PROBLEM SET 1 - Economics 335 - (Materials from Reading List Part I) J. Wissink Cornell University 1. Answer True, False, or Uncertain. Explain. a) If the assumptions of the First Fundamental Theorem of Welfare Economics were never violated there would be no role for the government in a capitalistic society. All Pareto efficient allocations dominate all inefficient allocations. If at some allocation it is true that: (1) MRSi x, y = MRSj x, y (2) (3) s,tMRTSx b) c) for all people i, j &amp; for all goods x, y and for all inputs s, t &amp; for all goods x, y, THEN it must be true that = s,tMRTSy MRScommon x, y = MRTsocial x, y at that particular allocation. Note: i and j are people; x and y are commodities; s and t are factors of production. d) If the initial endowment allocation in a pure exchange economy is Pareto efficient, then all consumers prefer their initial endowment to the core allocations. 2. Assume you are shipwrecked. There are ten of you in a lifeboat; you know that it will take exactly ten days to reach shore and that there are only rations for ten person-days. How would a utilitarian allocate the rations? How would a Rawlsian? Some people think that even the Rawlsian criterion is not sufficiently egalitarian. What might an extreme egalitarian advocate? What does Pareto efficiency require? Suppose uAbe = (2F + 1C) and uBetty = (1F + 1C). What allocations of food and clothing are on the &quot;contract curve&quot; in the Edgeworth-Bowley box for Abe and Betty? Repeat assuming that uAbe= min {2F, 1C} and uBetty = min {1F, 1C}. On a utility possibilities frontier indicate the difference between the Pareto efficient utility combinations and a social welfare optimum. Does the social welfare optimum necessarily have to be one of the Pareto efficient utility combinations? Suppose that $100 has just been given to the Smith family. Mr. and Mrs. Smith have only one child whose name is Ima Brat Smith. Suppose that money is the only thing that matters to the Smiths and that the utility each member receives from money, Y, is as listed below: Mr. Smith: ud(Yd ) = 5Yd and Mrs. Smith: um(Ym ) = 2Ym and Ima Brat: uk(Yk ) = 1Yk Note: d is for dad, m is for mom, and k is for kid. Therefore, Yd + Ym + Yk = $100. a) What division of the $100 results if the family maximizes a utilitarian SWF? 3. 4. 5. b) What division of the $100 results if the family uses an egalitarian SWF? Which method is more fair? Why or why not? 6. Jack invites a date, Jill, over for a Chinese dinner. Jack makes 5 egg rolls and Jill brings 2 fortune cookies. Indicate how the Edgeworth-Bowley box diagram might be used to analyze the way they should divide the food. Is it reasonable to assume that Jack's satisfaction depends only on the amount of food he consumes? Demonstrate using an Edgeworth-Bowley box how lump sum taxes and transfers can change the position of the core. For each of the programs listed below, discuss what market failures might be (or are) used as partial rationale: a) b) c) d) automobile safety belt requirements national defense <a href="/keyword/federal-deposit-insurance/" >federal deposit insurance</a> Corporation government prohibition of the use of narcotics. 7. 8. 9. Compare and contrast the problems of moral hazard and adverse selection. What kind of market failure may occur in the presence of each problem? 10. I have recently observed while walking from the parking garage to Uris Hall after parking my smallish Honda CRV with my high priced &quot;H&quot; permit, that the parking spaces in the garage have all been painted much too large. The &quot;welfare&quot; of the university community as a whole, could be made much better off if the garage were repainted to fit more smaller cars. That way, more people could park closer to where they finally want to go and only the few people with large cars would have to park in &quot;Siberia.&quot; COMMENT. Do you agree or disagree and why.