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EC202: Worked Example #3.15

EC202: Worked Example #3.15. Frank Cowell April 2005. T his presentation covers exactly the material set out in the file WorkedExamples.pdf, but with the addition of a few graphics and comments To start the presentation select S lideshow V iew Show or click on icon below left.

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EC202: Worked Example #3.15

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  1. EC202: Worked Example #3.15 Frank Cowell April 2005 • This presentation covers exactly the material set out in the file WorkedExamples.pdf, but with the addition of a few graphics and comments • To start the presentation select Slideshow\View Show or click on icon below left. • Mouse click or [Enter] to advance through slide show

  2. WX3.15: problem

  3. WX3.15: approach • Step 1: model behaviour of each type as a price taker • Write down budget constraint for the unknown p • Set up Lagrangean for each type • Find the FOCs • Get demand functions from the FOCs • Step 2: get excess demand function for one of the goods • Use the demand functions for each type from step 1 • Other EDF follows by Walras’ law • Step 3: find equilibrium price(s) as root(s) of EDF

  4. WX3.15: type-a person • Lagrangean for a: • FOCs for interior maximum: • Rearrange and use the budget constraint: • Demand by a for good 2:

  5. WX3.15: type-b person • Lagrangean for b: • FOCs for interior maximum: • Rearrange and use the budget constraint: • Demand by b for good 2:

  6. WX3.15: excess demand • Demand by the two types for good 2: • So the excess demand function for good 2 is • Letting q:= 2R1/R2 excess demand is zero where

  7. WX3.15: how many equilibria? • Excess demand is zero where p2/3= pq  1 pq  1 p2/3 p p* • There is clearly only one equilibrium p*.

  8. WX3.15: the equilibrium • Given R1 = 5 R2 = 16 • So q := 2R1/R2 = 5/8 • Equilibrium price must satisfy p2/3= (5/8) p 1 • Clearly p = 1 is too low • Try p = 8 (which has an integer cube root) • LHS = 4; so does RHS

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