Practice Problem: Chapter 2 #6
The rent control agency of NYC has found that aggregate demand is QD = 160-8P. Quantity is measured in tens of thousands of apartments. Price, the average monthly rental rate, is measured in hundreds of dollars. The agency also noted that the increase in Q at lower P results from more three-person
families coming into the city and demanding apartments. The city’s board of realtors acknowledges that this is a good demand estimate and has shown
that supply is QS = 70+7P.
What is the free market price? What is the change in city population if the agency sets a maximum average monthly rent of $300 and all those who
cannot find an apartment leave the city?
Chapter 3 2 ©2005 Pearson Education, Inc.
Chapter 2 #3
Set quantity supply = quantity demandP = 6 (convert to $600)Q = 112 (convert to 1,120,000)
Chapter 3 3 ©2005 Pearson Education, Inc.
Chapter 2: #6
If the rent control agency sets the rental rate at $300, the quantity supplied would then be 910,000 (QS = 70 + (7)(3) = 91), a decrease of 210,000 apartments from the free market equilibrium. (Assuming three people per family per apartment, this would imply a loss of 630,000 people.) At the $300 rental rate, the demand for apartments is 1,360,000 units, and the resulting shortage is 450,000 units (1,360,000-910,000). However, excess demand (supply shortages) and lower quantity demanded are not the same concepts. The supply shortage means that the market cannot accommodate the new people who would have been willing to move into the city at the new lower price. Therefore, the city population will only fall by 630,000, which is represented by the drop in the number of actual apartments from 1,120,000 (the old equilibrium value) to 910,000, or 210,000 apartments with 3 people each.
Chapter 3 4 ©2005 Pearson Education, Inc.
Practice Problem
Suppose the agency bows to the wishes of the board and sets a rental of $900 per month on all apartments to allow landlords a “fair” rate of return. If 50 percent of any increases in apartment offerings come from new construction, how many apartments are constructed?
Chapter 3 5 ©2005 Pearson Education, Inc.
Answer:
At a rental rate of $900, the supply of apartments would be 70 + 7(9) = 133, or 1,330,000 units, which is an increase of 210,000 units over the free market equilibrium. Therefore, (0.5)(210,000) = 105,000 units would be constructed. Note, however, that since demand is only 880,000 units, 450,000 units would go unrented
Chapter 3 6 ©2005 Pearson Education, Inc.
0
5
10
15
20
25
30
35
40
45
NotHanded
In(13)
0Failed
1NeedsTo BeBetter(28)
2Good(40)
3Excellent
(10)
Homework #1 Grade Distribution
Chapter 3 8 ©2005 Pearson Education, Inc.
Introduction
How are consumer preferences used to determine demand?
How do consumers allocate income to the purchase of different goods?
Chapter 3 9 ©2005 Pearson Education, Inc.
Consumer Behavior - Applications
1. How would General Mills determine the price to charge for a new cereal before it went to the market?
2. To what extent did the food stamp program provide individuals with more food versus merely subsidizing food they bought anyway?
Chapter 3 10 ©2005 Pearson Education, Inc.
Consumer Behavior Theory
There are three steps involved in the study of consumer behavior
1. Consumer Preferences To describe how and why people prefer
one good to another: algebra and graphs
2. Budget Constraints People have limited incomes/face prices
Chapter 3 11 ©2005 Pearson Education, Inc.
Consumer Behavior
3. Consumer Choices What combination of goods will consumers
buy to maximize their satisfaction, given preferences, income and prices?
Chapter 3 12 ©2005 Pearson Education, Inc.
Consumer Preferences
How might a consumer compare different groups of items available for purchase?
A market basket is a collection of one or more commodities
Individuals can choose between market baskets containing different goods
Chapter 3 13 ©2005 Pearson Education, Inc.
Consumer Preferences – Basic Assumptions
1. Preferences are complete Consumers can rank all market baskets
2. Preferences are transitive If they prefer A to B, and B to C, they must
prefer A to C (consistent)
3. Consumers always prefer more of any good to less
More is better
Chapter 3 14 ©2005 Pearson Education, Inc.
Majority Voting and Transitivity
Person: 1 2 3
Preference: Good X Good Y Good Z
Good Y Good Z Good X
Good Z Good X Good Y
Chapter 3 15 ©2005 Pearson Education, Inc.
Consumer Preferences
Consumer preferences can be represented graphically using indifference curves
Indifference curves represent all combinations of market baskets that the person is indifferent to A person will be equally satisfied with either
choice
Chapter 3 16 ©2005 Pearson Education, Inc.
Indifference Curves: An Example
Market Basket Units of Food Units of Clothing
A 20 30
B 10 50
D 40 20
E 30 40
G 10 20
H 10 40
Chapter 3 17 ©2005 Pearson Education, Inc.
Indifference Curves: An Example
Graph the points with one good on the x-axis and one good on the y-axis
Plotting the points, we can make some immediate observations about preferences More is better
Chapter 3 18 ©2005 Pearson Education, Inc.
The consumer prefersA to all combinations
in the yellow box, whileall those in the pink
box are preferred to A.
Indifference Curves: An Example
Food
10
20
30
40
10 20 30 40
Clothing
50
G
A
EH
B
D
Chapter 3 19 ©2005 Pearson Education, Inc.
•Indifferent between points B, A, & D•E is preferred to points on U1
•Points on U1
are preferred to H & G
Indifference Curves: An Example
Food
10
20
30
40
10 20 30 40
Clothing
50
U1
G
D
A
EH
B
Chapter 3 20 ©2005 Pearson Education, Inc.
Indifference Curves
Indifference curves slope downward to the right If they sloped upward, they would violate the
assumption that more is preferred to lessSome points that had more of both goods would
be indifferent to a basket with less of both goods
Chapter 3 21 ©2005 Pearson Education, Inc.
Indifference Curves
To describe preferences for all combinations of goods/services, we have a set of indifference curves – an indifference map Each indifference curve in the map shows
the market baskets among which the person is indifferent
Chapter 3 22 ©2005 Pearson Education, Inc.
U2
U3
Indifference Map
Food
Clothing
U1
ABD
Market basket Ais preferred to B.Market basket B ispreferred to D.
Chapter 3 23 ©2005 Pearson Education, Inc.
Indifference Maps
Indifference maps give more information about shapes of indifference curves Indifference curves cannot cross
Violates assumption that more is better Why? What if we assume they can cross?
Chapter 3 24 ©2005 Pearson Education, Inc.
Indifference Maps
Food
Clothing •B is preferred to D•A is indifferent to B & D•B must be indifferent to D but that can’t be if B is preferred to D
U1
U1
U2
U2
A
B
D
Chapter 3 25 ©2005 Pearson Education, Inc.
Indifference Curves
The shapes of indifference curves describe how a consumer is willing to substitute one good for another A to B, give up 6 clothing to get 1 food D to E, give up 2 clothing to get 1 food
The more clothing and less food a person has, the more clothing they will give up to get more food
Chapter 3 26 ©2005 Pearson Education, Inc.
A
B
D
EG
-1
-6
1
1
-4
-21
1
Observation: The amountof clothing given up for 1 unit of food decreasesfrom 6 to 1
Indifference Curves
Food
Clothing
2 3 4 51
2
4
6
8
10
12
14
16
Chapter 3 27 ©2005 Pearson Education, Inc.
Indifference Curves
We measure how a person trades one good for another using the marginal rate of substitution (MRS) It quantifies the amount of one good a
consumer will give up to obtain more of another good
It is measured by the slope of the indifference curve
Chapter 3 28 ©2005 Pearson Education, Inc.
Marginal Rate of Substitution
Food2 3 4 51
Clothing
2
4
6
8
10
12
14
16 A
B
D
EG
-6
1
1
11
-4
-2-1
MRS = 6
MRS = 2
FCMRS
Chapter 3 29 ©2005 Pearson Education, Inc.
Marginal Rate of Substitution
Indifference curves are convex (bowed inward) As more of one good is consumed, a
consumer would prefer to give up fewer units of a second good to get additional units of the first one
Consumers generally prefer a balanced market basket
Chapter 3 30 ©2005 Pearson Education, Inc.
Marginal Rate of Substitution
The MRS decreases as we move down the indifference curve Along an indifference curve there is a
diminishing marginal rate of substitution. The MRS went from 6 to 4 to 1
Chapter 3 31 ©2005 Pearson Education, Inc.
Marginal Rate of Substitution
Indifference curves with different shapes imply a different willingness to substitute
Two polar cases are of interest Perfect substitutes Perfect complements
Chapter 3 32 ©2005 Pearson Education, Inc.
Marginal Rate of Substitution
Perfect Substitutes Two goods are perfect substitutes when the
marginal rate of substitution of one good for the other is constant
Example: a person might consider apple juice and orange juice perfect substitutes
They would always trade 1 glass of OJ for 1 glass of Apple Juice
Chapter 3 33 ©2005 Pearson Education, Inc.
Consumer Preferences
Orange Juice(glasses)
Apple Juice
(glasses)
2 3 41
1
2
3
4
0
PerfectSubstitute
s
Chapter 3 34 ©2005 Pearson Education, Inc.
Consumer Preferences
Perfect Complements Two goods are perfect complements when
the indifference curves for the goods are shaped as right angles
Example: If you have 1 left shoe and 1 right shoe, you are indifferent between having more left shoes only
Must have one right for one left
Chapter 3 35 ©2005 Pearson Education, Inc.
Consumer Preferences
Right Shoes
LeftShoes
2 3 41
1
2
3
4
0
PerfectComplements
Chapter 3 36 ©2005 Pearson Education, Inc.
Consumer Preferences
We have assumed all our commodities are “goods”
There are commodities we don’t want more of - bads Things for which less is preferred to more
Examples Air pollution Asbestos
Chapter 3 37 ©2005 Pearson Education, Inc.
Consumer Preferences
How do we account for bads in our preference analysis? We redefine the commodity
Clean airPollution reductionAsbestos removal
Chapter 3 38 ©2005 Pearson Education, Inc.
Consumer Preferences: An Application
In designing new cars, automobile executives must determine how much time and money to invest in restyling versus increased performance Higher demand for car with better styling and
performance Both cost more to improve
Chapter 3 39 ©2005 Pearson Education, Inc.
Consumer Preferences: An Application
An analysis of consumer preferences would help to determine where to spend more on change: performance or styling
Some consumers will prefer better styling and some will prefer better performance
Chapter 3 40 ©2005 Pearson Education, Inc.
Consumer Preferences: An Application
These consumers
place a greater value
on performance than styling
Styling
Performance
Chapter 3 41 ©2005 Pearson Education, Inc.
Consumer Preferences: An Application
These consumers place a greater value on styling
than performance
Styling
Performance
Chapter 3 42 ©2005 Pearson Education, Inc.
Consumer Preferences: An Application
Knowing which group dominates the market will help decide where redesigning dollars should go
A recent study in the US shows that over the past two decades, most consumers have preferred styling over performance
Chapter 3 43 ©2005 Pearson Education, Inc.
Preferences and Numerical Values
The theory of consumer behavior does not require assigning a numerical value to the level of satisfaction
Although ranking of market baskets is good, sometimes numerical value is useful
Chapter 3 44 ©2005 Pearson Education, Inc.
Consumer Preferences
Utility A numerical score representing the
satisfaction that a consumer gets from a given market basket
If buying 3 copies of Microeconomics makes you happier than buying one shirt, then we say that the books give you more utility than the shirt
Chapter 3 45 ©2005 Pearson Education, Inc.
Utility
Utility function Formula that assigns a level of utility to
individual market baskets If the utility function is
U(F,C) = F + 2CA market basket with 8 units of food and 3 units of
clothing gives a utility of
14 = 8 + 2(3)
Chapter 3 46 ©2005 Pearson Education, Inc.
Utility - Example
Market Basket
Food Clothing Utility
A 8 3 8 + 2(3) = 14
B 6 4 6 + 2(4) = 14
C 4 4 4 + 2(4) = 12
Consumer is indifferent between A & B and prefers both to C
Chapter 3 47 ©2005 Pearson Education, Inc.
Utility - Example
Baskets for each level of utility can be plotted to get an indifference curve To find the indifference curve for a utility of
14, we can change the combinations of food and clothing that give us a utility of 14
Chapter 3 48 ©2005 Pearson Education, Inc.
Utility - Example
Food10 155
5
10
15
0
Clothing
U1 = 25
U2 = 50
U3 = 100A
B
C
Basket U = FC C 25 = 2.5(10) A 25 = 5(5) B 25 = 10(2.5)
Chapter 3 49 ©2005 Pearson Education, Inc.
Utility
Although we numerically rank baskets and indifference curves, numbers are ONLY for ranking
A utility of 4 is not necessarily twice as good as a utility of 2, just better
There are two types of rankings Ordinal ranking Cardinal ranking
Chapter 3 50 ©2005 Pearson Education, Inc.
Utility
Ordinal Utility Function Places market baskets in the order of most
preferred to least preferred, but it does not indicate how much one market basket is preferred to another
Interpersonal comparisons impossibleCardinal Utility Function
Utility function describing the extent to which one market basket is preferred to another
Chapter 3 51 ©2005 Pearson Education, Inc.
Budget Constraints
Preferences do not explain all of consumer behavior
Budget constraints also limit an individual’s ability to consume in light of the prices they must pay for various goods and services
Chapter 3 52 ©2005 Pearson Education, Inc.
Budget Constraints
The Budget Line Indicates all combinations of two
commodities for which total money spent equals total income
We assume only 2 goods are consumed, so we do not consider savings
Chapter 3 53 ©2005 Pearson Education, Inc.
The Budget Line
Let F equal the amount of food purchased, and C is the amount of clothing
Price of food = PF and price of clothing = PC
Then PFF is the amount of money spent on food, and PCC is the amount of money spent on clothing
Chapter 3 54 ©2005 Pearson Education, Inc.
ICPFPCF
The Budget Line
The budget line then can be written:
All income is allocated to food (F) and/or clothing (C)
Chapter 3 56 ©2005 Pearson Education, Inc.
The Budget Line
Different choices of food and clothing can be calculated that use all income These choices can be graphed as the budget
line
Example: Assume income of $80/week, PF = $1 and PC
= $2
Chapter 3 57 ©2005 Pearson Education, Inc.
Budget Constraints
Market Basket
Food
PF = $1
Clothing
PC = $2
IncomeI = PFF + PCC
A 0 40 $80
B 20 30 $80
D 40 20 $80
E 60 10 $80
G 80 0 $80
Chapter 3 58 ©2005 Pearson Education, Inc.
C
F
P
P
F
C Slope -
2
1-
The Budget Line
10
20
A
B
D
E
G
(I/PC) = 40
Food40 60 80 = (I/PF)20
10
20
30
0
Clothing
Chapter 3 59 ©2005 Pearson Education, Inc.
The Budget Line
As consumption moves along a budget line from the intercept, the consumer spends less on one item and more on the other
The slope of the line measures the relative cost of food and clothing
The slope is the negative of the ratio of the prices of the two goods
Chapter 3 60 ©2005 Pearson Education, Inc.
The Budget Line
The slope indicates the rate at which the two goods can be substituted without changing the amount of money spent
We can rearrange the budget line equation to make this more clear
Chapter 3 62 ©2005 Pearson Education, Inc.
Budget Constraints
The Budget Line The vertical intercept, I/PC, illustrates the
maximum amount of C that can be purchased with income I
The horizontal intercept, I/PF, illustrates the maximum amount of F that can be purchased with income I
Chapter 3 63 ©2005 Pearson Education, Inc.
The Budget Line
As we know, income and prices can change
As incomes and prices change, there are changes in budget lines
We can show the effects of these changes on budget lines and consumer choices
Chapter 3 64 ©2005 Pearson Education, Inc.
The Budget Line - Changes
The Effects of Changes in Income An increase in income causes the budget line
to shift outward, parallel to the original line (holding prices constant).
Can buy more of both goods with more income
Chapter 3 65 ©2005 Pearson Education, Inc.
The Budget Line - Changes
The Effects of Changes in Income A decrease in income causes the budget line
to shift inward, parallel to the original line (holding prices constant)
Can buy less of both goods with less income
Chapter 3 66 ©2005 Pearson Education, Inc.
The Budget Line - Changes
An increase inincome shifts
the budget lineoutward
Food(units per week)
Clothing(units
per week)
80 120 16040
20
40
60
80
0
(I = $160)L2
(I = $80)
L1
L3
(I =$40)
A decrease inincome shifts
the budget lineinward
Chapter 3 67 ©2005 Pearson Education, Inc.
The Budget Line - Changes
The Effects of Changes in Prices If the price of one good increases, the budget
line shifts inward, pivoting from the other good’s intercept.
If the price of food increases and you buy only food (x-intercept), then you can’t buy as much food. The x-intercept shifts in.
If you buy only clothing (y-intercept), you can buy the same amount. No change in y-intercept.
Chapter 3 68 ©2005 Pearson Education, Inc.
The Budget Line - Changes
The Effects of Changes in Prices If the price of one good decreases, the
budget line shifts outward, pivoting from the other good’s intercept.
If the price of food decreases and you buy only food (x-intercept), then you can buy more food. The x-intercept shifts out.
If you buy only clothing (y-intercept), you can buy the same amount. No change in y-intercept.
Chapter 3 69 ©2005 Pearson Education, Inc.
The Budget Line - Changes
(PF = 1)
L1
An increase in theprice of food to$2.00 changes
the slope of thebudget line and
rotates it inward.L3
(PF = 2)(PF = 1/2)
L2
A decrease in theprice of food to$.50 changes
the slope of thebudget line and
rotates it outward.
40Food(units per week)
Clothing(units
per week)
80 120 160
40
Chapter 3 70 ©2005 Pearson Education, Inc.
The Budget Line - Changes
The Effects of Changes in Prices If the two goods increase in price, but the
ratio of the two prices is unchanged, the slope will not change
However, the budget line will shift inward parallel to the original budget line
Chapter 3 71 ©2005 Pearson Education, Inc.
The Budget Line - Changes
The Effects of Changes in Prices If the two goods decrease in price, but the
ratio of the two prices is unchanged, the slope will not change
However, the budget line will shift outward parallel to the original budget line
Chapter 3 72 ©2005 Pearson Education, Inc.
Consumer Choice
Given preferences and budget constraints, how do consumers choose what to buy?
Consumers choose a combination of goods that will maximize their satisfaction, given the limited budget available to them
Chapter 3 73 ©2005 Pearson Education, Inc.
Consumer Choice
The maximizing market basket must satisfy two conditions:
1. It must be located on the budget line They spend all their income – more is better
2. It must give the consumer the most preferred combination of goods and services
Chapter 3 74 ©2005 Pearson Education, Inc.
Consumer Choice
Graphically, we can see different indifference curves of a consumer choosing between clothing and food
Remember that U3 > U2 > U1 for our indifference curves
Consumer wants to choose highest utility within their budget
Chapter 3 75 ©2005 Pearson Education, Inc.
Consumer Choice
U3
D
U2
C
Food (units per week)40 8020
Clothing(units per
week)
20
30
40
0
U1
A
B
•A, B, C on budget line•D highest utility but not affordable•C highest affordable utility•Consumer chooses C
Chapter 3 76 ©2005 Pearson Education, Inc.
Consumer Choice
Consumer will choose highest indifference curve on budget line
In previous graph, point C is where the indifference curve is just tangent to the budget line
Slope of the budget line equals the slope of the indifference curve at this point
Chapter 3 77 ©2005 Pearson Education, Inc.
Consumer Choice
Recall, the slope of an indifference curve is:
F
CMRS
C
F
P
PSlope
Further, the slope of the budget line is:
Chapter 3 78 ©2005 Pearson Education, Inc.
Consumer Choice
Therefore, it can be said at consumer’s optimal consumption point,
C
F
P
PMRS
Chapter 3 79 ©2005 Pearson Education, Inc.
Consumer Choice
It can be said that satisfaction is maximized when marginal rate of substitution (of C for F) is equal to the ratio of the prices (of F to C)
Note this is ONLY true at the optimal consumption point
Chapter 3 80 ©2005 Pearson Education, Inc.
Consumer Choice
Optimal consumption point is where marginal benefits equal marginal costs
MB = MRS = benefit associated with consumption of 1 more unit of food
MC = cost of additional unit of food 1 unit food = ½ unit clothing PF/PC
Chapter 3 81 ©2005 Pearson Education, Inc.
Consumer Choice
If MRS ≠ PF/PC then individuals can reallocate basket to increase utility
If MRS > PF/PC
Will increase food and decrease clothing until MRS = PF/PC
If MRS < PF/PC
Will increase clothing and decrease food until MRS = PF/PC
Chapter 3 82 ©2005 Pearson Education, Inc.
Consumer Choice
Food (units per week)
Clothing(units per
week)
40 8020
20
30
40
0
Point B does not maximize satisfaction
because theMRS = -10/10 = 1
is greater than the price ratio = 1/2
+10F U1
-10C
B
Chapter 3 83 ©2005 Pearson Education, Inc.
Consumer Choice: An Application Revisited
Consider two groups of consumers, each wishing to spend $10,000 on the styling and performance of a car
Each group has different preferences
Chapter 3 84 ©2005 Pearson Education, Inc.
Consumer Choice: An Application Revisited
By finding the point of tangency between a group’s indifference curve and the budget constraint, auto companies can see how much consumers value each attribute
Chapter 3 85 ©2005 Pearson Education, Inc.
Consumer Choice: An Application Revisited
Styling
Performance$10,000
$10,000 These consumerswant performance worth $7000 and
styling worth $3000
$3,000
$7,000
Chapter 3 86 ©2005 Pearson Education, Inc.
Consumer Choice: An Application Revisited
These consumers want
styling worth $7000 and
performance worth $3000
$3,000
$7,000
Styling
$10,000
$10,000
Performance
Chapter 3 87 ©2005 Pearson Education, Inc.
Consumer Choice: An Application Revisited
Once a company knows preferences, it can design a production and marketing plan
Company can then make a sensible strategic business decision on how to allocate performance and styling on new cars
Chapter 3 88 ©2005 Pearson Education, Inc.
Consumer Choice
A corner solution exists if a consumer buys in extremes, and buys all of one category of good and none of another MRS is not necessarily equal to PB/PA
Chapter 3 89 ©2005 Pearson Education, Inc.
A Corner Solution
Ice Cream (cup/month)
FrozenYogurt
(cupsmonthly)
B
A
U2 U3U1
A corner solutionexists at point B.
Chapter 3 90 ©2005 Pearson Education, Inc.
A Corner Solution
At point B, the MRS of frozen yogurt for ice cream is greater than the slope of the budget line
If the consumer could give up more frozen yogurt for ice cream, he would do so
However, there is no more frozen yogurt to give up
Opposite is true if corner solution was at point A
Chapter 3 91 ©2005 Pearson Education, Inc.
A Corner Solution
When a corner solution arises, the consumer’s MRS does not necessarily equal the price ratio
In this instance it can be said that:
YogurtFrozen
IceCream
P
PMRS
Chapter 3 92 ©2005 Pearson Education, Inc.
A Corner Solution
If the MRS is, in fact, significantly greater than the price ratio, then a small decrease in the price of frozen yogurt will not alter the consumer’s market basket
Chapter 3 93 ©2005 Pearson Education, Inc.
A Corner Solution - Example
Suppose Jane Doe’s parents set up a trust fund for her college education
The money must be used only for education
Although a welcome gift, an unrestricted gift might be better
Chapter 3 94 ©2005 Pearson Education, Inc.
A Corner Solution - Example
Original budget line, PQ, with a market basket, A, of education and other goods
Trust fund shifts out the budget line as long as trust fund, PB, is spent on education
Jane increases satisfaction, moving to higher indifference curve, U2
Chapter 3 95 ©2005 Pearson Education, Inc.
A Corner Solution - Example
P
Q Education ($)
OtherConsumption
($)
U2A
U1
B
•Jane better off on U2
•B is corner solution•MRS ≠ POG/PE
Chapter 3 96 ©2005 Pearson Education, Inc.
A Corner Solution - Example
P
Q Education ($)
OtherConsumption
($)
U2A
U1
B
•If gift is unrestricted, Jane can be at point C on U3
•Better off than with restricted gift
CU3
Chapter 3 97 ©2005 Pearson Education, Inc.
Marginal Utility and Consumer Choice
Marginal utility measures the additional satisfaction obtained from consuming one additional unit of a good How much happier is the individual from
consuming one more unit of food?
Chapter 3 98 ©2005 Pearson Education, Inc.
Marginal Utility - Example
The marginal utility derived from increasing from 0 to 1 units of food might be 9
Increasing from 1 to 2 might be 7Increasing from 2 to 3 might be 5Observation: Marginal utility is
diminishing as consumption increases
Chapter 3 99 ©2005 Pearson Education, Inc.
Marginal Utility
The principle of diminishing marginal utility states that as more of a good is consumed, the additional utility the consumer gains will be smaller and smaller
Note that total utility will continue to increase since consumer makes choices that make them happier
Chapter 3 100 ©2005 Pearson Education, Inc.
Marginal Utility and Indifference Curves
As consumption moves along an indifference curve: Additional utility derived from an increase in
the consumption one good, food (F), must balance the loss of utility from the decrease in the consumption in the other good, clothing (C)
Chapter 3 101 ©2005 Pearson Education, Inc.
Marginal Utility and Consumer Choice
Formally:
C)( MUF) (MU CF 0
No change in total utility along an indifference curve. Trade off of one good to the other leaves the consumer just as well off.
Chapter 3 102 ©2005 Pearson Education, Inc.
Marginal Utility and Consumer Choice
Rearranging:
CF
CF
/MU MUMRS
MRSFC
Since
MUMUFC
saycan We
Ffor C of /
//
Chapter 3 103 ©2005 Pearson Education, Inc.
Marginal Utility and Consumer Choice
When consumers maximize satisfaction:
CF /P PMRS
CF CF /P P /MUMU
Since the MRS is also equal to the ratio of the marginal utility of consuming F and C
Chapter 3 104 ©2005 Pearson Education, Inc.
Marginal Utility and Consumer Choice
Rearranging, gives the equation for utility maximization:
CCFF PMUPMU //
Chapter 3 105 ©2005 Pearson Education, Inc.
Marginal Utility and Consumer Choice
Total utility is maximized when the budget is allocated so that the marginal utility per dollar of expenditure is the same for each good.
This is referred to as the equal marginal principle.
Chapter 3 106 ©2005 Pearson Education, Inc.
Cost-of-Living Indexes
Social Security payments are given to qualifying individuals
Each year the benefit increases equal to the rate of increase of the Consumer Price Index (CPI) Ratio of the present cost of typical bundle of
goods/services in comparison to the cost during a base period
Chapter 3 107 ©2005 Pearson Education, Inc.
Cost-of-Living Indexes
Does the CPI give a good measure of inflation and therefore a measure of the cost of living changes?
Should the CPI be used to measure how much cost of living has increased, determining increases in government payment programs?
Chapter 3 108 ©2005 Pearson Education, Inc.
Cost-of-Living Indexes
The ideal cost of living index represents the cost of attaining a given level of utility at current prices relative to the cost of attaining the same utility at base prices
Takes into account the fact that consumers can and will substitute some goods for others
Chapter 3 109 ©2005 Pearson Education, Inc.
Cost-of-Living Indexes
To obtain the ideal cost of living index would require too much information, such as consumer preferences as well as prices and expenditures
Actual price indexes are based on consumer purchases, not preferences
Chapter 3 110 ©2005 Pearson Education, Inc.
Cost-of-Living Indexes
Laspeyres price index Amount of money at current year prices that
an individual requires to purchase a bundle of goods/services chosen in a base year divided by the cost of purchasing the same bundle at base-year prices
Ex: CPI
Chapter 3 111 ©2005 Pearson Education, Inc.
Cost-of-Living Indexes
The Laspeyres price index assumes that consumers do not alter their consumption patterns as prices change
Tends to overstate the true cost of living index
Using the CPI to adjust retirement benefits will tend to overcompensate most recipients, requiring greater government expenditure
Chapter 3 112 ©2005 Pearson Education, Inc.
Cost-of-Living Indexes
Paasche index Focuses on the cost of buying the current
year’s bundle Amount of money at current-year prices that
an individual requires to purchase a current bundle of goods/services divided by the cost of purchasing the same bundle in a base year
Chapter 3 113 ©2005 Pearson Education, Inc.
Cost-of-Living Indexes
Comparison of indexes Both are fixed weight indexes Quantities of various goods and services in
each index remain unchanged Laspeyres index keeps quantities at base
year levels Paasche index keeps unchanged quantities
at current year levels
Chapter 3 114 ©2005 Pearson Education, Inc.
Cost-of-Living Indexes
Paasche Index understates inflationOverstates the cost of the base year
bundle (current bundle at base year prices) – consumer would not have chosen that bundle with different relative prices
Thus, denominator overstated and index is understated
Chapter 3 115 ©2005 Pearson Education, Inc.
Cost-of-Living Indexes
Chain-Weighted Indexes Cost-of-living index that accounts for
changes in quantities of goods and services Introduced to overcome problems that arose
when long-term comparisons were made using fixed weight price indexes
Chapter 3 116 ©2005 Pearson Education, Inc.
Practice: Chapter 3, #15
15. Jane receives utility from days spent traveling on vacation domestically (D) and days spent traveling on vacation in a foreign country (F), as given by the utility function: U = 10DF. In addition, the price of a day spent traveling domestically is $100, the price of a day spent traveling in a foreign country is $400, and Jane’s annual travel budget is $4,000.
Illustrate the indifference curve associated with a utility of 800 and the indifference curve associated with a utility of 1200.
Chapter 3 117 ©2005 Pearson Education, Inc.
Practice
The indifference curve with a utility of 800 has the equation 10DF=800, or DF=80. Choose combinations of D and F whose product is 80 to find a few bundles. The indifference curve with a utility of 1200 has the equation 10DF=1200, or DF=120. Choose combinations of D and F whose product is 120 to find a few bundles.
Chapter 3 118 ©2005 Pearson Education, Inc.
Practice
Can Jane afford any of the bundles that give her a utility of 800? What about a utility of 1200?
Yes she can afford some of the bundles that give her a utility of 800 as part of this indifference curve lies below the budget line. She cannot afford any of the bundles that give her a utility of 1200 as this whole indifference curve lies above the budget line.
Chapter 3 119 ©2005 Pearson Education, Inc.
Practice
Find Jane’s utility maximizing choice of days spent traveling domestically and days spent in a foreign country. (We will need to set the slope of the budget line equal to the slope of the indifference curve by taking two derivatives.)
Chapter 3 120 ©2005 Pearson Education, Inc.
Practice
The optimal bundle is where the slope of the indifference curve is equal to the slope of the budget line, and Jane is spending her entire income. The slope of the budget line is -PD/PF = -1/4
The slope of the indifference curve is: MRS= -MUD/MUF = -10F/10D = -F/D
Setting the two equal we get:-F/D = -1/4 We now have two equations and two unknowns:4F=D
and 100D+400F=$4000 Solving the above two equations gives D=20 and F=5.
Utility is 1000. This bundle is on an indifference curve between the two
you had previously drawn.
Chapter 3 121 ©2005 Pearson Education, Inc.
Practice: Chapter 3, #4
Janelle and Brian each plan to spend $20,000 on the styling and gas mileage features of a new car. They can each choose all styling, all gas mileage, or some combination of the two. Janelle does not care at all about styling and wants the best gas mileage possible. Brian likes both equally and wants to spend an equal amount on the two features. Using indifference curves and budget lines, illustrate the choice that each person will make.
Chapter 3 122 ©2005 Pearson Education, Inc.
Practice
Assume styling is on the vertical axis and gas mileage is on the horizontal axis. Janelle has indifference curves that are vertical. As her indifference curves move over to the right, she gains more gas mileage and more satisfaction. She will spend all $20,000 on gas mileage. This is a corner solution.
Chapter 3 123 ©2005 Pearson Education, Inc.
Practice
Brian has indifference curves that are L-shaped. He will not spend more on one feature than on the other feature. He will spend $10,000 on styling and $10,000 on gas mileage. Styling and gas mileage are perfect complements for Brian.