Section-2-Utility-Possibilities-Frontier-slides

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Unformatted text preview: The Utility Possibilities Frontier Todd Sarver Northwestern University Econ 310-2 Fall 2011 Todd Sarver (Northwestern University) The UPF Econ 310-2 Fall 2011 1 / 28 Refresher: Notation Todd Sarver (Northwestern University) The UPF Econ 310-2 Fall 2011 2 / 28 Notation The symbol (called Sigma ) denotes a summation. Example: If there are 35 units of good x to be divide between 6 individuals, the feasibility constraint can be written as either x 1 + x 2 + x 3 + x 4 + x 5 + x 6 35 or 6 i =1 x i 35 . Todd Sarver (Northwestern University) The UPF Econ 310-2 Fall 2011 3 / 28 Notation The symbol (called Sigma ) denotes a summation. Example: If there are 35 units of good x to be divide between 6 individuals, the feasibility constraint can be written as either x 1 + x 2 + x 3 + x 4 + x 5 + x 6 35 or 6 i =1 x i 35 . The symbol Q (called Pi ) denotes a product. Example: Q n i =1 x i = x 1 x 2 x n Todd Sarver (Northwestern University) The UPF Econ 310-2 Fall 2011 3 / 28 Notation The symbol (called Sigma ) denotes a summation. Example: If there are 35 units of good x to be divide between 6 individuals, the feasibility constraint can be written as either x 1 + x 2 + x 3 + x 4 + x 5 + x 6 35 or 6 i =1 x i 35 . The symbol Q (called Pi ) denotes a product. Example: Q n i =1 x i = x 1 x 2 x n The notation [ a,b ] denotes an interval : the set of all numbers between a and b . Example: The interval [1 , 3] contains all points between 1 and 3, not just 1, 2, 3. For instance, 1 . 5 , 4 3 , and 2 are all in this interval. Todd Sarver (Northwestern University) The UPF Econ 310-2 Fall 2011 3 / 28 Notation The notation ( x 1 ,...,x n ) denotes a vector . The term x i is called the i th coordinate of this vector. Todd Sarver (Northwestern University) The UPF Econ 310-2 Fall 2011 4 / 28 Notation The notation ( x 1 ,...,x n ) denotes a vector . The term x i is called the i th coordinate of this vector. The notation means implies . For two statements a and b , a b means a implies b . That is, any time a is true, so is b . Example: x > 5 x 2 > 25 . Todd Sarver (Northwestern University) The UPF Econ 310-2 Fall 2011 4 / 28 Notation The notation ( x 1 ,...,x n ) denotes a vector . The term x i is called the i th coordinate of this vector. The notation means implies . For two statements a and b , a b means a implies b . That is, any time a is true, so is b . Example: x > 5 x 2 > 25 . The notation means if and only if . For two statements a and b , a b means a is true exactly when b is. That is, both a b and b a . Example: x 2 > 25 ; x > 5 since (- 6) 2 > 25 , and therefore x > 5 < x 2 > 25 . However, x > 5 x 3 > 125 ....
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This note was uploaded on 01/03/2012 for the course ECON 310-2 taught by Professor Sarver during the Spring '08 term at Northwestern.

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Section-2-Utility-Possibilities-Frontier-slides - The...

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