How do firms in Bertrand Model under homogenous product industry arrive at the equilibrium price? In what way is this model different from Cournot's Model Linear demand functions faced by two firms are:
Y1 =a1 bl Pp1 cp2 Y2 =a2 cp1 b2P2. Show that quantities are always lower and prices higher in Cournot competition vis-a-vis Bertrand competition.

2. What do you understand by a social welfare function? What properties of social optima would you consider necessary if such a function exists? Discuss these properties.

3. Discuss the two principles of justice as mentioned by Rawls. Do you think Rawls' theory of justice is relevant for the third world countries? Using the two principles of Rawls, justify your answer.

4. A monopolist operates under two plants, A and B. The marginal costs of the two plants are given by 360 14x and 310 15x x^2 with x representing units of output produced by each plant. If the price of this product is given by 396 calculate the overall marginal cost and determine profit maximising output in each plant.

5. Consider a 2 person, 2 commodity pure exchange economy with:
u1= q11^a q12; u2= q21^B q22
q11 q21 q1 and q12 q22= q2 Derive the contract curve as an implicit function of q11 and q12. What conditions on the coefficients a and B ensure the contract curve to be a straight line?

6. Write short notes on (any three) Producer's surplus Hotelling's Lemma Second Welfare Theorem Baumol's alternative theory of firm

7. A perfectly discriminating monopolist faces a linear demand fn P 100 -4q. Her total cost is a linear function of her output and is given as C =50 20q. Determine the equilibrium level of output and profit for the monopolist. Compare these equilibrium values with those if the monopolist was not in a position to practice discrimination.

8. Suppose the consumer's preferences are given by the utility function u Find the ordinary demand function and indirect utility function.

9. Differentiate between (any two) Homogenous and homothetic production functions Pooling and separating equilibria Basing point price and limit price.


10. The pay off matrix of strategies adopted in run and hide game between a hunter and a prey is given as: <img src='./qimages/9902-10.jpg'>

Find the mixed strategy Nash equilibrium of the game.

11. Explain how Shephard's Lemma can be used to derive the production function from the cost function.