### Section - A

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

Marks: 5 × 7 = 35

#### (a) Is the following statement **true** or **false**? Explain.
"If a consumer's utility function is of the form = \(x_1^{\frac{1}{3}}x_2^{\frac{1}{3}}\), she
faces prices p_{1} and p_{2} and her income is I, then her indirect utility function
is \(V = \frac{{{I^3}}}{{3{p_1}{p_2}}}\)."

_{1}and p

_{2}and her income is I, then her indirect utility function is \(V = \frac{{{I^3}}}{{3{p_1}{p_2}}}\)."

Solution video:

#### (b) Define complements and substitutes. In the two-commodity case, can the commodities be complements? Explain. Is your answer valid in the case of gross substitutes and complements? Explain

(Comment for solution.)

#### (c) Other things equal, what happens to consumer surplus if the price of a good falls? Why? Illustrate using a demannd curve.

(Comment for solution.)

#### (d) What is meant by "internlizing" an externality? How can a negative externality be internalized?

(Comment for solution.)

#### (e) What is productivity principle? How can this be achieved through market mechanism?

(Comment for solution.)

#### (f) What is Nash Equilibrium? Do all games have Nash Equilibrium? Can a game have more than one equilibrium?

Nash Equilibrium is a strategy profile such that each player's equilibrium strategy is the best response to other players' equilibrium strategy and no player can benefit from deviating to other strategies.

All games do not have Nash Equilibrium in pure strategy. For instance, Rock, Paper, Scissors game does not have any Nash Equilibrium in pure strategy.

A game can have more than one Nash Equilibrium. For instance, the Battle of Sexes game has multiple Nash Equilibriums.

#### (g) List out the sources of monopoly power.

(Comment for solution.)

#### (h) Explain the concept of co-integration in a time series analysis.

(Comment for solution.)

### Section - B

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

Marks: 15 × 6 = 90

#### 2. Hrishita likes sandwiches (S) and Coffee (C). Here indifference curve is bowed in towards the origin and do not intersect each other. The price of a sandwich is ₹5 and price of a cup of coffee is ₹3. She is spending all her income at the basket she is currently consuming, and her marginal rate of substitution of sandwiches for coffee is 2.

Is she at an optimum? If so, show why. If not, should she buy fewer sanwiches and more coffee, or the reverse? Argue in favour of your opinion.

Solution video:

#### 3. The demand for good X is estimated to be \(Q = 250,000 - 500P - 1 \cdot 5M - 240{P_R}\), where M is the (average) consumer income and \({P_R}\) is the price of a related good Y. The values of P, M and \({P_R}\) are expected to be ₹200, ₹60,000 and ₹100 respectively.

(a) Calculate the price elasticity of demand, income elasticity of demand and cross price elasticity.

(b) Is the demand for X elastic, inelastic or unit-elastic? How would a small increase in P affect total revenue?

(c) Is the good X normal or inferior? Are the goods X and Y substitutes or complements?

(Comment for solution.)

#### 4. Assume that a monopolist sells a product with the cost function C = F + 20Q, where C is total cost, F is a fixed cost, and Q is the level of output. The inverse demand function is P = 60 - Q, where P is the price in the market. (i) How much profit does the firm earn when it charges the price that maximizes profit? (ii) At what price will the firm earn zero economic profit?

(Comment for solution.)

#### 5. Distinguish between Differentiation and Integration.. Explain their application in economies with suitable examples.

(Comment for solution.)

#### 6. There are only two firms in an industry, firm 1 and firm 2. The market demand curve is given by the equation \(P = 12 - ({q_1} + {q_2})\) are the (total) cost functions facing the firms are \({C_i} = 4{q_i}\), where \(i = 1,2\). If firm 1 acts as a leader and firm 2 as a follower, what are the quantities that the two firms will produce in the equilibrium? What profits will they earn?

(Comment for solution.)

#### 7. Consider a manufactured good whose production process generates pollution. The annual demand for the good is given by \({Q^d} = 100 - 3P\). The annual market supply is given by \({Q^s} = P\). In bot equations, P is the price in rupees per unit. For every unit of output produced, the industry emits one unit of pollution. The marginal damage from each unit of pollution is given by 2Q.

(a) Find the equilibrium price and quantity in a market with no government intervention.

(b) Find the socially optimal quantity of the good. What is the socially optimal market price?

(Comment for solution.)

#### 8. What is autocorrelation? How can we detec it? How can it be removed from a single equation model?

(Comment for solution.)

### Section - C

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

Marks: 25 × 3 = 75

#### 9. Consider the production function \(Q = {({K^{0 \cdot 5}} + {L^{0 \cdot 5}})^2}\).

(a) What is the name of this type of production function?

(b) What is the elasticity of substitution for this production function?

(c) Does this production function exhibit increasing,decreasing, or constant returns to scale?

(d) Suppose that the production function took the form \(Q = {(100 + {K^{0 \cdot 5}} + {L^{0 \cdot 5}})^2}\). Does this production function exhibit increasing, decreasing or constant returns to scale?

(Comment for solution.)

#### 10. Consider a two-person, two-commodity, pure-exchange, competitive economy. The consumers' utility functions are \({U_1} = {q_{11}}{q_{12}} + 12{q_{11}} + 3{q_{12}}\) and \({U_2} = {q_{21}}{q_{22}} + 8{q_{21}} + 9{q_{22}}\) respectively (where \({q_{ij}}\) denotes the consumption of commodity \({Q_j}\) by consumer i, with i = 1, 2 and j = 1,2). Consumer 1 has initial endowments of 8 and 30 units of \({Q_1}\) and \({Q_2}\) respectively; consumer 2 has 10 units of each commodity.

Determine the excess demand function for the two consumers. Determine an equilibrium price ratio for this economy.

(Comment for solution.)

#### 11. What is the problem of multicollinearity in a regression model? What is its plausibility? Explain Farrer - Glauber method to detect it. How can it be removed?

(Comment for solution.)

#### 12. What is optimization problem in Economics? How does linear programming technique help in assigning optimal solution in given resourse use? Explain. (Marks - 25)

Solution video:

Sir question number 1 (a) mein last step mein jaise I ka exponent 1/3 + 1/3 = 2/3 vaise he jab 4 P1P2 ka exponent likha tou 1/3 kyu? 2/3 kyu nahi hoga uska bhi exponent?

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