Transcript File

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
Consumer Theory
• Assumes buyers are completely informed
about:
•
•
•
•
Range of products available
Prices of all products
Capacity of products to satisfy
Their income
5-2
Indifference Curves
• Locus of points representing different
bundles of goods, each of which yields
the same level of total utility
• Negatively sloped & convex
5-3
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
5-4
Properties of Consumer
Preferences
• Transitivity
• If X is preferred to Y, and Y is preferred to Z,
then X must be preferred to Z
5-5
Properties of Consumer
Preferences
• Nonsatiation
• More of a good is always preferred to less
5-6
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
5-7
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  U X
• MU=
Changes in Total Utility /
Change in No of Units Consumed
5-8
Constrained Utility Maximization
(Figure 5.8)
50
Quantity of pizzas
45
•A
40
•B
•D
•
E
R
30
IV
III
20
•
C
15
10
0
10
20
30
40
50
60
70
II
T
I
80
90
100
Quantity of burgers
5-9
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
Y MU X
MRS  

X MUY
5-10
How to get MRS Formula
• U = ƒ(XY)
by differentiation,
dU= ƒ1dX + ƒ2dY
(Here, U= Utility; X,Y= 2 goods)
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
Here,
5-11
Slope of an Indifference Curve &
the MRS (Figure 5.3)
Quantity of good Y
600
A
T
C (360,320)
320
I
T’
B
0
360
800
Quantity of good X
5-12
MRS = slope of indifference curve = slope of tangent line
5-13
The slope is 35/35 = 1
5-14
MRS = − ΔY /ΔX = 5 /10 = 1 2
5
10
5-15
Before, − ΔY /ΔX = 5/10 or 1/ 2,
After, − ΔX/ ΔY = 10/5 or 2
10:5 or 2:1
5
10
5-16
5-17
Consumer’s Budget Line
• Shows all possible commodity bundles
that can be purchased at given prices
with a fixed money income
M  PX X  PYY
or
M PX
Y

X
PY PY
5-18
Consumer’s Budget Constraint
(Figure 5.5)
5-19
Typical Budget Line
Quantity of Y
M
PY
(Figure 5.6)
•A
Y
M PX

X
PY PY
B
•M
Quantity of X
PX
5-20
Shifting Budget Lines (Figure 5.7)
100
80
R
A
Quantity of Y
Quantity of Y
120
F
100
A
B
N
C
B
D
160 200
240
125
200
250
Z
Quantity of X
Quantity of X
Panel A – Changes in money income
Panel B – Changes in price of X
5-21
The following figure shows a portion of a consumer’s indifference map. The
consumer faces the budget line ZL, and the price of Y is $20.
600
The consumer's income = $__________.
The price of X is $_____________.
20
5-22
The following figure shows a portion of a consumer’s indifference map. The
consumer 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
5-23
The following figure shows a portion of a consumer’s indifference map. The
consumer 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
5-24
The following figure shows a portion of a consumer’s indifference map. The
consumer 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=Px / PY
= 20 / 20
=1
5-25
The following figure shows a portion of a consumer’s indifference map. The
consumer faces the budget line ZL, and the price of Y is $20.
If the budget line pivots to ZM, the
10
consumer chooses _______
units of
15
good X and _________
units of good Y.
5-26
The following figure shows a portion of a consumer’s indifference map. The
consumer faces the budget line ZL, and the price of Y is $20.
Along budget line ZM, the price of X is
20
$_________
and the price of Y is
$________.
30
5-27
The following figure shows a portion of a consumer’s indifference map. The
consumer faces the budget line ZL, and the price of Y is $20.
MRS= 30/ 20 =1
The new MRS is equal to __________.
5-28
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
5-29
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.
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
5-30
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.
5-31
Derivation of Market Demand
Quantity demanded
Price
Consumer 1
Consumer 2
Consumer 3
Market
demand
$6
3
0
0
3
5
5
1
0
6
4
8
3
1
12
3
10
5
4
19
2
12
7
6
25
1
13
10
8
31
5-32
Derivation of Market Demand
Figure (5.10)
5-33