33
5-1 The Consumer’s Optimization Problem • Individual consumption decisions are made with the goal of maximizing total satisfaction from consuming various goods and services
5-1
The Consumer’s Optimization Problem
• Individual consumption decisions are made with the goal of maximizing total satisfaction from consuming various goods and services
5-2
Consumer Theory
• Assumes buyers are completely informed about:• Range of products available
• Prices of all products
• Capacity of products to satisfy
• Their income
5-3
Indifference Curves
• Locus of points representing different bundles of goods, each of which yields the same level of total utility
• Negatively sloped & convex
5-4
Properties of Consumer Preferences
• Completeness• For every pair of consumption bundles, A and B, the
consumer can say one of the following:• A is preferred to B• B is preferred to A• The consumer is
indifferent between A and B
5-5
Properties of Consumer Preferences
• Transitivity• If X is preferred to Y, and Y is preferred to Z,
then X must be preferred to Z
5-6
Properties of Consumer Preferences
• Nonsatiation• More of a good is always preferred to less
5-7
Utility
• The benefits consumers obtain from the goods and services they consume is called utility.
• A utility function shows an individual’s perception of the utility level attained from consuming each conceivable bundle of goods
5-8
Marginal Utility
• Addition to total utility attributable to the addition of one unit of a good to the current rate of consumption, holding constant the amounts of all other goods consumed
• MU= Changes in Total Utility /
Change in No of Units Consumed MU U X
5-9
Constrained Utility Maximization (Figure 5.8)
A•
I
C•
•B
II
R
T
Quantity of burgers
Qu
anti
ty o
f piz
zas
0 8020 10040 60
10
20
30
40
50
7010 9030 50
•E
III
•DIV
45
15
5-10
Marginal Rate of Substitution
• MRS shows the rate at which one good can be substituted for another while keeping utility constant• Negative of the slope of the indifference curve
• Diminishes along the indifference curve as X increases & Y decreases
• Ratio of the marginal utilities of the goods
X
Y
MUYMRS
X MU
5-11
How to get MRS Formula
• U = ƒ(XY) (Here, U= Utility; X,Y= 2 goods)
by differentiation,
dU= ƒ1dX + ƒ2dY Here, ƒ1= ΔU/ ΔX = MUx
ƒ2= ΔU/ ΔY = MUy
as per indifference curve, U remains constant. So, U = 0
→ ƒ1dX + ƒ2dY = 0
→ ƒ1dX = - ƒ2dY
→ ƒ1 / ƒ2 = - dX/dY
as indifference curve is neutral, so….
IdX/dYI = I ƒ1 / ƒ2 I = MUx/ MUy
So, MRSxy = MUx/ MUy
5-12
Slope of an Indifference Curve & the MRS (Figure 5.3)
Quantity of good X
Qu
an
tity
of
go
od
Y
0
I
C (360,320)
600
800
A
B
T
T’
360
320
5-13
MRS = slope of indifference curve = slope of tangent line
5-14
The slope is 35/35 = 1
5-15
MRS = − ΔY /ΔX = 5 /10 = 1 2
5
10
5-16
5
10
Before, − ΔY /ΔX = 5/10 or 1/ 2, After, − ΔX/ ΔY = 10/5 or 2
10:5 or 2:1
5-17
5-18
Consumer’s Budget Line
• Shows all possible commodity bundles that can be purchased at given prices with a fixed money income
X YM P X P Y
X
Y Y
PMY X
P P
or
5-19
Consumer’s Budget Constraint (Figure 5.5)
5-20
Typical Budget Line (Figure 5.6)
Quanti
ty o
f Y
Quantity of X
X
Y Y
PMY X
P P
•
•
A
B
Y
MP
X
MP
5-21
Shifting Budget Lines (Figure 5.7)
Panel B – Changes in price of X
200
100A
B
250
D
R
N
120
240
Qu
anti
ty o
f Y
Quantity of X
Panel A – Changes in money income
Qu
anti
ty o
f Y
Quantity of X
A
B
100F
Z
80
160
200
125
C
5-22
The following figure shows a portion of a consumer’s indifference map. Theconsumer faces the budget line ZL, and the price of Y is $20.
The consumer's income = $__________. The price of X is $_____________.
600
20
5-23
The following figure shows a portion of a consumer’s indifference map. Theconsumer faces the budget line ZL, and the price of Y is $20.
The equation for the budget line ZL is Y = ______________________.
30 - 1x
30/ 30
5-24
The following figure shows a portion of a consumer’s indifference map. Theconsumer faces the budget line ZL, and the price of Y is $20.
What combination of X and Y would the consumer choose? Why?
15X and 15Y
5-25
The following figure shows a portion of a consumer’s indifference map. Theconsumer faces the budget line ZL, and the price of Y is $20.
The marginal rate of substitution at the combination in part c is __________.
MRS=PMRS=Pxx / P / PYY
= 20 / 20= 20 / 20 = 1= 1
5-26
The following figure shows a portion of a consumer’s indifference map. Theconsumer faces the budget line ZL, and the price of Y is $20.
If the budget line pivots to ZM, the consumer chooses _______ units of good X and _________ units of good Y.
10
15
5-27
The following figure shows a portion of a consumer’s indifference map. Theconsumer faces the budget line ZL, and the price of Y is $20.
Along budget line ZM, the price of X is $_________ and the price of Y is$________.30
20
5-28
The following figure shows a portion of a consumer’s indifference map. Theconsumer faces the budget line ZL, and the price of Y is $20.
The new MRS is equal to __________.MRS= 30/ 20 =1MRS= 30/ 20 =1
5-29
The figure below shows a portion of a consumer’s indifference map, and a budget line. The consumer’s income is $1,200 and the price of Y is $6.
Using the given budget line, what is one point on the consumer’s demand for X?(Both Price & Quantity)
Px = $1,200/200 = $6 and X = 100
5-30
The figure below shows a portion of a consumer’s indifference map, and a budget line. The consumer’s income is $1,200 and the price of Y is $6.
Pivot the budget line and derive two other points on the consumer’s demand for X.
At A, Px = $1,200/100 = $12 and X = 50
At B, Px = $1,200/200 = $6 and X = 100
At C, Px = $1,200/300 = $4 and X = 150
5-31
Market Demand
• Market demand is a list of prices and the quantities consumers are willing and able
• to purchase at each price in the list, other things being held constant.
• Marketdemand is derived by horizontally summing the demand curves for all the individuals in the market.
5-32
Derivation of Market Demand
Quantity demanded
Price Consumer 1 Consumer 2 Consumer 3Market
demand
$6
2
1
5
4
3
3
1213
5
8
10
0
7
10
1
3
5
0
6
8
0
1
4
3
2531
6
1219
5-33
Derivation of Market Demand Figure (5.10)
