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Unformatted text preview: f the Walrasian Production economy will automatically satisfy the three optimal conditions required by the Pareto optimal production economy (namely, exchange efficiency, production efficiency, and overall efficiency) as follows: MRSA = MRSB = PX PY MRTSX = MRTSY = r w (exchange efficiency) (production efficiency) For overall efficiency, the proof hinges on the following property: under perfect competition, zero profit conditions allow the ratio of output prices to be expressed as a ratio of marginal costs. By definition, this ratio of marginal costs is nothing more than the marginal rate of transformation. MRS = PX PY = rkX + wlX rkY + wlY (consumer equilibrium) (zero profit condition) 201 = MCX MCY MRS = MRT (ratio of marginal costs) (overall efficiency) In summary, we have the following First Fundamental Theorem of Welfare Economics for a production economy: If the general equilibrium conditions of the Walrasian Production Economy are satisfied then the optimal conditions of the Pareto Optimal Production Economy are also satisfied. In general, we can say that under perfect competition general equilibrium implies Pareto optimality. [General Equilibrium]
Perfect Competition => [Pareto Optimality] Note the critical role of the requirement of perfect competition in this statement of the theorem. THE SECOND FUNDAMENTAL THEOREM The Second Fundamental Theorem of Welfare Economics provides a second link which runs from Pareto Optimal Theory back to Walrasian General Equilibrium Theory. The key question of the Second Fundamental Theorem of Welfare Economics is: Given a specific Pareto Optimal allocation, is there a set of prices which makes that particular Pareto Optimal allocation a general equilibrium (competitive equilibrium) solution? Wait just a minute! Why does this matter to anyone?!? We are interested in the Second Fundamental Theorem of Welfare Economics because once we have established it, it implies the following important feature of a market economy: It is possible to use the market pricing mechanism to achieve a given Pa...
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This note was uploaded on 05/25/2010 for the course ECON 301 taught by Professor Sning during the Spring '10 term at University of Warsaw.
- Spring '10