Answer any two questions from this section.

1.(a) Why is the first welfare theorem considered to be useful Give reasons in support of your answer.
You are given two goods, product and leisure L. Their prices are p and w. Consumer's utility is U and X is equal to sqrtt ,where t =employment level. If production possibility curve is defined by
X sqrt(24 Find the Pareto optimum and show that it is competitive equilibrium allocation.
Find the labour supply at profit maximisation level if consumer's income is given as I 24 w where n =profit.

(iii) What is labour market equilibrium derived on the basis of above information?

2.(a) Discuss the market structure under which Cournot model offers useful insights.
Find the Cournot equilibrium if market demand is

Q=3200 -1600 where
Q Ql Q2 and cost functions of two
firms 1 and 2 are TC1(Q1) 0·25
and TC2(Q2) =0·5 Q2.

3.(a) Why is the adverse selection likely to exist in a market What mechanism would you like to suggest for overcoming the allocation problem?
In a used car market, quality of bad and good cars are measured in monetary units. Suppose price of used cars varies from Rs 2,000 to Rs 6,000 with uniform probability distribution. Answer the following:
If a buyer thinks that both types of cars are there in the market, what is the maximum price she is willing to pay?
At the price of above, what is the quality of the cars in the market?

(iii) Find the equilibrium in the market of used cars you are given above.

(iv) Suppose now buyers value each car at a price 20% higher than the owner. If the selling prices for the owners are same as before, what would be the new equilibrium?

4.(a) Why is Paretian Criterion considered important in Welfare economics?
Making use of indifference curve tool, analyse the Paretian Criterion.
What impact would the compensating payment have on Paretian Criterion Give reasons to support your answer.

Answer any five questions from this section.

5. A cartel comprises 10 firms, each with total cost TC =200 If the market demand is given as p 140 solve for cartel's output level, market price and profit.

6. Two room-mates, Tina and John have two goods Pepsi and Music. Their utility functions are given as

UT MT) PT MT and
UJ MJ)=PJ-[MJ^2).

If each one is having 30 pepsies and 24 hours music, find the Pareto optimality condition for them.

7.(a) What is the efficiency condition for public goods? There are 2 goods, Fish and Train representing private and public goods. respectively. If n people in that economy are having utility function, Ui and production possibility frontier is given as F^2 3T^2 =1800, what is Pareto optimal provision of T
8. Given the following extensive form game, find the subgame perfect Nash equilibrium. write its normal form and solve for its Nash equilibrium. compare the solutions obtained from extensive and normal forms of the game and state which of these offers better solution. <img src='./qimages/14233-8c.jpg'>

9. Utility from wealth for a person is given by U ln where U is the utility and w is the level of wealth. The person has a prospect of good income of 4000 with probability 0·4 and low income of 1000 with probability of 0·6. How much would she pay to insure against income uncertainty?

10. Use the utility function u x2) x1^1/2 y2^1/3 and the budget constraint m P1x1 P2x2 to calculate demand, indirect utility function, Hicksian demand and expenditure function.

11. Write short notes on any two of the following: Envelope Theorem
Pooling Equilibrium Translog Production Function