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Chapter 3

Chapter 3. Utilities Indifference curves . Budget line. Good 2. 150. 100. 50. Good 1. 0. 50. 100. 150. Points on the budget line indicate all the bundles of goods that the consumer can afford. Indifference Curve.

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Chapter 3

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  1. Chapter 3 Utilities Indifference curves

  2. Budget line Good 2 150 100 50 Good 1 0 50 100 150 Points on the budget line indicate all the bundles of goods that the consumer can afford.

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

  4. Indifference curves Good 2 (x 2) b w 20 140 a 100 Good 1 (x 1) 10 0 Points on the same indifference curve represent bundles yielding the same amount of utility.

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

  6. The Shape of Indifference Curves • Indifference curves • Cannot slope upward • Nonsatiation assumption • Cannot cross each other • Transitivity and nonsatiation assumptions • Farther from the origin – higher utility • Nonsatiation assumption • Cannot cross each other • Are bowed in toward the origin • Convexity assumption • Farther from the origin - higher utility

  7. Indifference curves cannot slope upward Good 2 (x 2) x y E B a D C Good 1 (x 1) 0 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.

  8. Indifference curves cannot cross each other Good 2 (x 2) b c I2 a I1 Good 1 (x 1) 0 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

  9. Farther from the origin -> higher utility Good 2 (x 2) w Bundle w must be preferred to bundle a because it contains more of both goods a Good 1 (x 1) 0

  10. Bowed-in (b) (a) Good 2 (x 2) Good 2 (x 2) c c b b a a 0 0 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

  11. 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

  12. The Marginal Rate of Substitution • Diminishing marginal rate of substitution • From convexity • Move along the indifference curve • Same utility level • MRS decreases

  13. Convex preferences and the MRS Good 2 (x 2) 100 +∆x2 -∆x1 60 c d a b -∆x1 +∆x2 10 9 I1 Good 1 (x 1) 0 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

  14. 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

  15. (b) (a) Good 2 (x 2) Good 2 (x 2) 10 9 5 a 4 -∆x1 -∆x1 +∆x2 0 3 8 11 Good 1 (x 1) 0 Good 1 (x 1) +∆x2 (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.

  16. 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

  17. (d) (c) Good 2 (x 2) Good 2 (x 2) +∆x2 +∆x2 -∆x1 +∆x2 -∆x1 11 I1 -∆x1 10 c b a b a 0 5 6 Good 1 (x 1) 0 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.

  18. Perfect substitutes Pepsi 0 Coke Mary’s marginal rate of substitution is constant at any bundle of Pepsi and Coke.

  19. Optimal Consumption Bundle • 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

  20. The optimal consumption bundle Good 2 (x 2) B +1 -3 -4 +1 k e m n x z F 0 Good 1 (x 1) B’ At the optimal point e, the indifference curve is tangent to the boundary BB’ of the economically feasible consumption set.

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