Paul and David consume apples and oranges. Paul’s utility function is UP (AP,OP) = 2AP + OP and David’s utility function is UD(AD,OD) = AD + 2OD, where AP and AD are apple consumptions for Paul and David, and OP and OD are orange consumptions for Paul and David. There are a total of 12 apples and 12 oranges to divide between Paul and David. Paul has blue indifference curves. David has red ones. Draw an Edgeworth box showing some of their indifference curves. Mark the Pareto optimal allocations on your graph.
(a) Write one inequality that says that Paul likes his own bundle as well as he likes David’s and write another inequality that says that David likes his own bundle as well as he likes Paul’s.
(b) Use the fact that at feasible allocations, AP + AD = 12 and OP + OD = 12 to eliminate AD and OD from the first of these equations. Write the resulting inequality involving only the variables AP and OP. Nowin your Edgeworth box, use blue ink to shade in all of the allocations such that Paul prefers his own allocation to David’s
(c) Use a procedure similar to that you used above to find the allocations where David prefers his own bundle to Paul’s. Describe these points with an inequality and shade them in on your diagram with red ink. ___________
(d) On your Edgeworth box, mark the fair allocations.