Course in Public Economics-John Leach Questions Chapter 3

Homework AssignmentA: I want you do chapter 3, questions 2-4 but with the followingaddendum. While solving these I want you to list out the steps beforethey are performed so that I can see that you understand what you aredoing.A2: Consider the equilibrium problem from class (where the utilityfunctions are as in the notes and the text for Chapter 3). SupposeHarriet has to pay a 10% tax on ale (to be rebated to both George andHarriet in equal measure as a lump sum transfer) but George doesn’t.Show without solving the problem that our competitive equilibriumallocations will not be pareto optimal.B: I also want you to answer the following questions about philosophy:B1: Consider “Rawlsian fairness”: Consider a world with George andHarriet. Assume 1 unit of each good and identical preferenceu(a,b)=a^(0.5)b^(0.5). What would be a fair outcome in a Rawlsianworld? (You have some freedom in how to implement this. I want youto capture the max min idea put forward by Rawls.) Suppose insteadGeorge’s utility function was multiplied by 2, how would this affect youranalysis [Hint: There isn’t a unique right answer to this or the nextquestion for most implementations of the theory.] Suppose Georgereceived=-1000 utils if his consumption of ale fell below 2/3, whatwould be “Rawlsian fair” here? What if he would get the same highlynegative utility from from consumption falling below 2/3 in eithergood?[Bonus: Let’s reinterpret the model say that each agents share apreference Ca +b where C=2 if a coin that is about to be flipped isvalued heads and =0.1 if it lands as tales. Suppose George has one unitof ale and Harriet has one unit of bread. What would a fair allocationlook like, if goods must be distributed before the coin is flipped? Whatif Harriet’s preferences were Ca+1.5*b? Would both agents, after thecoin is flipped consider the allocation fair? In this last case, how wouldthe measure of fairness, from the point of view of an economist,change if goods could be allocated after the flip? Now let’s say,George knows the outcome of the coin flip, but no one else does beforegoods are distributed. Would George still consider the previousoutcome fair if he was otherwise in the veil of ignorance? [To clarify, Iam supposing that the economist allocating resources does not knowthe outcome of the flip, but George knows whether he is better orworse off than Harriet based on knowledge of the coin flip.] Is thereoverlap between what George and Harriet would consider fair? Canyou think of a reason in this world, the economist performing theallocation would systematically give George more utility than Harrietfor either value the coin takes?]B2: Consider Nozickian fairness: Remember the idea is that bothagents can only be offered allocations that give them higher utility than what they can guarantee themselves. Assume that there are 11 units ofale in the economy and one of bread. Assume that Harriet owns all thebread and one unit of ale. Assume George owns only 10 units of ale.Also assume the utility function is of the type U(a,b)= a^(0.5)(b)^(0.5).If there is just one Harriet and one George what would be the set ofoutcomes from implementing Nozick’s fairness? Lets say instead thereare a thousand of replicants of both George and Harriet. Further inpairs, each version of George and Harriet could move to a foreigncountry where they are required to split their resources equallybetween the pair that moves, but 10% of all the resources they attemptto move are lost. What would the outcomes permissible underNozickian fairness be like in this world? [Note, the word “world” hasthe same meaning as the word “environment” in the slides.][Bonus: What if, instead of moving as pairs, each of our 1000 Georgeand Harriets, moved individually and ended up with the competitiveequilibrium allocation on the new island. You may alternatively assumeany large number of individuals]