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E lots of y and little x 6 f lots of x and little y 15

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Unformatted text preview: f indiff curve @[x,y] = M RS(i.e: tangent/[x,y] at point [x,y] => MUx/MUy 4. Convex Shape due to diminishing marginial utility 5.e -> lots of y and little x 6. f -> lots of x and little y 15 / 21 Indifference Curves Indifference Curve “Results” Indifference Curve: All {X , Y } combinations giving same utility level Northeast Rule any point on i1 better than any point on i2 ----------------------indiff curve for every [x,y] combination ----------------------cannot bend backwards ---------------------connot cross Gazzale (University of Toronto) ECO100: Consumer Choice I i1 i2 16 / 21 Indifference Curves Marginal Rate of Substitution: Summary Definition MRSX ,Y Given {X , Y , . . . , Z }, how many units of Y must you give me to exactly compensate me for taking away one unit of X ? We Can Show ￿ ￿ MRSX ,Y X , Y , . . . , Z = MUX MUY 2-Good Case With x on the horizontal and y on the vertical, the |slope| of the MUx indifference curve at {x , y } equals MRSx ,y (x , y ) = MUy Interpretation: Trades I am willing to make I am willing to give up |MRS | units of Y in order to get 1 more unit of X . Example Gazzale (University of Toronto) ECO100: Consumer Choice I 17 / 21 $1Bill MRS steep io $1 bills vs. $5 bills EX. Left and Right shoes Computer and keyboard MRS small/ ie flat ' Standard' indifference curve general willingness to substitute diminishing MRS io $5 Bill Perfect Substitues Constant M RS io Perfect complements inability to substitute M RS undefined at kink The Budget Constraint Now: What can I buy? A Consumer’s Two-Good Budget Constraint Goods X and Y with prices PX and PY Assume consumer spends all income, denoted I Consumption choice must satisfy PX X + PY Y = I More generally, saving/borrow as good “Z ” Gazzale (University of Toronto) ECO100: Consumer Choice I 18 / 21 The Budget Constraint Two-Good Budget Line (Constraint), Graphically I = 90, Px = 3; Py = 9 income Quantity Y Intercept!: buy only Y>90/9 = 10 buy only X>90/3 = 30 --------Slope of budget line abs(rise/run)= (income/py)/ (income/px) =px/py 25 UNAFFORDABLE 20 15 10 Budget line Spend all of your income 5 AFFORDABLE 5 Gazzale (University of Toronto) 10 15 20 ECO100: Consumer Choice I 25 30 Quantity X 19 / 21 The Budget Constraint Budget Line, Interpreted P Slope of the budget constraint (budget line): − PX Y Interpretation I: Trades I can make with the market I must give up |slope| units of Y (the vertical one) in order to get 1 more unit of X (the horizontal one). Our example: I must give up 1 units of Y (the $9 one) in order to 3 get 1 more unit X (the $3 one) Alternatively: I must give up more unit of Y . 1 |slope| = 3 units of X in order to get 1 Interpretation II: X ’s Opportunity Cost (in terms of Y ) Gazzale (University of Toronto) ECO100: Consumer Choice I 20 / 21 Optimal Choice Optimal Choice 1. Northeast Rule A -> Optimum Slope Budget line = MRS px/py = MUx/MUy MUx/px = MUy/py(i.e Last Dollar Rule) --------------------B cannot be optimum At B MRS = 3/2 != slope of BL = 1/3 MUx/MUy!=Px/Py => MUx/ Px > MUy/Py(need to spend m ore on x) Gazzale (University of Toronto) ECO100: Consumer Choice I 21 / 21...
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