1. A firm operating in a monopolistic market produces two commodities Q1 and Q2. It faces the following demand curves:

Q1 =40-2P1 +P2
Q2 =15 P1-P2

Its total cost function is C Q1Q2 Q2^2.

Find out its profit maximizing levels of P1, P2, Q1 and Q2. Also confirm that these levels really maximize profits.

2. An economy has only two industries, A and B. To produce one unit in A it needs 1/6 unit of output from A and 1/4 unit from B. Industry B needs 1/4 unit from each A and B to produce a unit of its own output. Suppose the final demands ,for both the industries are 60 units each.

Write down Leontief system for this economy.

Find out the gross outputs of A and B needed to satisfy the given final demand.

3. What is First Mover's Advantage? Using the following information about a duopoly work out the advantage if Firm 1 sets its output first and Firm 2 follows it.

Both firms have zero marginal costs.
Market demand curve:

P
Q Q2)

4. Explain the Prisoner's dilemma model with the help of a suitable example. Will the two agents co-operate? Is the equilibrium stable?

5. Explain Cramer's Rule with the help of a suitable example.

6. Demonstrate Shephard's Lemma.

7. What is Hawkins -Simon condition? What are its economic implications

8. What is a How would you interpret the coefficients in a dual

9. Using iterative method, solve the following difference equation:

yt+l =yt given yo =15

10. Solve the following Cobweb model and determine whether the equilibrium is stable or not:

Qt^d 19-6Pt
Qt^a =6Pt-1

11. Evaluate:

lim x^2 sqrt(x)-8


lim x^4


12. What is inverse of a matrix? How do you find it out using technique of elementary row/column operations Explain, using a suitable example. Verify your result using adj-det techniques.