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ECON10A_3 (1)

# ECON10A_3 (1) - Review 1 u x y MUx(x,y)= x How much utility...

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1/4/2008 1 Review

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1/4/2008 2 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 - =
1/4/2008 3 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 - =

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1/4/2008 4 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 - = - =
1/4/2008 5 Marginal Rate of Substitution Informal Definition: If you gave up one unit of good x how many units of good y would you need to stay just as happy as you were before. This is the slope of the Indif Curve tangent at (X,Y)! X Y

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1/4/2008 6 “Informal” vs. “formal” definition of MRS Formal: MRS is slope of tangent to indif curve at (x,y) MRS(x,y)= Informal: If I gave up one unit of good x how many units of good y would I need to stay just as happy as I was before These are slightly different! Which is right? Right way to say it: If you take away a small amount of good x from me, how many times as much good y would you have to give me to make me as happy as I was before? Find the limit of this ratio as the amount of good 1 you take away approaches zero. Informal def captures the intuition and we will use it. Same for marginal utility. (Now forget this slide) X Y y x u u mu mu x y = - =
1/4/2008 7 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! Test for diminishing MRS Does x↑y↓ imply MRS ↓ Test for diminishing mu x Does x↑ imply mu X Test for diminishing mu y Does y↑ imply mu y X Y

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1/4/2008 8 3 IMPORTANT UTILITY  FUNCTIONS Linear: U(x 1 ,x 2 )=ax 1 +bx 2 Cobb-Douglass: U(x 1 ,x 2 )=ax 1 α x 2 β Leontief: U(x 1 ,x 2 )=min[x 1 /a, x 2 /b]
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ECON10A_3 (1) - Review 1 u x y MUx(x,y)= x How much utility...

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