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General equilibrium handout

General equilibrium handout - Individual i ’s cardinal...

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Perfect Competition, General Equilibrium, and Social Welfare Handout Assumptions of perfect competition: 1. Many buyers and sellers 2. Homogeneous output 3. No external effects 4. Perfect information 5. Individuals act in their own best interest If an assumption of perfect competition is violated, we say there is a market failure (or market friction ). ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Partial equilibrium: The equilibrium of supply and demand in a single market. General equilibrium: The equilibrium of supply and demand in all markets simultaneously. 1 st Fundamental Theorem of Welfare Economics : Under the assumptions of perfect competition, the general equilibrium is Pareto efficient. 2 nd Fundamental Theorem of Welfare Economics : Under certain conditions including perfect competition, every Pareto efficient allocation can be achieved as the general equilibrium by an appropriate lump sum redistribution of the initial endowment. ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐
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Unformatted text preview: Individual i ’s cardinal utility function , u i ( x ), says how well ‐ off (in meaningful units) individual i ’s is from getting consumption bundle x . Note : An individual’s preferences can be represented by an ordinal utility function. Hence only an ordinal (not a cardinal) utility function can be inferred by observing an individual’s behavior. Analyzing cardinal utility requires additional, untestable (philosophical) assumptions. A social preference is a preference ranking over individuals’ (cardinal) utilities. A social welfare function , W , is a utility function over individuals’ (cardinal) utilities. Examples of social welfare functions: Rawlsian (minimax): W ( u 1 , u 2 ) = min{ u 1 , u 2 } Utilitarian : W ( u 1 , u 2 ) = u 1 + u 2 Cobb ‐ Douglas : W ( u 1 , u 2 ) = u 1 a u 2 b , where 0< a,b <1 Social welfare functions allow us to decide which Pareto efficient allocation is the “best” one....
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