### Section - A

1. Answer all of the following ** six** parts in about 100 words each.

Marks: 5 × 7 = 35

#### (a) Why do we need constancy assumption of marginal utility of money in Cardinal Ulitity Analysis? Justify your answer.

In the Cardinal Utility Analysis, money is used as a unit of measurement of utility. It is eaasential for a unit of measurement to be constant. For example, the size of a ruler remains constant so that we can compare the length of different objects on the basis of the length of the ruler. If scale would be elastic than it is useless to compare length of two objects measured with that scale. Similarly, if marginal utility of money changes with change in income then it would not be possoble to use it as a unit of measurement.

#### (b) Define the method of Compensating Variation of Income and the method of Cost Difference. Why is the latter method superior to the former one?

(Comment for solution.)

#### (c) Distinguish between laws of variable proportions and laws of returns to scale. Find out the elasticity of substitution in the case of fixed coefficient type production function.

(Comment for solution.)

#### (d) Find out the cost elasticity of output at the minimum point of the average cost curve in the short-run.

(Comment for solution.)

#### (e) Define Peak- load pricing. How does it differ from third degree price discrimination? Analyse graphically.

(Comment for solution.)

#### (f) Consider the equilibrium of a firm under perfect competition. Find out the condition for normal profit, or supernormal profit or loss (whichever is applicable for the firm) without using the average cost curve. Explain only diagrammatically.

(Comment for solution.)

#### (g) Explain the concept of divergence in the context of social and private welfare.

(Comment for solution.)

### Section - B

Answer any **five** out of the following seven questions in about 200 words each.

Marks: 18 × 5 = 90

#### 2 (a). How can you measure the price elasticity of demand at any point on a straight line demand curve?

(Comment for solution.)

#### 2 (b). Compare between price elasticity at a given price and also at a given quantity for a set of parallel demand functions.

(Comment for solution.)

#### 3 (a). Write down the form of CES production functionn and interpret its parameters. Show that the Cobb-Douglas production function is a special case of CES function.

(Comment for solution.)

#### 3 (b). Find out the elasticity of substitution of the CES production function.

(Comment for solution.)

#### 4. What do you mean by price discrimination? Under what circumstances is price discrimination profitable? Trace out the equilibrium situation under price discrimination.

(Comment for solution.)

#### 5. State and explain the Kaldor-Hicks compensation priciple. How does Scitovsky provide an improvement of Kaldor-Hicks compennsation principle?

(Comment for solution.)

#### 6. State, prove and give an economic interprtation of Euler's theorem. Show that at the minimum point of the long-run average cost, the total product is exhausted.

(Comment for solution.)

####
7 (a). Consider two regression equations of y on x and x on y. Show that the arithmatic mean of two regression coefficients is greater than
the correlation coefficient, provided the correlation coefficient, provided the correlation coefficient is positive. Under which condition do
the two regression lines coincide? (Marks - 12)

7 (b). In a bivariate distribution, a researcher gets two lines of regression as
\[2x - y + 1 = 0\]
\[3x - 2y + 7 = 0\]
Identify the two regression lines and find the mean of x and y.

Solution Video:

#### 8. If a single buyer focuses on a single seller, what are the outcomes likely to appear? Do you think that the exploitation of labour will emerge? Justify in favour of your arguments. Find out the equilibrium condition of a firm in the presence of perfect competition in both the prodduct and input market.

(Comment for solution.)

### Section - C

Answer any ** three** of the following five questions in about 300 words each.

Marks: 25 × 3 = 75

#### 9 (a). Let the demand function for a good be \[q = A{p^\alpha }{y^\beta }\] where q = the quantity demanded, p = the price per unit and y = the income. What do the parameters \(\alpha \) and \(\beta \) imply and what is the sum of \(\alpha \) and \(\beta \)? Interpret your result.

(Comment for solution.)

#### 9 (b). consider the utility function \(u = \log {x_1} + {x_2}\) which is to be maximized subject to the budget constraint \(m = {p_1}{x_1} + {p_2}{x_2}\), where \({p_1}\) and \({p_2}\) are the prices per unit of the goods \({x_1}\) and \({x_2}\) respectively, and m is the income of the consumer. Derive the demand for \({x_1}\) and \({x_2}\) and interpret your results.

(Comment for solution.)

#### 9 (c). Given the demand function and total ost function of a perfectly competitive firm as p = 32 - X, \(c = {X^2} + 8X + 4\), p being price, c being cost and X = output.

Find out the output, price, profit and total revenue corresponding to maximization of total profit.

(Comment for solution.)

#### 10 (a). Describe the Leontief static open input-output model along with its assumptions.

(Comment for solution.)

#### 10 (b). State the Hawkins-Simon conditions and explain their economic meaning and significance.

(Comment for solution.)

#### 10 (c). Find out the total demand for industries 1, 2 and 3 if the coefficient matrix A and the final demand vector B are as follows:

\(A = \left( {\begin{array}{*{20}{c}}{0 \cdot 3}&{0 \cdot 4}&{0 \cdot 1}\\{0 \cdot 5}&{0 \cdot 2}&{0 \cdot 6}\\{0 \cdot 1}&{0 \cdot 3}&{0 \cdot 1}\end{array}} \right)\,\) and \(B = \left( {\begin{array}{*{20}{c}}{20}\\{10}\\{30}\end{array}} \right)\)

(Comment for solution.)

#### 11 (a). What do you mean by multicollinearity?

(Comment for solution.)

#### 11 (b). How does it affect the precision of estimates?

(Comment for solution.)

#### 11 (c). Consider a simple model \[{y_i} = {\beta _2}{x_{2i}} + {\beta _3}{x_{3i}} + {u_i};\,i = 1,\,2,\,...,\,n\] and the variables are in deviation form. The disturbance term \({u_i}\) satisfies all the classical assumptions. Suppose \({x_{2i}}\) and \({x_{3i}}\) are multicollinear. Should you drop either \({x_{2i}}\) or \({x_{3i}}\) to have precise estimates of the remainiing parameters? If so, under what condition are you permitted to do so?

(Comment for solution.)

#### 12 (a). Explain the meaning of spurious regression.

(Comment for solution.)

#### 12 (b). How are the values of Durbin-Watson d static and \({R_2}\) indicative of spurious regression?

(Comment for solution.)

#### 12 (c). Show that in the case of spurious regression between \({Y_t}\) and \({X_t}\), where both \({Y_t}\) and \({X_t}\) are generated by random walks, (i) the errors have a permanent effect; (ii)the jvariance of the errors is infinitely large. What should you interpret from your result?

(Comment for solution.)

#### 13 (a). Explain what do you mean by heteroscedasticity.

(Comment for solution.)

#### 13 (b). Given the model \({Y_i} = {\beta _1} + {\beta _2}{X_{2i}} + {u_i}\), where \(E(u_i^2) = {\sigma ^2}X_i^2\) and i = 1, 2, 3, ..., n, find out the OLS and GLS variance of the regression slope.

(Comment for solution.)

#### 13 (c). Show that if \({X_i}\) takes the values 1, 2, 3, 4, 5, \(Var({\hat \beta _2}) > Var({b_2})\), where \({\hat \beta _2}\) is the OLS estimator of \({\beta _2}\) and \({b_2}\) is the GLS estimator of \({\beta _2}\).

(Comment for solution.)

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