### Section - I

1. Attempt any ** nine** parts of the following questios. Answers to each part should be of approximately 50 words.

Marks: 7 × 5 = 35

#### (a) Define the compensated demand curve. How does it differ from the uncompensated demand curve?

(Comment for solution.)

#### (b) What do you mean by corner solution? In the case of perfect complementory goods, where do you get the corner solution?

Solution video:

#### (c) Given that the average revenue curve is a rectangular hyperbola, what will be the shape of the marginal revenue curve? Comment briefly.

(Comment for solution.)

#### (d) Suppose that a monopolist faces a demand curve with price elasticity less than one should the monopolist adopt the policy of price-increase in order to increase revenue? Justify your answer.

(Comment for solution.)

#### (e) Define cross elasticity of demand. Based on such definition, how can you distinguish between the substitute goods and the complementary goods?

(Comment for solution.)

#### (f) Using graphical approach, solve the following linear programming problem:

Minimize : C = 80X + 60Y

Subject to :

2X + 2Y ⋝ 3

2X + 0Y ⋝ 1

X, Y ⋝ 0

Solution video:

#### (g) Consider a Cobb-Douglas production function \(Y = A{K^\alpha }{L^\beta }\) where K and L are respectively the capital and labour to produce output Y. Show that if all the factors are paid according to their marginal products, the total product will be exhausted if \(\alpha + \beta = 1\).

(Comment for solution.)

#### (h) Consider a linear demand function q = a -bp, where q = quantity demanded, p = price per unit and a,b > 0. Find out the average and the marginal revenue and draw the diagram.

(Comment for solution.)

#### (i) Establish mathematically the relationship between average cost (AC) and marginal cost (MC).

(Comment for solution.)

#### (j) Define and distinguish between the normal profit and the super-normal profit under perfect competition. In the short run, find out graphically the amount of profit corresponding to the equilibrium without using the average cost curve.

(Comment for solution.)

#### (k) In the game theory comment on the terms 'maxi-min' and 'mini-max'.

**Maxi-min** is the maximum payoff in the row-minimum in a zero-sum-game where raw minimum is a set of minimum payoffs from each raw in a payoff matrix.**Mini-max** is the minimum payoff in the column-maximum in a zero-sum-game where column maximum is a set of maximum payoffs from each column in a payoff matrix.

Suggested vido to understand these concepts more clearly - Game Theory Basics - 2

### Section - II

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

Marks: 15 × 7 = 105

#### 2. Define income effect, substitution effect and price effect of any change in price Show that the price effect can be decomposed into the income effect and the substitution effect.

(Comment for solution.)

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

(Comment for solution.)

#### 4. Consider the utility function \(u = \sqrt {{q_1}{q_2}} \) where q_{1} and q_{2}
are the quantities of two commodities on which the consumer spends his monthly income ₹5,000. If the price per unit of
q_{1} and q_{2} be ₹50 and ₹20 respectively, find out the optimal quantities of q_{1} and q_{2}.
(Marks - 15)

Solution video:

#### 5. Define linear homogeneous production function with the help of CES production function. Also establish that CES production function is strictly quasi-concave for positive L and K, where L, K are labour and capital respectively.

(Comment for solution.)

#### 6. What do you mean by price discrimination? Under which condition is the price discrimination profitable? Trace out the equilibrium situation under price discrimination.

(Comment for solution.)

#### 7. How can you get the wage offer curve and the supply curve of labour? How can you justify the backward bending supply curve of labour?

(Comment for solution.)

#### 8. What is meant by excess capacity? Why is it bad? Are there any benefits of excess capacity associated with monopolistic competition?

(Comment for solution.)

#### 9. If D = 250 - 50p and S = 25p + 25 are the demand and supply functions repectively, calculate the equilibrium price and the quantity. Hence calculate both consumer's and producer's surpluses under equilibrium.

(Comment for solution.)

#### 10. Define and distinguish between rent and quasi-rent. What do you mean by 'transfer earnings? Elucidate the statement that no economic rent is earned when the supply of a factor is perfectly elastic.

(Comment for solution.)

### Section - III

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

Marks: 30 × 2 = 60

#### 11. How does Lorenz curve exxplain income inequality? Explain with one suitable example. Define Gini coefficient with the help of Lorenz curve and show that \[Gini = [1 - 2 \times (Area\,below\,Lorenz\,curve)].\]

(Comment for solution.)

#### 12(a). In computing the correlation coefficient between two variables X and Y from 25 pairs of observations, the intermediate results are: \[n = 25\] \[\sum\limits_i {{X_i}} = 125\] \[\sum\limits_i {X_i^2} = 650\] \[\sum\limits_i {{Y_i}} = 100\] \[\sum\limits_i {X_i^2} = 460\] \[\sum\limits_i {{X_i}{Y_i}} = 508\] Later on at the time of checking it was found that two pairs of observations which should be

X | 8 | 12 |

Y | 6 | 8 |

X | 6 | 14 |

Y | 8 | 6 |

(b) Find out the variance of numbers 1, 2, 3, ...., 50 and the coefficient of variation. What is the advantage of computing the coefficient of variation over the variance? (Marks - 5+3+2=10)

Solution video:

#### 13(a). Explain the terms as follows and their importance in the context of inference analysis: Degree of freedom, Level of significance, and Power of the test.

(Comment for solution.)

#### 13(b). Briefly discuss the principal component analysis and the rationale for its use.

A pdf related to principal component analysis has been available in the Google Drive Folder. See the
Econometrics file of the folder.

Also see Q. No. 12 (b) and (c) General Economics - 1 Previous Year Paper Solution 2019.

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