geneq - Applied General Equilibrium Analysis I. Partial...

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April 12, 2001 Applied General Equilibrium Analysis I. Partial versus General Equilibrium. A. Most of our policy analysis can be characterized as partial. For example, if we want to examine the effect of a price floor on an industry such as agriculture, we analyze: S(p 1 ,p 2 ,w 1 ,w 2 ) D(p 1 ,p 2 ,Y) Q 1 p 1 1. Assuming that S 1 (p 1 ,p 2 ,w 1 ,w 2 ) is the supply curve for good 1 as a function of the price of good 1, p 1 , given the price of good 2, p 2 , and the input prices w 1 and w 2 , and that D(p 1 ,p 2 ,Y) is the demand for good 1 as a function of the price of good 1, p 1 , given the price of good 2 and income, Y, we can analyze the impact of the price floor. This analysis is usually cloaked in ceterus paribus assumptions regarding other prices. 2. The only problem is that we know that other prices change as we remove the price floor.
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AEB 6184 Applied General Equilibrium Notes Professor Charles B. Moss April 12, 2001 2 Good 1 Good 2 The demand for good 2 shifts outward if good 1 and good 2 are substitutes (for the consumer the effect of the removal of the price floor is a price increase.) On the supply side, the decreased price of good 1 leads to an outward shift in supply for good 2 given that the production of good 1 and good 2 compete for limited resources. 3. This interaction is complicated as the first market reacts. Specifically, the increased price of good 2 leads to a leftward shift in the supply curve in the market for good 1 and an upward shift in the demand for good 1.
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AEB 6184 Applied General Equilibrium Notes Professor Charles B. Moss April 12, 2001 3 Good 1 Good 2 4. These interactions are further complicated by changes in the factor market. Specifically, if the industry represented a significant demand for the variable factor, the initial elimination of the price floor implies a decline in the value of the input. Hence, the overall demand for the input shifts to the left. B. Modeling the interaction between the two markets involves moving from a partial equilibrium analysis to a general equilibrium analysis. 1. Early work on general equilibrium analysis involves the concept of a Walrasian equilibrium. The primary idea of the Walrasian equilibrium was the concept that some price vector could be found for any endowment that equated the supply and demand, or resulted in zero excess demand: ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 0 0 , , - = - - = i i i i i i W p W p p w p S W p D p x x x a. ξ I (p) is the excess demand for good i, it is a function of the price vector. Demand is determined by the initial endowment of goods W. b. p i ( ξ i (p)-W i ) is the complementary slackness conditions. This condition implies that either the price of the i th good is zero, or its excess demand is zero. 2. Under the traditional formulation, Walrasian equilibria were hypothesized by tatonnement. Following the preceding discussion, we could iterate through the equilibrium until all the excess demand curves met the Walrasian conditions. Basically, economist simply assumed that the process would yield a viable solution.
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geneq - Applied General Equilibrium Analysis I. Partial...

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