### Section - A

1. Answer any ** seven** parts of the following questios. Answers to each part should be of approximatel 50 words.

Marks: 5 × 10 = 50

#### (a) State and explain Kaldor - Hicks compensation principle.

(Comment for solution.)

#### (b) The demand function \({Q_1} = 50 - {P_1}\) intersects another demand function \({Q_2}\) at price P = 10. The elastcity of demand for \({Q_2}\) is six times larger than that of \({Q_1}\) at that point. Find out the demand function for \({Q_2}\).

(Comment for solution.)

#### (c) Suppose the Government as a monopolist firm produces electricity and sells it to people at price per unit 'p'. The demand function for the electricity, of the people is \(q = \alpha {p^{ - \beta }}\). If the elasticity of demand for electricity in absolute sense is found to be 0.894, should the Government increase the price per unit to increase the revenue? Justify your answer.

(Comment for solution.)

#### (d) Suppose that there are two goods, namely, chocolate cake and ice cream, such that there might well be some optimal amount of chocolate cake and ice cream that a consumer may want to eat per week. Any less than that amount would make her worse off, but any more than that amount would also make her worse off. Find the shape of the Indifference Curve and justify your answer.

#### (e) Define consumer's and producer's surplus Given the demand function \(P = 113 - {q^2}\) and the supply function \(P = {(q + 2)^2}\) under perfect competition, find out the consumers' surplus and produers' surplus.

(Comment for solution.)

#### (f) Elucidate the statement that no economic rent is earned when the supply of a factor is perfectly elastic.

(Comment for solution.)

#### (g) Explain the concept of social welfare. Does perfect competition ensure maximum social welfare?

(Comment for solution.)

#### (h) Show that in a translog production function, elasticity of substitution is not constant.

(Comment for solution.)

#### (i) Define and distinguish between level of significance and confidence inserval. What do you mean by 'power of the test'?

(Comment for solution.)

#### (j) Find out the total demand for industries 1, 2, and 3, if the coefficient matrix A and final vector B are given as \[A = \left[ {\begin{array}{*{20}{c}}{0 \cdot 3}&{0 \cdot 4}&{0 \cdot 1}\\{0 \cdot 5}&{0 \cdot 2}&{0 \cdot 6}\\{0 \cdot 1}&{0 \cdot 3}&{0 \cdot 1}\end{array}} \right]{\rm{ and }}\,\,\,B = \left[ {\begin{array}{*{20}{c}}{20}\\{10}\\{30}\end{array}} \right]\]

(Comment for solution.)

#### (k) Explain the distinction between the parametric and non-paraetric tests.

(Comment for solution.)

### Section - B

Answer any **SIX** of the following questions in about 150 words.

Marks: 15 × 6 = 90

#### 2. Consider the utility function as \(U = \sqrt {{q_1}{q_2}} \), where q_{1} and q_{2}
are two commodities on which the consumer spends his entire income of the month. Let the price per unit of q_{1}
and q_{2} be ₹40 and ₹16 respectively and the monthly income of the consumer be ₹4,000. Find out the optimal quantities of
q_{1} and q_{2}.

Solution video:

#### 3. Define Linear homogenous production function and give an example. Show that in the case of the linear homogenous production function the expansion path must be a straight line passing through the origin.

(Comment for solution.)

#### 4. How can you graphically derive the long-run marginal cost curve from the short-run marginal cost curves?

(Comment for solution.)

#### 5. What is meant by excess capacity? Why is it bad? Are there any benefits of the excss capacity associatedd with monopolistic competition?

(Comment for solution.)

#### 6. How is the monopoly power measured? State Lerner's measure of degree of monopoly power. Show that the degree of monopoly power is te inverse of the price elasticity of demand.

(Comment for solution.)

#### 7. Derive the long-run supply curve in the constant cost industry under perfect competition. Under what conditions can the long-run supply curve of a competitive industry slope downward?

(Comment for solution.)

### Section - C

Attempt any ** three** of the following questios in about 300 each.

Marks: 25 × 3 = 75

#### 8. Consider the competitive market with excise tax such that the suppler receives the price netted of tax. Answer the following questions.

(i) What is the equilibrium price in the presence of tax?

(ii) Under which condition will the price be undefined?

(iii) Show that the market price is totally unaffected in the case of perfectly inelastic supply curve.

(iv) If the tax yield (T) is a fraction (t > 0, which is the rate of tax) of quantity (q), find out the tax yield and the conditions under which tax yield varies directly with the rate of tax (t).

(v) Find out the value of the rate of tax such that the tax yield is maximum.

(Comment for solution.)

#### 9. What do you mean by collusive oligopoly? Distinguish between cartel and price-leadership with respect to the determination of price and quantity. Write a note on barometric price-leadership model.

(Comment for solution.)

#### 10. Consider a simple model of classical regression as \({Y_i} = \beta {X_i} + {u_i},\) where \({u_i}\) stands for random disturbance term with the standard assumptions and \({u_i} \sim N(0,\,\,{\sigma ^2})\), and \({X_i}\) is non-stochastic and i = 1, 2,..., n.

(a) Find out the OLS estimator for \(\beta \), say \({\hat \beta _{OLS}}\).

(b) Show that the OLS estimator for \(\beta \) is BLUE. Prove ab-initio.

(c) Prove that \(\bar \beta = \frac{{\bar Y}}{{\bar X}}\), where \(\bar Y\) and \(\bar X\) are means respectively, is unbiases but less efficient estimator of \(\beta \) than \({\hat \beta _{OLS}}\).

See Section 6.1 of Chapter - 6 and Appendix - 6A of Basic Econometrics 5th edition by Damodar N. Gujarat and Dawn C. Porter

#### 11 (a). Consider the Leontief static input-output model along with its assumptions. How can you confirm that the model is either open or closed? State the fundamental objective of Leontief static open input-output model.

(Comment for solution.)

#### 11 (b). State the Hawkinsk-Simon condition and explain its economic meaning and significance.

(Comment for solution.)

#### 11 (c). Derive the consumption possibility locus.

(Comment for solution.)

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