# ECON100A_3 - MarginalUtility u x y MU(x,y)= x x How much...

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1/4/2008 1 Marginal Utility MU x (x,y)= : How much utility you get from one more unit of x. Depends on x,y and utility function MU y (x,y)= Example: U(x,y)=x 2 +y . MU x (1,2)= : A. 1 B. 2 C. 4 x y x u ) , ( y y x u ) , (

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1/4/2008 2 Diminishing Marginal Utility Utility function exhibits diminishing marginal utility for good x if and only if x ↑→ MU x (x,y) Example: U(x,y)=xy . MU x (x,y)=y Does this exhibit diminishing marginal utility for good x? A. Yes B. No C. Can’t tell
1/4/2008 3 MRS and Marginal Utility MU x (x,y)= : How much utility you get form one more unit of x. Depends on x,y and utility function MRS(x,y)= If you gave up a unit of x, how much y you would need to be has happy as before Relationship: x y x u ) , ( u u dx dy = y) (x, mu y) (x, mu y) MRS(x, y x - =

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1/4/2008 4 Proof Recall MRS is slope of indif curve at (x,y) In the limit Slope of indif curve is negative, but we usually take MRS as abs value of slope. (Usually drop negative sign). X Y x mu y mu u x y + = x mu y mu x y + = 0 x mu y mu x y - = y x u u mu mu x y = - = y) (x, mu y) (x, mu y) MRS(x, y x - =
1/4/2008 5 Another way to do it Say mu x =3, mu y =4. You lose a unit of x, how much utility do you lose? mu x (You lose 3 utils) How much y do you need get one more util? 1/mu y (you need ¼ of a unit of y to get 1 util) How many units of y does it take to get back 3 utils? (This is the MRS) mu x (1/mu y )=3 (¼) =3/4 4 / 3 ) ( y) (x, mu y) (x, mu y) MRS(x, y x - = - =

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1/4/2008 6 Utility and Hypothesis of Diminishing  MRS Recall definition: The more X you have (and the less Y) the less you need to be compensated for giving up one unit of X. (Indif curves get flatter as you down them.) NOT THE SAME THING AS DIMINISHING MARGINAL UTILITY!
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