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**Utilities Indifference curves**

Chapter 3 Utilities Indifference curves

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Budget line Good 2 150 50 100 Good 1 150 100 50 Points on the budget line indicate all the bundles of goods that the consumer can afford.

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Indifference Curve Indifference curve: locus of bundles that provide the consumer with the same level of satisfaction

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**Indifference curves Good 2 (x 2) w a 20 b 140 100 Good 1 (x 1) 10**

10 Points on the same indifference curve represent bundles yielding the same amount of utility.

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**Indifference Curves Indifference map**

Set of indifference curves for a consumer Every bundle On an indifference curve Indifference curves Farther from origin ->Higher utility

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**The Shape of Indifference Curves**

Cannot slope upward Nonsatiation assumption Cannot cross each other Transitivity and nonsatiation assumptions Farther from the origin – higher utility Are bowed in toward the origin Convexity assumption Farther from the origin - higher utility

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**Indifference curves cannot slope upward**

Good 2 (x 2) E B x a y D C Good 1 (x 1) If an indifference curve ran from a to x, then bundle x would be no better than bundle a despite containing more of both goods. This upward slope of the indifference curve would be a violation of the nonsatiation assumption.

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**Indifference curves cannot cross each other**

Good 2 (x 2) I2 I1 a b c Good 1 (x 1) If indifference curves I1 and I2 crossed at a, then by transitivity of preferences bundle b would be no better than bundle c despite containing more of both goods. This crossing of indifference curves would be a violation of the nonsatiation assumption

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**Farther from the origin -> higher utility**

Good 2 (x 2) Bundle w must be preferred to bundle a because it contains more of both goods w a Good 1 (x 1)

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**Bowed-in (a) (b) Good 2 (x 2) Good 2 (x 2) a a c c b b Good 1 (x 1)**

Good 1 (x 1) (a) Bowed-out indifference curves violate convexity of preferences. Bundle c is a weighted average of bundles a and b, but yields lower utility level because it is on an indifference curve that is closer to the origin. (b) Bowed-in indifference curves satisfy the convexity of preferences. Bundle c, a weighted average of bundles a and b, yields a higher utility level

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**The Marginal Rate of Substitution**

Marginal rate of substitution (MRS) Particular point on indifference map One consumer Ratio of exchanging goods Same utility MRS = - ∆x2 / ∆x1

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**The Marginal Rate of Substitution**

Diminishing marginal rate of substitution From convexity Move along the indifference curve Same utility level MRS decreases

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**Convex preferences and the MRS**

Good 2 (x 2) 10 9 60 100 a I1 +∆x2 -∆x1 b -∆x1 +∆x2 c d Good 1 (x 1) 10 20 100 110 As the consumer is given bundles containing more and more of good 2, she values an individual unit of good 2 less and less

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**Indifference Curves and Tastes**

Flat indifference curves Goods that yield no utility Straight-line indifference curves Goods that are perfect substitutes MRS - constant along an indifference curve In a two-good world Indifference curve - straight line

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**(a) (b) Good 2 (x 2) Good 2 (x 2) 9 5 4 10 +∆x2 a -∆x1 +∆x2 -∆x1**

Good 1 (x 1) 3 8 11 (a) Flat indifference curves. The good measured on the horizontal axis is yielding no utility for the consumer. (b) Straight-line indifference curves: perfect substitutes. The same amount of good 2 is always needed to compensate the consumer for the loss of one unit of good 1.

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**Indifference Curves and Tastes**

Right-angle indifference curves Goods that are perfect complements Must be consumed in a fixed ratio to produce utility In a two-good world Right angle indifference curves Bowed-out indifference curves Nonconvex preferences

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**(c) (d) Good 2 (x 2) 10 11 Good 2 (x 2) +∆x2 +∆x2 -∆x1 b +∆x2 -∆x1 b a**

I1 -∆x1 a Good 1 (x 1) 5 6 Good 1 (x 1) (c) Right-angle indifference curves: perfect complements. Adding any amount of only one good to bundle a yields no additional utility. (d) Bowed-out indifference curves: nonconvex preferences and the MRS. As the consumer is given bundles containing more and more of good 2, he values an individual unit of good 2 more and more.

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**Perfect substitutes Pepsi Coke**

Mary’s marginal rate of substitution is constant at any bundle of Pepsi and Coke.

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**Optimal Consumption Bundle**

Maximize consumer’s utility Within the economically feasible set Best bundle According to consumer’s preferences Characteristics of optimal bundles Indifference curve tangent to budget line Slope of indifference curve = MRS = -∆x2/∆x1 Slope of budget line = price ratio = p1/p2 MRS = p1/p2

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**The optimal consumption bundle**

Good 2 (x 2) B B’ +1 x -4 -3 z e k +1 n m F Good 1 (x 1) At the optimal point e, the indifference curve is tangent to the boundary BB’ of the economically feasible consumption set.

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