Explain Arrow’s Impossibility Theorem
The Arrow's impossibility theorem is a social-choice paradox illustrating the impossibility of having an ideal voting structure that is reflective of specific fairness criteria, such as Pareto efficiency. Arrow's impossibility theorem states that a clear order of preferences cannot be determined while adhering to mandatory principles of fair voting procedures.
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Envelope theorem
Consider the pay-off matrix of a game given below:
(a) Find all the Nash equilibrium of this game. Which player(s), if any, would have a
dominant strategy?
(b) Suppose that player 1 moves first by choosing either A or N. Players 2 observe
player 1’s action and then choose I or, O. For every action combination, the
4
player’s pay-offs are the same as in the above pay-off matrix. Draw a tree of this
new game. How many strategies does player 1 have and what are they? Find all the
sub-game perfect equilibria of this game.
Assume that there are four firms supplying a homogenous product. They have identical
cost functions given by C(Q) =40 Q. If the demand curve for the industry is given by
, find the equilibrium industry output if the producers are Cournot
competitors. What would be the resultant market price? What are the profits of each
firm?
What is indirect utility function? How will you derive an indirect utility function from a direct utility function? Explain Roy’s identity?
Hidden information
What is indirect utility function? How will you derive an indirect utility function from a
direct utility function? Explain Roy’s identity?
Write short notes on any two of the following:
(a) Envelope theorem
(b) Hidden information
(c) Actuarially Fair Premium