## Practice Exercises for Advanced Microeconomic Theory

by Muñoz-Garcia

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Contents (pg. v)
Preface (pg. ix)
Chapter 1 - Preferences and Utility (pg. 1)
Exercise #1 - Checking properties of preference relations - I (pg. 1)
Exercise #3 - Monotonicity and strong monotonicity (pg. 15)
Exercise #5 - Convex preferences (pg. 16)
Exercise #7 - Monotonic transformations - I (pg. 17)
Exercise #9 - Lexicographic preference relation (pg. 18)
Exercise #11 - WARP and rationality (pg. 22)
Exercise #13 - Lexicographic preference and WARP (pg. 23)
Exercise #15 - Homogeneity and addition (pg. 24)
Exercise #17 - Quasi-hyperbolic discounting (pg. 24)
Chapter 2 - Demand Theory (pg. 29)
Exercise #1 - Finding Walrasian demands - I (pg. 29)
Exercise #3 - Finding Walrasian demand for the CES utility function (pg. 35)
Exercise #5 - Checking WARP (pg. 36)
Exercise #7 - WARP for undergrads - II (pg. 41)
Exercise #9 - An introduction to income and substitution effect with a quasi-linear utility function (pg. 42)
Exercise #11 - Relationship between WARP and CLD (pg. 45)
Exercise #13 - Quasi-linear preferences (pg. 47)
Exercise #15 - CES utility function (pg. 49)
Exercise #17 - Concavity of the support function (pg. 51)
Exercise #19 - Separable utility function (pg. 52)
Exercise #21 - Stone-Geary utility function with three goods (pg. 53)
Exercise #23 - Properties of the expenditure function (pg. 55)
Exercise #25 - Duality: equivalence between the UMP and EMP (pg. 57)
Exercise #27 - Compensated (Hicksian) elasticities (pg. 58)
Chapter 3 - Applications of Demand Theory (pg. 61)
Exercise #1 - Taxes versus subsidies (pg. 61)
Exercise #3 - Compensating and equivalent variation (pg. 66)
Exercise #5 - Welfare measures with a quasi-linear utility (pg. 70)
Exercise #7 - Consumer theory and welfare (pg. 73)
Exercise #9 - Using the compensating variation to identify price changes (pg. 78)
Exercise #11 - Finding the compensating and equivalent variation with little information (pg. 80)
Exercise #13 - Consumer and producer theory within the household (pg. 81)
Exercise #15 - Aggregation: properties of the social welfare function (pg. 84)
Exercise #17 - Gorman form for vi(piwi) (pg. 87)
Exercise #19 - Aggregate demand (pg. 89)
Chapter 4 - Production Theory (pg. 91)
Exercise #1 - Properties of a standard production function (pg. 91)
Exercise #3 - Increasing average product (pg. 95)
Exercise #5 - Average and marginal product - II (pg. 96)
Exercise #7 - Law of supply (pg. 97)
Exercise #9 - Shephard's lemma (pg. 97)
Exercise #11 - CES production function (pg. 98)
Exercise #13 - Output distribution between two plants (pg. 100)
Exercise #15 - Comparing two technologies (pg. 104)
Chapter 5 - Choice under Uncertainty (pg. 109)
Exercise #1 - Independence axiom (pg. 109)
Exercise #3 - von Neumann-Morgenstern utility function (pg. 110)
Exercise #5 - Regret theory (pg. 112)
Exercise #7 - An introductory example on risk aversion (pg. 114)
Exercise #9 - Hyperbolic absolute risk aversion, HARA (pg. 116)
Exercise #11 - Investing in two different assets (pg. 118)
Exercise #13 - Second-order stochastic dominance (pg. 120)
Exercise #15 - Coecient of risk aversion (pg. 121)
Exercise #17 - Non constant coecient of absolute risk aversion (pg. 121)
Exercise #19 - Coecient of absolute risk aversion and concave transformations (pg. 123)
Exercise #21 - Risk aversion (pg. 124)
Exercise #23 - Uncertainty about the future (pg. 126)
Exercise #25 - Uncertainty in production decisions (pg. 129)
Chapter 6 - Partial and General Equilibrium (pg. 133)
Exercise #1 - Equilibrium number of firms in perfectly competitive markets (pg. 133)
Exercise #3 - Per unit taxes versus ad valorem taxes (pg. 135)
Exercise #5 - Perfect competition with heterogeneous goods (pg. 137)
Exercise #7 - Finding offer curves for different preferences (pg. 138)
Exercise #9 - Pure exchange economy (pg. 140)
Exercise #11 - Gross substitutability and uniqueness of equilibrium (pg. 144)
Exercise #13 - Pareto allocations with externalities (pg. 145)
Exercise #15 - When goods are bads (pg. 147)
Exercise #17 - Excess demand in Cobb-Douglas preferences (pg. 152)
Exercise #19 - Excess demand functions: homogeneity and Walras' law (pg. 154)
Exercise #21 - Production economy (pg. 156)
Exercise #23 - Pareto and efficient allocations in the household (pg. 160)
Exercise #25 - Effect of distortionary taxes (pg. 165)
Chapter 7 - Monopoly (pg. 171)
Exercise #1 - Monopoly with linear inverse demand (pg. 171)
Exercise #3 - Subsidies to monopolists (pg. 172)
Exercise #5 - Monopoly with durable goods: leasing versus selling (pg. 173)
Exercise #7 - Second-degree price discrimination (pg. 177)
Exercise #9 - Cost reducing investment (pg. 179)
Exercise #11 - Monopolist with intertemporal network effects (pg. 183)
Chapter 8 - Game Theory and Imperfect Competition (pg. 189)
Exercise #1 - A unique strategy profile that surviving IDSDS must also be NE (pg. 190)
Exercise #3 - Deletion order in IDSDS (pg. 190)
Exercise #5 - Equilibrium predictions from IDSDS versus IDWDS (pg. 191)
Exercise #7 - Four categories of simultaneous-move games (pg. 193)
Exercise #9 - Bayesian Nash equilibrium in the workplace (pg. 196)
Exercise #11 - Cournot with equity swaps (pg. 198)
Exercise #13 - Cournot competition with product differentiation (Deneckere 1983) (pg. 201)
Exercise #15 - Antitrust efforts and collusion (pg. 204)
Exercise #17 - Profitable and unprofitable mergers (pg. 205)
Exercise #19 - Fixed costs and discontinuities (pg. 207)
Exercise #21 - Strategic managerial incentives (pg. 210)
Exercise #23 - Fixed costs with collusion (Bernheim and Whinston 1990) (pg. 213)
Exercise #25 - Cournot game revisited (pg. 214)
Exercise #27 - Collusion with temporary reversion (pg. 216)
Exercise #29 - Impure forms of cooperation (pg. 217)
Chapter 9 - Externalities and Public Goods (pg. 219)
Exercise #1 - Externalities and car accidents (pg. 220)
Exercise #3 - Positive and negative externalities (pg. 224)
Exercise #5 - Regulating externalities under incomplete information (pg. 226)
Exercise #7 - Entry in the commons (pg. 232)
Exercise #9 - Voluntary contributions to a public good with Cobb-Douglas preferences (pg. 234)
Exercise #11 - Externalities in consumption (pg. 237)
Exercise #13 - Reference points in public good games (pg. 240)
Exercise #15 - Adding regulation to the Salant et al. (1984) model (pg. 242)
Chapter 10 - Contract Theory (pg. 247)
Exercise #1 - Moral hazard (pg. 247)
Exercise #3 - Moral hazard|continuous probabilities (pg. 252)
Exercise #5 - Moral hazard with two periods (Hopenhayn and Nicolini 1997) (pg. 254)
Exercise #7 - Moral hazard under linear contracts (pg. 257)
Exercise #9 - Moral hazard in teams (Holmstrom 1982) (pg. 260)
Exercise #11 - Solving the lemons problem by offering quality certificates (pg. 263)
Exercise #13 - Principal-agent problem (pg. 269)
Exercise #15 - A special type of principal-agent problem (pg. 272)
Exercise #17 - Screening-monopoly pricing (pg. 273)
Exercise #19 - Screening two types of customers (pg. 279)
Exercise #21 - Efficiency wages and the principal-agent problem (Shapiro and Stiglitz 1984) (pg. 283)
References (pg. 285)

#### Felix Muñoz-Garcia

Felix Muñoz-Garcia is Associate Professor on the School of Economic Sciences at Washington State University.

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