Ami Pro - LN012110

# Ami Pro - LN012110 - UCSD Economics 113 Mr. T. Kravitz...

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Lecture Notes, January 21, 2010, and following Convexity A set of points S in is said to be convex if the line segment between any two points R N of the set is completely included in the set. S is convex if x, y S, implies . z z   x   1   y ,0    1   S S is said to be strictly convex if x, , implies y S , x y    1 . x   1  y interior S The notion of convexity is that a set is convex if it is connected, has no holes on the inside and no indentations on the boundary. A set is strictly convex if it is convex and has a continuous strict curvature (no flat segments) on the boundary. Economically, this notion corresponds to "diminishing marginal utility" "diminishing marginal rate of substitution" "diminishing marginal product" . Properties of Convex Sets Let be convex subsets of R N . Then: C 1 , C 2 is convex, C 1 C 2 is convex, C 1 C 2 is convex C 1 The Market, Commodities and Prices N commodities x = (x 1 , x 2 , x 3 , . .., x N ) R N , a commodity bundle The market takes place at a single instant, prior to the rest of economic activity. commodity = good or service completely specified description location date (of delivery) Price system : . p i 0 for all i = 1, . .., N. p   p 1 , p 2 ,..., p N   0 Value of a bundle x R N at prices p is p x.

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## This note was uploaded on 09/30/2011 for the course ECON 113 taught by Professor Starr,r during the Fall '08 term at UCSD.

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Ami Pro - LN012110 - UCSD Economics 113 Mr. T. Kravitz...

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