Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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4. Demonstrate that if the markets for two commodities are in equilibrium, the third market must also be in equilibrium.
![1. Consider a 3-consumer, 3-commodity exchange economy. Index the consumers as a, b, c and
commodities as 1,2,3. Use the letter e to indicate endowments, x to indicate commodities, and
p to indicate prices. Also use superscript for commodities and subscripts for consumers. For
example, the endowment of commodity 1 held by consumer a should be denoted as ea.
NOTE: DO NOT USE THE SIGN. USE THE NORMAL "+" SIGN FOR ADDITONS. You have to
write out the elements of each vector in your equation using the appropriate notation as
described above. For example, if x is a (3 × 1) vector and if its elements are denoted as
X1, X2, X3, you should write
[x₁
x2
[X3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe333b570-3dc5-4bee-bced-cf379c81a351%2F6de1604a-1b3d-4e2f-ad45-3ca22d381bc6%2Fbk2fw5j_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consider a 3-consumer, 3-commodity exchange economy. Index the consumers as a, b, c and
commodities as 1,2,3. Use the letter e to indicate endowments, x to indicate commodities, and
p to indicate prices. Also use superscript for commodities and subscripts for consumers. For
example, the endowment of commodity 1 held by consumer a should be denoted as ea.
NOTE: DO NOT USE THE SIGN. USE THE NORMAL "+" SIGN FOR ADDITONS. You have to
write out the elements of each vector in your equation using the appropriate notation as
described above. For example, if x is a (3 × 1) vector and if its elements are denoted as
X1, X2, X3, you should write
[x₁
x2
[X3
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