PRACTICING YOUR PROOFS ax P We 1. Define the cross price elasticity of good i with respect to the price of good j as E₁ = друх use the cross-price elasticity to determine if goods are complements (E <0) or substitutes (E,>0). Using this definition and the budget constraint, prove the existence of Cournot's Aggregation Condition, which states that -0,Σ₁₁E, where 6, is the budget share of good j, as defined in class. (Hint: Think of a world with only two goods, so that i=1,2. It'll make your life easier. Start by taking the derivative of the budget constraint with respect to the price of good 2. If it's easier for you to avoid the subscripts and have the two goods be X and Y, pretend Y is the second good.)
PRACTICING YOUR PROOFS ax P We 1. Define the cross price elasticity of good i with respect to the price of good j as E₁ = друх use the cross-price elasticity to determine if goods are complements (E <0) or substitutes (E,>0). Using this definition and the budget constraint, prove the existence of Cournot's Aggregation Condition, which states that -0,Σ₁₁E, where 6, is the budget share of good j, as defined in class. (Hint: Think of a world with only two goods, so that i=1,2. It'll make your life easier. Start by taking the derivative of the budget constraint with respect to the price of good 2. If it's easier for you to avoid the subscripts and have the two goods be X and Y, pretend Y is the second good.)
Chapter5: Income And Substitution Effects
Section: Chapter Questions
Problem 5.12P
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Transcribed Image Text:PRACTICING YOUR PROOFS
ax P We
1. Define the cross price elasticity of good i with respect to the price of good j as E₁ = друх
use the cross-price elasticity to determine if goods are complements (E <0) or substitutes (E,>0).
Using this definition and the budget constraint, prove the existence of Cournot's Aggregation
Condition, which states that -0,Σ₁₁E, where 6, is the budget share of good j, as defined in
class.
(Hint: Think of a world with only two goods, so that i=1,2. It'll make your life easier. Start by
taking the derivative of the budget constraint with respect to the price of good 2. If it's easier for
you to avoid the subscripts and have the two goods be X and Y, pretend Y is the second good.)
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