e100_wntr2010__lec4_topost

e100_wntr2010__lec4_topost - Econ 100: Lecture 4 A peer...

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Econ 100: Lecture 4 • A peer tutor available for this course: see SmartSite for hours
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Marginal Rate of Substitution • MRS of X for Y: amount of good Y (vertical axis) consumer would require to give up one unit of good X (horizontal axis) • (or: amount of good Y consumer is willing to give up to obtain 1 extra unit of good X) • Slope of indifference curve is negative of MRS (assertion: will prove below)
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Deriving Slope of Indifference Curves Y U X U dX dY dY Y U dX X U dY Y U dX X U dU Y X U U 0 ) , (
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MRS=Ratio of MU(x), MU(y) Y Y X U X Y X U dX dY ) , ( ) , ( SLOPE of indifference curve (change in vertical direction/ change in horizontal direction) is equal to the ratio of marginal utilities
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What does convexity of i-curve mean for MRS? • Assumption that i-curves are convex is same as saying SLOPE falls (in absolute) value as we move down (southeast) an indifference curve • Diminishing slope is the same as assuming that MRS declines as quantity of good on horizontal axis increases
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Check whether MRS (of X for Y) is decreasing • U(X,Y) = 10X .5 Y
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Check whether MRS (of X for Y) is decreasing (as X increases) • U(X,Y) = 10X .5 Y • MU X = 5X -.5 Y • MU Y = 10X .5 • MRS= 5X -.5 Y/10X .5 = Y/2X
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Check whether MRS (of X for Y) is decreasing (as X increases & Y decreases) • MRS= Y/2X • As X increases &Y decreases, MRS declines, so this utility function is consistent with a diminishing marginal rate of substitution of X for Y
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Assuming diminishing MRS rules out: Y X U0 U1 U2
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e100_wntr2010__lec4_topost - Econ 100: Lecture 4 A peer...

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