ch3 and 4_Econ 281_Fall 20100

ch3 and 4_Econ 281_Fall 20100 - Utility Utility is the...

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Utility Utility is the total benefit that a person gets from the consumption of a good or service. Utility increases as the quantity consumed of a good increases. (The more, the better) Let’s start with the case in which you derive satisfaction by the consumption of only one good.

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Our Assumption: Utility is increasing in quantity The more, The better U T I L I T Y QUANTITY
MU is the change in total utility that results from a one-unit increase in the quantity of a good consumed. Quantity Total Utility (U) Marginal Utility (MU) 0 0 -- 1 15 15 2 27 12 3 36 9 4 42 6 5 47 5 6 51 4

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The Principle of diminishing marginal utility is the general tendency for marginal utility to decrease as the quantity of a good consumed increases. The Diminishing marginal utility principle just says that U increases at a decreasing rate. Why? U strongly rises for the first units of the good but it increases less and less as more units are consumed
Utility with two goods Example, U(x,y) = (xy) 0.5 Good x is Food and good y is Clothing. Consider basket A= (2 units of food and 8 units of clothing). Write it in this way (x first, y second) and it is A= (2,8). The utility of basket A is U(A) =U(2,8)= (2*8) 0.5 =(16) 0.5 =4 Also: If B=(4,4) and C=(8,2) then U(A)=U(B)=U(C)=(xy) 0.5 =4

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IMPORTANT: An indifference curve is the set of baskets that entail the same total utility level (eg :A, B and C stay on the indifference curve for which U=4) When U(A)=U(B)=U(C ) we say that the consumer is indifferent between the baskets A B and C
The indifference curves of   U = (xy)  0.5     for U=2,4,6,8  in a two dimensional graph   are below

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Graph of U(x,y) = (xy) 0.5
Hence, when both MUx and MUy are positive, then the slope of the indifference curve is negative Let MUx>0 and MUy >0 How are the Indifference curve shaped in a two- dimensional graph?

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Useful Utilities Perfect substitutes Perfect complements Cobb-Douglas Quasi linear utility function
Perfect Substitutes U= ax+by where a and b are positive constants Indifference curves, equation: U= ax+by, that is y=-(a/b) *x+U/b Indifference curves, Slope –(a/b) Example in figure: U= P+2W (P= pancackes and W =Waffels) An indifference curve equation is: W= -P/2+U/2 (Slope –1/2)

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Perfect Complements U= min{ ax, by} where a and b are positive constants Indifference curves: L shaped, the kinks stay on the line y=(a/b)x Example in figure: shoes U= min {left shoes, right shoes} The kinks stay on the line y=x
Cobb-Douglas U= A X a Y b with A, a and b positive constants . Indifference curve: is an hyperbola Indifference curve equation: Y=(U/A) 1/b * X -a/b Example in figure: food and clothing for a=b=0.5 and A=1 U= (xy) 0.5 Indifference curves: Y=U 2 / X

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Quasi-linear Utility function U=v(x)+by where b is a positive number and v(x) is increasing in x The indifference curves are North shifts of the curve v(x)

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Marginal rate of substitution (MRS xy) While holding the level of utility constant MRS xy= number of units of y you are willing to forgo to get an
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ch3 and 4_Econ 281_Fall 20100 - Utility Utility is the...

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