ECON487 lec1.pdf - Lecture 1 Op,mal Pricing for Monopoly with Mul,ple Goods Jacob LaRiviere 1 Composite Commodity Theory Assume there are n goods(e.g

# ECON487 lec1.pdf - Lecture 1 Op,mal Pricing for Monopoly...

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Lecture 1: Op,mal Pricing for Monopoly with Mul,ple Goods Jacob LaRiviere 1

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Composite Commodity Theory Assume there are n goods (e.g., apples, bananas, carrots, etc…) but we really only care about one of them (e.g., apples). How do we handle this problem as economists? Lets start with the very general consumer’s problem: constrained maximizaGon. Needed assumpGons are completeness, reﬂexivity and transiGvity.
Composite Commodity Theory SuggesGon: Say that we only solved this opGmizaGon problem for goods 2, …, n. Take the first good as a parameter [e.g., like ‘ m ’ in y(x)=mx+b ] Assume there are n goods (e.g., apples, bananas, carrots, etc…) but we really only care about one of them (e.g., apples). How do we handle this problem as economists? Lets start with the very general consumer’s problem: constrained maximizaGon. Needed assumpGons are completeness, reﬂexivity and transiGvity. max ↓࠵?↓ 1 , ࠵?↓ 2 ,…, ࠵?↓࠵? ࠵?(࠵?↓ 1 , ࠵?↓ 2 ,…, ࠵?↓࠵?) ࠵? . ࠵? . ࠵?↓ 1 ∙ ࠵?↓ 1 +…+ ࠵?↓࠵? ࠵?↓࠵?

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Composite Commodity Theory SuggesGon: Say that we only solved this opGmizaGon problem for goods 2, …, n. Take the first good as a parameter [e.g., like ‘ m ’ in y(x)=mx+b ] This leads to a bunch of soluGon funcGons for all of the variables… Assume there are n goods (e.g., apples, bananas, carrots, etc…) but we really only care about one of them (e.g., apples). How do we handle this problem as economists? Lets start with the very general consumer’s problem: constrained maximizaGon. Needed assumpGons are completeness, reﬂexivity and transiGvity. max ↓࠵?↓ 1 , ࠵?↓ 2 ,…, ࠵?↓࠵? ࠵?(࠵?↓ 1 , ࠵?↓ 2 ,…, ࠵?↓࠵?) ࠵? . ࠵? . ࠵?↓ 1 ∙ ࠵?↓ 1 +…+ ࠵?↓࠵? ࠵?↓࠵? max ࠵?↓ 2 ,…, ࠵?↓࠵? ࠵?(࠵?↓ 2 ,…, ࠵?↓࠵? ; ࠵?↓ 1 ) ࠵? . ࠵? . ࠵?↓ 2 ∙ ࠵?↓ 2 +…+ ࠵?↓࠵? ࠵?↓࠵? ࠵?
Composite Commodity Theory SuggesGon: Say that we only solved this opGmizaGon problem for goods 2, …, n. Take the first good as a parameter [e.g., like ‘ m ’ in y(x)=mx+b ] This leads to a bunch of soluGon funcGons for all of the variables… NOTE : I now is ࠵? ; we’re neSng out expenditures on goods 2, 3, …, n. Assume there are n goods (e.g., apples, bananas, carrots, etc…) but we really only care about one of them (e.g., apples). How do we handle this problem as economists? Lets start with the very general consumer’s problem: constrained maximizaGon. Needed assumpGons are completeness, reﬂexivity and transiGvity. max ↓࠵?↓ 1 , ࠵?↓ 2 ,…, ࠵?↓࠵? ࠵?(࠵?↓ 1 , ࠵?↓ 2 ,…, ࠵?↓࠵?) ࠵? . ࠵? . ࠵?↓ 1 ∙ ࠵?↓ 1 +…+ ࠵?↓࠵? ࠵?↓࠵? max ࠵?↓ 2 ,…, ࠵?↓࠵? ࠵?(࠵?↓ 2 ,…, ࠵?↓࠵? ; ࠵?↓ 1 ) ࠵? . ࠵? . ࠵?↓ 2 ∙ ࠵?↓ 2 +…+ ࠵?↓࠵? ࠵?↓࠵? ࠵?

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