Consider an exchange economy with two consumers Alice and Bill (denoted by AAand B)B) andtwo goods denoted by xx and yy. The consumers view these two goods as perfect substitutes.

1. Sketch the consumers' indifference curves and construct the set of Pareto Efficient Allocations (PEAs).
2. Demonstrate that any allocation is Pareto-efficient.
3. Find the PEAs if now consumer BB considers three units of good xx to be worth two units of good yy.
4. Explain carefully the key assumptions of the Second Theorem of Welfare Economics and its implications.