jnu mphil questions..

[Amit Goyal]

Here are the answers:
A1.   (d) None of the above
A2.   (c) (0, 25)
A3    (c) (25/8, 25/8)

[vandita24x7]

Sir pls explain 1 and 3...

vandita

On 26 Apr 2014 14:15, "Amit Goyal [via Discussion forum]" <[hidden email]> wrote:

Here are the answers:
A1.   (d) None of the above
A2.   (c) (0, 25)
A3    (c) (25/8, 25/8)

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[Amit Goyal]

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)

[vandita24x7]

Thanks a lot sir. Sir can u pls suggest some reference or give any link where i can prepare for such general equilibrium questions....

vandita

On 26 Apr 2014 14:40, "Amit Goyal [via Discussion forum]" <[hidden email]> wrote:

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. 1 strictly prefers x to y, y to w, and w to z.
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)



There are two individuals, 1 and 2. Each individual has an initial endowment of 30. There is a
machine with the following property : Should individuals 1 and 2 provide respectively
endowments xi and x2 to the machine, the machine first computes the aggregate contribution,
xi + x2. This done, the machine responds by providing each of the individuals fresh
endowments equal to 5(x1 + x2)1/2. Thus the utility of individual i from the contribution profile
(x1, x2) is Ui (x1, x2) = 5(x1 + x2)1/2 + (30 - xi ). Note also that the endowment given to the
machine by individual i, xi, cannot exceed her initial endowment of 30.

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... [show rest of quote]

[Amit Goyal]

I think past year exams are the best source.

[shelly gupta]

Amit sir could you please explain Q2 as well..  because at any other points other than (0,25) also utility is higher

On 26 Apr 2014 14:15, "Amit Goyal [via Discussion forum]" <[hidden email]> wrote:

Here are the answers:
A1.   (d) None of the above
A2.   (c) (0, 25)
A3    (c) (25/8, 25/8)

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[Amit Goyal]

For Q2 You maximize the following wrt x1 and x2:
10(x1+x2)^{1/2} + 60 - x1 - x2
and you get
x1+x2 = 25
as set of all solutions.
Thus, (0, 25) is one of the solution.

[shelly gupta]

thanks a lot sir!!