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?
To determine the equilibrium industry output, market price, and profits of each firm in a Cournot competition scenario, we need to follow these steps:
1. Identify the Demand Curve:
The demand curve for the industry is given by \(P(Q) = 120 - Q\), where \(Q\) is the total industry output.
2. Identify the Cost Function:
The cost function for each firm is given
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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?
Write short notes on any two of the following:
(a) Envelope theorem
(b) Hidden information
(c) Actuarially Fair Premium
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.
Discuss the approaches adopted by Pigou and Pareto for analyzing the problem of welfare economics.
Envelope theorem
What is indirect utility function? How will you derive an indirect utility function from a
direct utility function? Explain Roy’s identity
Sita expects her future earnings to be worth Rs. 100. If she falls ill, her expected future
earning will be Rs 25. There is a belief that she may fall ill with probability of
2/3 while the probability of remaining in good health is 1/3
Let her utility function be given as U(y) = y^(1/2)
suppose that an insurance company offers to fully insure sita against loss of earnings
caused by illness against an actuarially fair premium.
(a) Will Sita accepts the insurance. Explain.
(b) What is the maximum amount that Sita would pay for the insurance?