Final Exam - Definitions, Theorems, Proofs
• Theory of the consumer
– Axioms: Completeness, ...
– Walras’ law
– Transformation property of utility functions + proof.
– UMP vs. EMP
– Slutsky equation, Shepard’s lemma, Roy’s identity with proof.
• Production:
– Definition and properties of a production possibility set. I assume that everybody also knows
the concept of a production function. (in particular properties 1-11 of production possibility
sets).
– Definitions of profit maximization problem and profit function
– Hotelling’s lemma + proof by means of the envelope theorem
– Law of supply + proof.
• Decisions under uncertainty:
– Definitions of different kinds of lotteries.
– Lotteries and the simplex.
– Von Neumann Morgenstern Axioms
– Von Neumann Morgenstern utility representation
– Transformation property of expected utility functions plus proof
– Properties of indifference curves
– Definition of risk aversion, equivalent definitions;
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• General Equilibrium
– Edgeworth box and examples (in particular you have to know what is a competitive equilibrium
in the Edgeworth box, what is the Pareto set and the contract curve, does equilibrium exist, is
it unique, the impacts of non-convexities).
– You should be able to discuss aspects and implications of the first and the second fundamental
theorem of welfare economics in the Edgeworth box.
– One Firm one consumer economy
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