(15 points) Alannah and Bobbi are identical consumers in a pure exchange economy. Their preferences are given by U(xi) = (x 1 i)(x 2 i) for i = A,B (i.e. Alannah and Bobbi have identical preferences). Alannah has 3 units of good 1 and 1 unit of good 2. Bobbi has 1 unit of good 1 and 3 units of good 2.

a) Construct the Edgeworth Box for this economy and show the initial allocation of endowment (label it W) including indifference curves through that point. Calculate the utility for both Alannah and Bobbi at the initial allocation of the endowment ().

b) Suppose that Alannah and Bobbi exchange goods. Alannah gives 2 units of good 1 to Bobbi and Bobbi gives 2 units of good 2 to Alannah. Find and plot the new allocation in the Edgeworth Box (label it Z). Calculate Alannah's and Bobbi's utility at the new allocation point Z. Would such an allocation represent a Pareto improvement? Explain your answer.

c) Suppose instead that Alannah gives 1 unit of good 1 to Bobbi and Bobbi gives 1 unit of good 2 to Alannah. Find and plot the new allocation in the Edgeworth Box (label it S). Calculate Alannah's and Bobbi's utility at the new allocation point S. Would such an 2 allocation represent a Pareto improvement? Explain your answer using indifference curves to illustrate it.