Consider a two good economy that has two consumers, Anne and Bill. Anne enters the economy with endowment ea = (2, 9) and bill enters with endowment eb = (4, 4). Let Anne’s and Bill’s preferences be represented by the utility functions, ua (c1, c2) = c1^2c2 ub (c1, c2) = c1c2, where c1 is consumption of good 1 and c2 is consumption of good 2. We will first consider a market equilibrium where Anne and Bill exchange goods at prices p1 and p2 for goods 1 and 2, respectively. By Walras’ Law, we will normalize a price, so in the following set p2 = 1.

1. Relative to the allocation where Anne and Bill simply consume their respective endowments, (a, b) = (ea, eb), is the equilibrium allocation a Pareto improvement? That is, does the equilibrium allocation make at least one consumer better off without making anybody worse off?

2. What is the value of Anne’s endowment relative to that of Bill’s?

3. State all allocations (a, b) that are on the contract curve.