1. Rational consumer choice
ECO61 Microeconomic Analysis
Udayan Roy
Fall 2008

2. Consumer Choice
We have seen how the consumer’s preferences are represented
And how the consumer’s budget constraint is represented
Now it’s time to bring preferences and constraints together to ask the consumer:
What’s your choice? How do you decide what to buy?

3. Example

4. Consumer Maximization: What’s the best affordable choice?
PZ = $1, PB = 2, M = 50
itos per semester r
, Bur 25 B c f e I 3 d a I2 I1 50 Z
, Pizzas per semester

5. Consumer Maximization: Interior Solution
Would Lisa be able to consume any bundle along I3 (i.e. bundle f)?
No! Lisa does not have enough income to afford any bundle along I3
Would Lisa be able to consume any bundle along I1?
Yes; she could afford bundles d, c, and a.
Nevertheless, there are other affordable bundles that should be preferred and affordable.
For instance bundle e
Bundle e is called a consumer’s optimum.
If Lisa is consuming this bundle, she has no incentive to change her behavior by substituting one good for another.
itos per semester r
, Bur 25 B c f 20 B e 10 I 3 d I2 A a I1 10 30 50 Z
, Pizzas per semester

6. Consumer Maximization: Interior Solution
The budget constraint and the indifference curve have the same slope at the point e where they touch.
Therefore, at point e:
itos per semester r
, Bur 25 B
Slope of indifference curve
Slope of budget line e I2 50 Z
, Pizzas per semester

7. An algebraic example
As was explained in chapter 2, the ≤ symbol can be replaced by the = symbol.

8. Ch. 2: Budget constraint algebra

9. Algebraic example (contd.)
So, our choice problem becomes
… which changes the choice problem to
As these two terms cancel out, there’s no harm placing them here.

10. Algebraic example (contd.)
But
Therefore, our choice problem becomes

11. Algebraic example (contd.)
Then the budget constraint implies

12. Algebraic example (Done!)
The choice problem
has the solution:

13. Consumer Maximization: Corner Solution
MRSZB ≤ PZ/PB. The consumer would like to buy even less pizza, were the amount of pizza not already zero.
itos per semester r e
, Bur 25 B I 3 I 2
Budget line I 1 50 Z
, Pizzas per semester

14. Optimal Bundles on Convex Sections of Indifference Curves

15. Food Stamps
Nearly 11% of U.S. households worry about having enough money to buy food and 3.3% report that they suffer from inadequate food.
Households that meet income, asset, and employment eligibility requirements receive coupons that can be used to purchase food from retail stores.
According to Microeconomics, fifth edition, by Jeffrey Perloff, the data here is from Hunger and food insecurity in the fifty states: by Ashley Sullivan and Eunyoung Choi, Center on Hunger and Poverty, Brandeis University, August 2002.

16. Food Stamps (cont).
The Food Stamps Program is one of the nation’s largest social welfare programs with expenditures of $33.1 billion for nearly 29.1 million people in 2006.
Would a switch to a comparable cash subsidy increase the well-being of food stamp recipients?
Would the recipients spend less on food and more on other goods?

17. Food Stamps Versus Cash: Cash Wins
Budget line under a cash grant M
+ 100 f C e M I 3
All other goods per month d I 2 I 1 B
Budget line with f
ood stamps A O r
iginal b
udget line
100 M M
+ 100 F
ood per month

18. Food Stamps Versus Cash: Both Win
Budget line under a cash grant M
+ 100 C
The best choice under both policies e M
All other goods per month d B A O r
iginal
Budget line with b
udget line
food stamps
100 M M
+ 100 F
ood per month

19. Gifts: cash or kind?
In the hit TV show Seinfeld, Elaine was once furious when Jerry gave her cash as a birthday gift
She was not objecting to the amount, which was $182
Does Jerry deserve such harsh treatment?

20. Figure 5.11: Effect of a Change in the Price of Soup on Consumption
5-20

21. The demand curve

22. Deriving an Individual’s Demand Curve
(a) Indif f
erence Cu r v
es and Budget Const r
aints
Deriving an Individual’s Demand Curve
ear
12.0 y
Initial optimal bundle of Beer and Wine
, Gallons per
Budget Line, L
Wine, (W) Pb M
W = - b e 1
2.8 PW PW L 1 ( pb
= $12) I 1
26.7
Beer (b), Gallons per year
Initial Values
Pb = price of beer = $12
PW = price of wine = $35
M = Income = $419.
(b) Demand Cu r v e
, $ per unit p b
12.0 E 1
26.7
Beer (b), Gallons per year

23. Deriving an Individual’s Demand Curve
(a) Indif f
erence Cu r v
es and Budget Const r
aints
Deriving an Individual’s Demand Curve
ear
12.0 y
, Gallons per
Budget Line, L
Wine, (W) e 2 Pb M
4.3 e
W = - b 1
2.8 PW 2 PW I L 1 ( p
= $12) I 1 L 2 ( p
= $6) b b
26.7
44.5
Beer (b), Gallons per year
New Values
Pb = price of beer = $6
PW = price of wine = $35
M = Income = $419.
(b) Demand Cu r v e
, $ per unit p b
12.0 E 1
Price of Beer goes down! E
6.0 2
26.7
44.5
Beer (b), Gallons per year

24. Deriving an Individual’s Demand Curve
(a) Indif f
erence Cu r v
es and Budget Const r
aints
Deriving an Individual’s Demand Curve
ear
12.0 y
, Gallons per
Budget Line, L
Wine, (W)
Price-consumption curve e 3
5.2 e 2 Pb Y
4.3 I 3
W = - b e 1
2.8 PW I 2 PW L 1 ( p
= $12) I 1 L 2 ( p
= $6) L 3 ( p
= $4) b b b
26.7
44.5
58.9
Beer (b), Gallons per year
New Values
Pb = price of beer = $4
PW = price of wine = $35
Y = Income = $419.
(b) Demand Cu r v e
, $ per unit p b
12.0 E 1
Price of Beer goes down again! E
6.0 2 E
4.0 3
D1, Demand for Beer
26.7
44.5
58.9
Beer (b), Gallons per year

25. Figure 5.17: Effect of a Change in Income on Consumption
5-25

26. Normal vs. Inferior Goods
If a good is normal, an increase in income raises the amount that is consumed
If a good is inferior, an increase in income decreases the amount that is consumed
Consumption of many goods falls as income rises because people shift toward higher-quality products that fill similar needs
Examples: replace posters with art reproductions, margarine with butter
5-26

27. Changes in income shift the demand curve: normal good case

28. Effects of a Price Change
substitution effect - the change in the quantity of a good that a consumer demands when the good’s price changes, holding other prices and the consumer’s utility constant.
income effect - the change in the quantity of a good a consumer demands because of a change in income, holding prices constant.

29. Substitution and Income Effects with Normal Goods
Initial Values
PD = price of DVDs = $20
PC = price of CDs = $15
M = Income = $300.
ear y
, Units per s VD D
vie o M C
D = M PD -
Budget Line, L1 PC D, 15 L1 C
D =
$300
$20 -
$15 e1 I1 12 20 C
, Music CDs Units per y
ear

30. Substitution and Income Effects with Normal Goods
Initial Values
PD = price of DVDs = $20
PC = price of CDs = $15
M = Income = $300.
ear y
Budget Line, L
, Units per M PC C s VD
D = - D PD PD
vie o M D,
$300
$15
$30 15
D = - C L1
$20
$20 L2 e2 e1 I1
PC goes up… I2 6 12 20 C
, Music CDs Units per y
ear
Total effect = -6

31. Substitution and Income Effects with Normal Goods
Initial Values
PD = price of DVDs = $20
PC = price of CDs = $15
M = Income = $300.
Initial Values
PD = price of DVDs = $20
PC = price of CDs = $15
M = Income = $300.
ear y L*
, Units per
$20 C
D = M PD -
Budget Line, L2 PC
$300
$30 s VD D
vie o M D, 15 L1 L2
What if we compensated Laura so she could afford the same utility she had before the price of CDs increased?
In other words, how much income she would need to afford indifference curve I1, with the new price of CDs ($30) e* e2 e1 I1 I2 6 9 12 20 C
, Music CDs Units per y
ear
Income effect = -3
Substitution effect = -3
Total effect = -6
= Substitution Effect + Income Effect = -3 + (-3)

32. Giffen Good
When the price of movie tickets decreases the budget constraint rotates out…
ear y L 2
ets per ck L 1 e 2 Ti
etball, k
Bas I 2
allowing the consumer to increase her utility. e 1 I 1
Total effect M o
vie s , Ti ck
ets per y
ear
Nevertheless, the total effect is negative. WHY?

33. Giffen Good Even though the substitution effect is positive….
…the income effect is larger and negative (since this is an inferior good).
ear y L 2
ets per ck L 1 e 2 Ti
etball, k
Bas I 2 L * e 1 e * I 1
Total effect
Substitution ef f
ect M o
vie s , Ti ck
ets per y
ear
Income ef f
ect

34. Labor-Leisure Choice Leisure - all time spent not working.
The number of hours worked per day, H, equals 24 minus the hours of leisure or nonwork, N, in a day:
H = 24 − N.
The price of leisure is forgone earnings.
The higher your wage, the more an hour of leisure costs you.

35. Labor-Leisure Choice: Example
Jackie spends her total income, M, on good Y.
The price of good Y is $1 per unit.
Her utility, U, depends on how many goods and how much leisure she consumes:
U = U(Y, N).
Jackie’s earned income equal:
wH.
And her total income, M, is her earned income plus her unearned income, M*:
Y = wH + M*.

36. Demand for Leisure Budget Line, L1 Y = w1H Y = w1(24 − N).
(a) Indif f
erence Cu r v
es and Const r
aints a y
Time const r
aint
, Goods per d Y I 1
Budget Line, L1
Y = w1H
Y = w1(24 − N). L 1 – w 1 1 e 1 Y 1 N1
= 16 24 N
, Leisure hours per day 24 H 1
= 8 H,
Work hours per day
(b) Demand Curve
Each extra hour of leisure she consumes costs her w1 goods. w , W
age per hour w 1 E1 N1
= 16
N, Leisure hours per day H 1
= 8
H, Work hours per day

37. Demand for Leisure Budget Line, L1 Budget Line, L2 Y = w1H
(a) Indif f
erence Cu r v
es and Const r
aints a y I 2
Time const r
aint L 2
, Goods per d – w 2 Y I 1 1 e 2 Y 2
Budget Line, L1
Y = w1H
Y = w1(24 − N). L 1 – w 1 1 e 1 Y 1 N 2
= 12 N1
= 16 24 N
, Leisure hours per day 24 H 2
= 12 H 1
= 8 H,
Work hours per day
(b) Demand Curve
Budget Line, L2 w , W
age per hour
Y = w2H
Y = w2(24 − N).
w2 > w1 E w 2 2 w 1 E1
Demand for leisure N 2
= 12 N1
= 16
N, Leisure hours per day H 2
= 12 H 1
= 8
H, Work hours per day

38. Supply Curve of Labor

39. Income and Substitution Effects of a Wage Changey a I 2
Time const r
aint L 2
, Goods per d
Since income effect is positive, leisure is a normal good. I 1 Y L * e e * 2 L 1 e 1 N * N N 24 N
, Leisure hours per d a y 1 2 24 H * H H H , W o r
k hours per d a y 1 2
Substitution effect
Total effect
Income effect

40. Labor Supply Curve That Slopes Upward and Then Bends Backward
(a) Labor-Leisure Choice
(b) Supply Cu r v
e of Labor y
Supply curve of labor a L 3 I 3
Time const r
aint E 3
age per hour
, Goods per d W I 2 , Y w E 2 I 1 e 3 L 2 e 2 E 1 L 1 e 1 H 2 H 2 H 3 H 3 24 H H 24 1 1 H , W o r
k hours per d a y H , W o r
k hours per d a y
but at high wages, an increase in the wage causes the worker to work less….
At low wages, an increase in the wage causes the worker to work more….

41. Why leisure is different
When the price of apples goes up,
the substitution effect reduces the consumption of apples, and
Moreover, the consumer’s income decreases in terms of purchasing power. This too reduces the consumption of apples, assuming apples are a normal good
When the wage rate (w), which is also the price of leisure, goes up, the substitution effect works as in the apples example and reduces leisure
But, the higher wage implies not a decrease but an increase in income. This increases leisure, assuming leisure is a normal good
So, although an increase in the price of apples should reasonably be expected to reduce the consumption of apples, an increase in the price of leisure should not be expected to reduce the consumption of leisure
That is, a backward bending labor supply should by no means be considered a freak phenomenon
If our consumer happens to be an apple farmer, what would her demand curve look like?

42. Leisure and consumption
wR is the reservation wage: the minimum wage at which this individual will work
The price of leisure (N) is the wage (w) that is lost
The budget constraint is wN + PYY = M = 24w + M*
The slope is -w/PY y a
Time const r
aint
, Goods per d Y
(24w R+ M*) /PY
Consumption with non-labor income (M*/PY) N * N N 24 N
, Leisure hours per d a y 1 2 24 H * H H H , W o r
k hours per d a y 1 2

43. Leisure and consumption
As the wage rate increases, labor supply first increases and then decreases
This is an instance of a backward-bending labor supply curve y a
Time const r
aint
, Goods per d Y
(24w R+ M*) /PY
Consumption with non-labor income (M*/PY) N * N N 24 N
, Leisure hours per d a y 1 2 24 H * H H H , W o r
k hours per d a y 1 2