# Microeconomics

Topics: Game theory, Nash equilibrium, Utility Pages: 9 (2420 words) Published: August 24, 2013
Section A
a. Explain the concept of dominant strategy equilibrium.
1. http://tuvalu.santafe.edu/~jkchoi/game4.pdf
2. http://econweb.umd.edu/~borowitz/dominant_strategy_equilibrium.pdf

b. Discuss the concept of Nash equilibrium.
1.http://www.economics.utoronto.ca/osborne/igt/nash.pdf

2. http://www.columbia.edu/~rs328/NashEquilibrium.pdf

c. Is every dominant strategy equilibrium a Nash equilibrium? 1. http://economics.fundamentalfinance.com/game-theory/nash-equilibrium.php

d. What do you understand by subgame-perfect equilibrium? 1. http://faculty.apec.umn.edu/thurley/documents/APEC8991/Notes/Fall2010/SubgamePerfectEquilibrium.pdf

2. http://www.cs.tau.ac.il/~canetti/f09-materials/f09-scribe9.pdf

3. http://www.econ.ucla.edu/iobara/SPE201B.pdf

2)

a. What is indirect utility function?
1. http://www.princeton.edu/~dixitak/Teaching/MicroHighCalculus/Notes&Slides/Lec04.pdf 2. http://www.econ.hku.hk/~wsuen/teaching/micro/dual.html

b. Given a direct utility function, how will you derive the indirect utility function? 1.

c. Explain Roy’s identity.

Section B
3) Derive the elasticity of substitution for the Cobb-Douglas production function q ’ f (K, L) ’ AKaL1−a 4) What is meant by externalities? How can the problem of externalities be solved? Explain the Coase’s Theorem.

5) Explain Arrow’s Impossibility Theorem, giving the various assumptions. 6) What is meant by asymmetric information? In what way does the presence of asymmetric information lead to a departure from the usual competitive equilibrium? Explain the relation among moral hazard, adverse selection and signaling, giving suitable examples.

7) What do you understand by actuarially fair insurance? Do you agree with the proposition that a riskaverse person will optimally buy full insurance if the insurance is actuarially fair? Give reasons in support of your answer.

MEC-001: Microeconomic Analysis
Assignment
Course Code: MEC-001
Marks: 100

Note:   Answer all the questions.  While questions in Section A carry 20 marks each, those of Section B carry 12 marks each. Section A

1.         Explain the concept of Nash equilibrium. How it is related to (a) Dominant strategy equilibrium and (b) Sub-game perfection?

Ans.     In a ‘n’ player normal form game G = {S1, S2,…..……,Sn; u1, u2,..……….,un}, the strategies (s*1,s*2,…….,s*n) constitute a Nash equilibrium if, for each player I, si is player i’s best response to the strategies specified for the (n-1) other players, (s*1,s*2,………, s*i-1, s*i+1,…….,s*n) :

or U1 (s*1,s*2,………, s*i-1, s*i, s*i+1,…….,s*n) ≥ U1 (s*1,s*2,………, s*i-1, s*i, s*i+1,…….,s*n)             where i = 1,2,…,n

or, for every feasible strategy si in Si; that is s*i solves

max U1 (s*1,s*2,………, s*i-1, s*i, s*i+1,…….,s*n) s*2ЄS*i

Nash equilibrium is strategically stable and self-enforcing because no single player wants to deviate from her predicted strategy.

Dominant Strategy – A player in a simultaneous move game may have nay finite number of pure strategies at her disposal. One of these strategies called as dominant strategies if it outperforms all of her other strategies, no matter what any other player does. In the normal form game G = {S1, S2,…..……,Sn; u1, u2,..……….,un}, let s1i and s11i be feasible strategies for the player I (i.e s1i and s11i are members of Si). Strategy s11i strictly dominates strategy s1i, if for each possible combination of other players’ strategies, i’s payoff from playing s1i is strictly less than i's payoff from playing s11i. Symbolically,

U1 (s1,s2,………, si-1, s1i, si+1,…….,sn) < U1 (s1,s2,………, si-1, s11i, si+1,…….,sn) for each (s1,s2,………, si-1, si+1,…….,sn) that can be constructed from other players’ strategy spaces (S1,S2,………, Si-1, Si+1,…….,Sn). Strategy s11i is called strictly dominant strategy for player i. The...