1. Given the production function: y L^B and Lost function: c rK wL, find out the minimized cost as a function of output level and factor prices. Also make comments on the shape of this function.

2. Solve this two commodity market model and obtain expressions for PI, P2 and q1, q2

<img src='./qimages/7539-2.jpg'>

3. Find mixed strategy Nash Equilibrium.

<img src='./qimages/7539-3.jpg'>

What happens to this solution if players adopt max-min principle?

4. Consider a 3 -sector economy of agriculture, mining and manufacturing its

<img src='./qimages/7539-4.jpg'>

Calculate its gross output vector.

Does the above data satisfy Hawkins ­Simon condition?

5. Explain method of dynamic programming for solution of a dynamic optimization problem.

6. Derive shephard's Lemma.

7. Consider the following system of linear equations.

2x +3y 6
5x 10
where z are unknowns and b are constants. Find out the condition(s) under which Crammer's Rule will admit a unique solution.

8. How does the sign of second derivative help us identify suitability of different types of functions for economic analysis

9. Differentiate between strongly dominated strategy and weakly dominated strategy.

10. Find total differentials of

u




11.(a) Explain the idea of an envelope theorem.

Define a 'compensated' demand function.

<img src='./qimages/7539-11c.jpg'>

find AB.

Transform this primal into a dual
Max u u
Subject to Px x+pyy M.

Given find Lim q

What is a differential equation? Explain.