Q1. This question consists of two parts, (a) and (b), related to a pure-exchange economy:

• a.) Consider a pure-exchange economy of two individuals (A and B) and two goods (X and Y) Individual A is endowed with 5 units of good X and 3 units of good Y, while individual B with 3 and 4 units of goods X and Y respectively. Assuming utility functions of individuals A and B to be UA=XA YA² and UB=XB² YB where X₁ and Y¡ for i= {A, B} represent individual i's consumption of good X and Y respectively, what will be the set of Pareto optimal allocation in this economy? (N/A - Numerical)
• b.) Determine the conditions that need to be fulfilled by an allocation to be termed as Pareto efficient allocation. (350 words)

Q2. Given a Cobb-Douglas utility function U (X, Y) = X1/2 Y1/2 Where X and y are the two goods that a consumer consumes at per unit prices of Px and Py respectively. Assuming the income of the consumer to be M, determine the following:

• a.) Marshallian demand function for goods X and Y. (N/A - Numerical)
• b.) Indirect utility function for such a consumer. (N/A - Numerical)
• c.) The maximum utility attained by the consumer where Px = 5, Py = ₹ 5 and M= ₹ 5000. (N/A - Numerical)
• d.) Derive Roy's identity. (N/A - Numerical)

Q3. If U (X1, X2) = 10x10.3 x20.7, M=200, p1=5 and p2=2, set up the Lagrange function and derive the simplest form of dU(x1,x2) / dx1 = P1 / P2 dU(x1,x2) / dx2.

Q4. This question consists of two parts, (a) and (b), related to game theory:

• a.)) Distinguish between Strategic (or Normal Form) and Extensive Form Games. (200 words)
• b.)) Solve the following game using iterated elimination of strictly dominated strategies. (N/A - Problem Solving)

Q5. This question consists of two parts, (a) and (b), related to expected utility theory and gambles:

• a)) Explain the expected utility theory. (200 words)
• b)) Two players have the opportunity to participate in a gamble with two possible outcomes as: Outcome Rs 10 Probabilities 0.3 Rs 30 0.7 The players' utility functions for the money outcomes, are as follows: Player 1: U₁(M) = √M + 6 Player 2: U2(M) = (M + 5)² Determine the difference in the amounts that you must offer to these two players. (N/A - Numerical)

Q6. This question consists of two parts, (a) and (b), related to market structures and functions:

• a.)) What is excess capacity and how is it related to the model of monopolistic competition? (200 words)
• b)) Demand function and supply function are given as P=25-X² and P=2X+1 respectively, find out producer surplus and consumer surplus. (N/A - Numerical)

Q7. Write short notes on following:

• a)) Compensated Demand Curve (100 words)
• b)) Homogeneous and Homothetic production functions (100 words)
• c)) Arrow prat measure of risk averseness (100 words)
• d)) Pooling and separating equilibrium (100 words)