Lecture-1-Pricing-Concepts-class (1)

Lecture-1-Pricing-Concepts-class (1) - Lecture 1 Optimal...

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Lecture 1: Optimal Pricing for Monopoly with Multiple 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 maximization. Needed assumptions are completeness, reflexivity and transitivity.
Composite Commodity Theory Suggestion: Say that we only solved this optimization 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 maximization. Needed assumptions are completeness, reflexivity and transitivity.

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Composite Commodity Theory Suggestion: Say that we only solved this optimization 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 solution functions for all of the parameters… 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 maximization. Needed assumptions are completeness, reflexivity and transitivity.
Composite Commodity Theory Suggestion: Say that we only solved this optimization 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 solution functions for all of the parameters… NOTE : I now is ; we’re netting 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 maximization. Needed assumptions are completeness, reflexivity and transitivity.

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Composite Commodity Theory Idea: with these “solution functions” for the goods we don’t care about, lets plug them back in to the original utility function… This reduces the problem to a function of a bunch of parameters (e.g., m and b ) rather than variables (e.g., y and x ). This is useful; parameters aren’t complicated but variables are!
Composite Commodity Theory Idea: with these “solution functions” for the goods we don’t care about, lets plug them back in to the original utility function… This reduces the problem to a function of a bunch of parameters (e.g., m and b ) rather than variables (e.g., y and x ). This is useful; parameters aren’t complicated but variables are!

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