dse 2004

[SoniaKapoor]

http://economicsentrance.weebly.com/uploads/1/1/0/5/1105777/26_jun_2004_option_a.pdf


please help me with question 3 and 4..thank you.

[Granpa Simpson]

For Q3 c will be the answer..you can get this by checking the options.
Option a: is Pareto Efficient because if you take the bundles (500,500) for 1st consumer and (500,500) for the second, then since the utility function is min{x,y}, it is clear that no transfer can be made which makes atleast one of the agents better off without making the other worse off. Also this bundle is preferred to the endowment since in endowment bundle the utility for both are zero, however in (500,500) its 500 for both.
Option b: (1000,0) and (0,1000) cannot be pareto efficient, consider the transfer (999,1) and (1,999) in this case both the agents utility increases to 1. So a transfer can be made which increases the utility of both the consumers compared to the stated one. Thus this bundle is not Pareto efficient.
Option c: all the points on the set will be Pareto efficient by the logic used in option a.
Option d: this is not Pareto efficient by the logic used for option b.
Thus we can rule out b and d. Out of a and c, c seems more plausible because in the question it has been told to find the set of all Pareto efficient points which is c, a being a subset of c.

[Granpa Simpson]

Q4) You can use Second Theorem of Welfare Economics which states that under the condition of convex, monotone and continuous utility functions a Pareto Efficient outcome will lead to a Competitive Solution..which means the answer will be same as Q3..This is the way i have solved.