Section - I

1. Attempt any five parts of the following questios. Answers to each part should be of approximatel 50 words.

Marks: 7 × 5 = 35

(a) How do you draw a Lorenz curve? Explain its use.

(Comment for solution.)

(b) What is 'shadow price'? Why are shadow prices used in project analysis as against market prices?

(Comment for solution.)

(c) What is Engel's law? Which sector/product(s) of an economy operate under this law?

(Comment for solution.)

(d) State the first and second fundamental theorems of welfare economics, and comment on their usefulnesses.

(Comment for solution.)

(e) State the Kuhn - Tucker conditions.

(Comment for solution.)

(f) Explain how Pareto's law of distribution is useful in measuring income distribution.

(Comment for solution.)

(g) Explain total factor productivity and mention any two popular measures of the same.

(Comment for solution.)

Section - II

Attempt any seven of the following questions. Each answer is to be in about 150 words.

Marks: 15 × 7 = 105

2. Show how a demand function may be derived from the Cobb-Douglas utility function.

Solution (Only for IES Google Classroom Members)

3. Formulate a translog cost function and show how the elasticity of input substitution may be obtained.

(Comment for solution.)

4. What is "moral hazard" in economic theory? Discuss a situation that would describe a moral hazard problem.

(Comment for solution.)

5. What is "free-rider" problem? Discuss the possible solutions ot this problem.

(Comment for solution.)

6. State and explain the Coase theorem in the context of pollution control.

(Comment for solution.)

7. Explain Leontief's static input-outut model and describe its limitations.

(Comment for solution.)

8. What is "prisoner's dilemma"? How is it related to strictly dominant strategy?

Solution (Only for IES Google Classroom Members)

9. What is a superlative index number? How is it related to the theory of aggregation?

(Comment for solution.)

10. Define a quadratic form, and state the conditions under which it is (i) positive definite, (ii) positive sem-definite, and (iii) negative definite.

(Comment for solution.)

Section - III

Attempt any two of the following questios, in about 500 each.

Marks: 30 × 2 = 60

11. Explain the principl of least squares as a basis for multiple regression analysis. Also state the underlying standard assumptions of ordinary least Squares estimation. Explain further the consequences of violation of such assumptions.

(Comment for solution.)

12. In the case of a pure exchange econom how do you characterize Walrasian equilibrium? Also establish the conditions under which such an equilibrium exists.

(Comment for solution.)

13 (a). State and prove Euler's theorem. Is i relevant in the context of a firm?

(Comment for solution.)

13 (b). Distinguish between technical and allocative efficiency in the context of a firm. Give an example.

(Comment for solution.)

13 (c). Distinguish between parametric and non - parametric tests in testing of hypotheses.

(Comment for solution.)

1. Sir, when I substitute the demand function for good x in equation of budget constraint, i am unable to obtain the demand function of y. There is no Beta value while rearranging the equation..

2. But i got the correct demand function of Good Y when i substituted the value of demand function for good x in the equation where you found value of Y first and also used it in the budget constraint.

1. $x = \frac{{\alpha I}}{{{p_x}}}$
Substituting:
$I = {p_x} \times \frac{{\alpha I}}{{{p_x}}} + {p_y}y$
$I = \alpha I + {p_y}y$
${p_y}y = I - \alpha I$
$y = \frac{{I(1 - \alpha )}}{{{p_y}}}$
We know that:
$\alpha + \beta = 1$
$\beta = 1 - \alpha$
Therefore,
$y = \frac{{\beta I}}{{{p_y}}}$

3. Thank you sir