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Re: can someone please post solutions to pareto optimal questions of dse 2014?

Posted by knowpraveen on Jun 14, 2015; 7:27am
URL: http://discussion-forum.276.s1.nabble.com/can-someone-please-post-solutions-to-pareto-optimal-questions-of-dse-2014-tp7597203p7597754.html

For the next one, we have a budget constraint as follows - Px is considered to be numeraire and Py = p. Let's say, which gives p=0, for the price vector (Px, Py)=(1,0).

The budget equation is therefore, x1+p.x2=10p for Agent 1. The equation for x1 and x2 for Agent 2 is (10-x1)/(11-x2) = 1, which is as per the contract curve equation, y1=y2. Therefore, on solving these, with p=0, we get x2=1 and y2=9 ie, the allocation has to be (0,1) and (11,9) for agents 1 and 2 respectively which is not given in the list of options. 

On Sun, Jun 14, 2015 at 11:44 AM, knowpraveen [via Discussion forum] <[hidden email]> wrote:
It's given that (a,b) is preferred to (c,d) is a>=c or b>d. Consider a line drawn from the origin cutting across the indifference curves for such a utility function. The points at which it cuts across satisfy the aforementioned conditions, when goods are preferred as we move in the positive direction across the diagonal of an edgeworth box for a two good-two person economy. So, its okay to assume that it's a Cobb-Douglas function, say U(x1,x2)=x1.x2.  

For the second condition, the utility curves are that of perfect complements as is obvious. So, the contract curve would be a straight line y1=y2, for utility function U(y1,y2)=min(y1,y2) as the other utility function for the agent 1 takes it up as well.

So, there are infinite competitive equilibrium allocations possible on this contract curve.

I hope its clear.

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