-linear utility functions:

Person 1: U1(x1, y1) = ln(x1) + y1 Person 2: U2(x2, y2) = 2ln(x2) + y2

Person 1 has an endowment of e1 = (2, 1). Person 2s endowment is e2 = (1, 2).

1. In an Edgeworth Box diagram, show which allocations are in the core.

2. Solve for the set of Pareto optimal allocations (i.e. the contract curve) in the Edgeworth Box. Illustrate the contract curve in an Edgeworth Box diagram.

3. Let good y be the numeraire (i.e. set py = 1 and let px = p). Solve for the Walrasian competitive equilibrium allocation and price ratio.