Re: jnu mphil questions..

Posted by Amit Goyal on Apr 26, 2014; 9:10am
URL: http://discussion-forum.276.s1.nabble.com/jnu-mphil-questions-tp7587819p7587850.html

Explanation of Q1. The following example will rule out all the options:
Suppose the society consists of two individuals {1, 2}
and there are four social alternatives {x, y, w, z} out of which only one will be implemented.
Suppose preference of individual 1 is
x P y P w P z
i.e. 1 strictly prefers x to y, y to w, and w to z.
And suppose preference of individual 2 is
y P z P w P x
i.e. 2 strictly prefers y to z, z to w, and w to x.
Clearly x and y are pareto optimal but w and z are not.
It can be easily seen that x is neither pareto superior to w, nor to z.


Explanation of Q3. To solve for Nash equilibrium,
first maximize wrt x1, the utility of 1:
5(x1 + x2)^{1/2} + (30 - x1)
to get the best response function as:
x1 = 25/4 - x2

and then maximize wrt x2, the utility of 2:
5(x1 + x2)^{1/2} + (30 - x2)
to get the best response function as:
x2 = 25/4 - x1

Solving the above two best response simultaneously, we see that one of the Nash equilibrium is
(25/8, 25/8)