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Lecture 2

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Department
Economics
Course
ECO3145
Professor
Leslie Shiell
Semester
Fall

Description
ECO 3145 Mathematical Economics I Lecture 2 Static Optimization Unconstrained1Chiang ch 9194 111116I Univariate functions1 stationary point definition a pointsuch thatx0xf diagram2 optimumdefinition a pointsuch that the function is at a maximum or a minimum x note every optimum is a stationary point but not every stationary point is an optimum3 necessary vs sufficient conditions see Chiang pp8283 pp8889 example stationarity is a necessary condition for an optimum but not sufficient notationconsider the statementis an optimum is a stationary point xx the arrow is read only if or implies and indicates that the righthand side is necessary for the lefthand side to be trueis the statement true or falsenow consideris an optimum is a stationary point xx the reverse arrow is read if or is implied by and indicates that the righthand side is sufficient for the lefthand side to be trueis the statement true or falsenow consideris an optimum is a stationary point xx the double arrow is read if and only if and indicates that the righthand side is both necessary and sufficient for the lefthand side to be trueis the statement true or false exercisesConsider the following two statements iand iiachieves an 0xfxfoptimum atIs statement i a necessary or sufficient condition for statement ii xor both Arrange statements i and ii using the appropriate arrows to show the correct relationship ie or Chiang pp8788 p92 12 1th Page references are given as follows pXX pZZ The first reference is to the 4 edition and the second reference rdsmall font is to the 3 edition 31452doc Shiell 1
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