1. Utilities Indifference curves
Chapter 3
Utilities
Indifference curves

2. 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.

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) w a 20 b 140 100 Good 1 (x 1) 1010
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
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

7. 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.

8. 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

9. 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)

10. 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

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) 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

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. (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.

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. (c) (d) Good 2 (x 2) 10 11 Good 2 (x 2) +∆x2 +∆x2 -∆x1 b +∆x2 -∆x1 b aI1
-∆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.

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

19. 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 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.