Bergson-Samuelson Social welfare function
The Bergson-Samuelson social welfare function is a theoretical construct used in welfare economics to evaluate the overall welfare of society. It was first proposed by Swedish economist Erik Bergson in 1938 and later expanded upon by American economist Paul Samuelson in 1947.
The Bergson-Samuelson social welfare function is based on the idea that society's welfare can be measured by aggregating the utility or well-being of its individual members. The ______ ____ __________ ____ _______ _____ __________.
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a.) Given the Von Neumann-Morgenstern utility function of an individual, U (W) =W ½ , where W stands for amount of money. Comment upon attitude towards risk of such an individual with the help of a diagram.
b) Now suppose this individual possesses a building worth ₹1600. If the building catches fire, its value falls to ₹ 400. Let the probability of building catching fire be ¼. On the basis of the given information, find out whether the individual would be willing to pay a risk premium of ₹ 76 to the insurance company in order to eliminate the risk associated with the factory building.
Determine the conditions that need to be fulfilled by an allocation to be termed as Pareto efficient allocation.
a.) Define games of complete and incomplete information
b.) From the following pay-off matrix, where the payoffs (the negative values) are the years of possible imprisonment for individuals A and B, determine:
(i) The optimal strategy for each individual.
(ii) Do individuals A and B face a prisoner’s dilemma?
| Individual B | |||
| Individual A | Confess | Don’t Confess | |
| Confess | (-5, -5) | (-1, -10) | |
| Don’t Confess | (-10, -1) | (-2, -2) |
Bergson-Samuelson Social welfare function
5. a.) Differentiate between the Cournot and the Bertrand model of Oligopoly.
b.) Consider an industry with two firms 1 and 2, each producing output Q1 and Q2 respectively and facing the industry demand given by P=140-Q, where P is the market price and Q represents the total industry output, that is Q= Q1 + Q2. Assume that each faces a marginal cost of ₹ 20 per unit with no fixed costs. Solve for the Cournot equilibrium in such an industry
Moral Hazard
Consider a Cobb-Douglas utility function
U (X, Y) = Xα Y (1- α) ,
Where X and y are the two goods that a consumer consumes at per unit prices of Px and Py respectively. Assuming the income of the consumer to be ₹M, determine:
a. Marshallian demand function for goods X and Y.
b. Indirect utility function for such a consumer.
c. The maximum utility attained by the consumer where α =1/2, Px =₹ 2, Py = ₹ 8 and M= ₹ 4000.
d. Derive Roy’s identity