## General Equilibrium Theory: An IntroductionGeneral Equilibrium Theory: An Introduction treats the classic Arrow-Debreu general equilibrium model in a form accessible to graduate students and advanced undergraduates in economics and mathematics. Topics covered include mathematical preliminaries, households and firms, existence of general equilibrium, Pareto efficiency of general equilibrium, the First and Second Fundamental Theorems of Welfare Economics, the core and core convergences, future markets over time and contingent commodity markets under uncertainty. Demand, supply, and excess demand appear first as (point-valued) functions, then optionally as (set-valued) correspondences. The mathematics presented (with elementary proofs of the theorems) includes a real analysis, the Brouwer fixed point theorem, and separating and supporting hyperplane theorems. Optional chapters introduce the existence of equilibrium with set-valued supply and demand, the mathematics of upper and lower hemicontinuous correspondences, and the Kakutani fixed point theorem. The treatment emphasizes clarity and accessibility to the student through use of examples and intuition. |

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### Contents

V | 1 |

VI | 3 |

VII | 9 |

VIII | 20 |

IX | 31 |

X | 38 |

XII | 41 |

XIV | 45 |

LXI | 132 |

LXII | 133 |

LXIII | 135 |

LXIV | 138 |

LXVI | 141 |

LXVII | 143 |

LXVIII | 144 |

LXIX | 146 |

XV | 46 |

XVI | 53 |

XVII | 55 |

XVIII | 56 |

XIX | 63 |

XX | 65 |

XXI | 66 |

XXII | 69 |

XXIII | 70 |

XXV | 71 |

XXVI | 73 |

XXVII | 74 |

XXVIII | 75 |

XXIX | 78 |

XXX | 79 |

XXXII | 80 |

XXXIII | 84 |

XXXIV | 87 |

XXXV | 90 |

XXXVI | 92 |

XXXVII | 93 |

XXXVIII | 96 |

XXXIX | 97 |

XL | 99 |

XLII | 100 |

XLIII | 104 |

XLV | 109 |

XLVI | 111 |

XLVII | 112 |

XLVIII | 115 |

XLIX | 118 |

L | 119 |

LI | 120 |

LII | 122 |

LIII | 125 |

LV | 126 |

LVI | 127 |

LVIII | 129 |

LX | 131 |

LXX | 151 |

LXXII | 155 |

LXXIII | 157 |

LXXIV | 158 |

LXXV | 160 |

LXXVI | 161 |

LXXVIII | 162 |

LXXIX | 163 |

LXXX | 165 |

LXXXI | 168 |

LXXXII | 169 |

LXXXIII | 170 |

LXXXIV | 175 |

LXXXV | 177 |

LXXXVI | 179 |

LXXXVII | 185 |

LXXXVIII | 190 |

LXXXIX | 193 |

XC | 194 |

XCII | 197 |

XCIII | 201 |

XCIV | 204 |

XCV | 206 |

XCVI | 207 |

XCVIII | 209 |

XCIX | 213 |

CI | 215 |

CII | 216 |

CIII | 220 |

CIV | 226 |

CV | 229 |

CVI | 230 |

CVII | 232 |

CIX | 235 |

CX | 237 |

CXI | 238 |

241 | |

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### Common terms and phrases

artificially bounded economy artificially restricted economy assumptions attainable Brouwer Fixed-Point Theorem budget constraint budget set C.IV C.VII Chapter characterized coalition compact competitive equilibrium consumption plans consumption set contingent commodity continuous function convergent convex set convex valued core allocation Debreu defined demand and supply demand behavior denoted Edgeworth box elements endowment equilibrium allocation example excess demand function finite firms and households fixed point futures markets Hence income indifference curves inputs j e F Kakutani Fixed-Point Theorem labeled large economy Lemma lower hemicontinuous market date mathematical maximization opportunity set optimizing output oysters Pareto efficient point-valued preferences price adjustment price vector production plans production technology profits proof real numbers represents result Robinson Crusoe sequence simplex Sj(p Sperner's Lemma strict convexity subset supply and demand technology set unbounded upper hemicontinuous utility function Walrasian auctioneer Welfare Economics Zk(p

### Popular passages

Page 245 - ... (1896-7), Cours d'Economique politique, Lausanne. Samuelson, PA (1947), Foundations of Economic Analysis, Cambridge, Mass. Shubik, M. (1959), Game Theory, Cambridge, Mass. Smith, A. (1976 [1776]), Wealth of Nations, Oxford. Walras, M. (1954 [1874]), Elements of Pure Economics, trans. W. Jaffe, London. Weintraub, ER (1983), 'On the existence of competitive equilibrium: 1930-1954', Journal of Economic Literature, 21.