Transcript Gains from Trade and Specilaization

Individual Choice
Principles of Microeconomics
Professor Dalton
ECON 202 – Fall 2013
1
Models of Consumer Behavior
 Marginal Utility approaches
• Ordinal analysis
• Cardinal analysis
• problem of handling complements and
substitutes
 Indifference Curve approach
• Ordinal utility
• Handles complements and substitutes well
2
Terminology Warning!
 Economists use the terms value,
utility and benefit interchangeably
when speaking of individual choice.
Marginal utility =
Marginal value =
Marginal benefit
3
Ordinal Analysis: Marginal Utility
Alternative Uses for horses (in order of
declining value)
1st
2nd
3rd
4th
Pull plow
Pull wagon
Ride for farmer
Ride for farmer’s wife
Most valuable use
of a horse
Least valuable
use of a horse
5th Ride for farmer’s children
4
Law of Diminishing
Marginal Utility
For all human actions, as the
quantity of a good increases,
the utility from each
additional unit diminishes.
5
Ordinal Analysis: Marginal Utility
Suppose the farmer owns three horses
1st
2nd
3rd
4th
Farmer will use one
Pull plow
horse to pull plow, one
Pull wagon
horse to pull wagon, and
Ride for farmer
one to ride himself
Ride for farmer’s wife
5th Ride for farmer’s children
6
Ordinal Analysis: Marginal Utility
The farmer rides the “third” horse because the
marginal benefit from riding the horse himself is
greater than the marginal benefit from having
his wife ride a horse.
The marginal cost of his riding the horse is the
foregone marginal benefit from his wife riding
the horse.
The marginal benefit from riding the horse himself
is greater than the marginal cost of his riding
the horse.
7
Cardinal Analysis: Marginal Utility
 Uses cardinal measure of utility
 Makes distinction between Total and
Marginal utility
 “law of diminishing Marginal Utility”
still holds
 Produces the Equimarginal rule and
allows for utility maximization
8
Total utility [TU] is defined as the amount of utility an
individual derives from consuming a given quantity of a good
during a specific period of time. TU = f (Q, preferences, . . .)
Utility
TU
Q
TU
120
100
2
30
55
75
60
1
3
4
5
6
90
7
100
105
105
8
100
80
40
20
.
1
.
2
.
3
.
.
.
.
.
TU
4
5
6
7 Q/t
9
Marginal Utility
 Marginal utility [MU] is the change in total
utility associated with a 1 unit change in
consumption.
 As total utility increases at a decreasing
rate, MU declines.
 As total utility declines, MU is negative.
 When TU is a maximum, MU is 0.
• “Satiation point”
10
Marginal Utility [MU] is the change in total utility [ΔTU]
caused by a one unit change in quantity [ΔQ] ;
MU = ΔTU
ΔQ
Utility
DQ=1
DQ=1
DQ=1
Q
TU
1
2
3
4
5
6
7
8
30
55
DTU=25
75
20
90
100
105
105
100
MU
DTU=30
30
25
DTU=20
15
10
5
0
-5
The first unit consumed increases TU by 30.
MU
The 2nd unit increases TU by 25.
30
25
20
..
10
..
1DQ2
3
4
.. .
MU
5
6
7
.
Q/t
The marginal utility is associated with the
midpoint between the units as each additional
unit is added.
11
Individual Choice
 If there are no costs associated with
choice, the individual consumes until MU
= 0, thereby maximizing TU.
 Typically, individuals are constrained by a
budget [or income] and the prices they
pay for the goods they consume.
 Net benefits are maximized where MU =
MC; as long as the MU of the next unit of
good purchased exceeds the MC, it will
increase net benefits.
12
Individual Choice
 The individual purchases more of a
good so long as their expected MU
exceeds the price they must pay for
the good:
 Buy so long as MU (MB) > MC;
 Don’t buy if MU (MB) < MC.
 The maximum net utility (consumer
surplus) occurs where MU (MB) =
MC.
13
Constrained Optimization
 Individual choices become a function of the price
of the good, income, prices of related goods and
preferences.
 QX = f (PX , I, PY, Preferences, . . . )
•
•
•
•
Where:
PX = price of good X
I = income
PY = prices of related goods
• “preferences” is the individual’s utility function
14
Consider an individual’s utility preference for 2 goods, X & Y;
Utility X
Qx
1
2
3
4
5
6
TUx MUx
30
55
30
25
75 20
90
7
100
105
105
8
100
15
10
5
0
-5
If the two goods were “free,”
[ or no budget constraint],
the individual would consume
each good until the MU of
that good was 0, 7 units
of good X and 6 of Y.
Once the goods have a price
and there is a budget
constraint, the individual
will try to maximize the
utility from each additional
dollar spent.
Utility Y
Qy
1
2
3
4
TUy MUy
60
90
60
30
110
20
120
10
5
6
128
7
120
8
100 - 20
128
8
0
-8
15
Given the budget constraint, individuals will attempt to
gain the maximum utility for each additional dollar spent,
“the marginal dollar.”
Utility X
Qx
1
2
3
4
5
6
TUx MUx
30
55
30
25
75 20
90
7
100
105
105
8
100
15
10
5
0
-5
MUX
PX
10.
8.33
6.67
5.00
3.33
1.67
0
For PX = $3, the
MUX per dollar
spent on good
X is…
For PY = $5, the
MUY per dollar
spent on good
Y is…
MUY
PY
Utility Y
Qy
12
1
6
2
4
3
4
2
1.6
0
5
6
TUy MUy
60
90
60
30
110
20
120
10
7
128
128
120
8
0
-8
8
100 - 20
16
Given the budget constraint, individuals will attempt to
gain the maximum utility for each additional dollar spent,
“the marginal dollar.”
Utility X
Qx
1
2
3
4
5
6
TUx MUx
30
55
30
25
75 20
90
7
100
105
105
8
100
15
10
5
0
-5
MUX
PX
10.
8.33
6.67
5.00
3.33
1.67
0
If the objective is
PX = $3,utility
the
toFor
maximize
MUX prices,
per dollar
given
spent on good
preferences,
and
X is… spend each
budget,
additional $ on the
For PY = $5, the
good that
yields
MUY per dollar
the greater utility
spent on good
for that
Y is…
expenditure.
MUY
PY
Utility Y
Qy
12
1
6
2
4
3
4
2
1.6
0
5
6
TUy MUy
60
90
60
30
110
20
120
10
7
128
128
120
8
0
-8
8
100 - 20
17
Constrained Optimization
Budget = $30
MUX
PX
10.
8.33
$3
$3
6.67
$3
$3
5.00
3.33
1.67
0
$3





if
if
MUX
PX
MUX
PX
>MU
P
Y
Y
, BUY X !
<P
MUY , BUY Y !
Y
Continue to maximize the MU
per $ spent until the budget
of $30 has been spent.
MUY
PY



$5
$5
$5
12
6
4
2
1.6
0
18
Constrained Optimization
 If MUx/Px > MUy/Py then an additional
dollar spent on good X increases TU by
more than an additional dollar spent on
good Y.
 If MUx/Px < MUy/Py then an additional
dollar spent on good X increases TU by
less than an additional dollar spent on
good Y.
19
Constrained Optimization
 When the entire budget is spent, if
MUx/Px > MUy/Py, then one should buy
more X and less Y.
 When the entire budget is spent, if
MUx/Px < MUy/Py, then one should buy
less X and more Y.
 When the entire budget is spent, if
MUx/Px = MUy/Py, then one has
“maximized utility subject to the budget
constraint”.
20
Constrained Optimization
MUx/Px = MUy/Py
is an equilibrium condition
for individual choice.
21
MUX
MUY subject to the constraint:
=
PX
PY
PX X + PY Y = I
insures the individual has maximized their total utility and
has not spent more on the two goods than their budget.
This model can be expanded to include as many goods as
necessary:
MUX
MUY
MUZ
=
=
= . . . . . . . = MUN
PX
PZ
PY
PN
subject to
PX X + PY Y + Pz Z + . . . + PN N = I
22
Constructing a Demand Curve
From the information of utility maximization,
given prices and income, one can
construct a demand curve for a good by
varying the price of that good, with other
information held constant (ceteris
paribus).
23
Given preferences, prices [PX = $3, PY = $5] and
budget [$30], the individual’s choices were:
MUX
PX
Five units of X and 3 units of Y were purchased
10.
8.33
$3
$3
6.67
$3
$3
5.00
3.33
1.67
0
$3
Graphically…





PX



.
5
4
PX = 3
MUY
PY
$5
12
$5
6
$5
4
This point lies on the
demand curve for
good X.
2
1
1
2
3
4
55
6
7
2
1.6
0
QX/t
24
MU
MUXX
Now, suppose the price of X [PX ] increases to $5.
The MUx/Px falls, and now at the combination of 5 X
and 3 Y, the MUx/Px < MUy/Py. There is now an incentive
to buy less X and more Y.
PPXX
Choices about spending the $30 are now:
[$3]
[$5]
10. 6
8.33
5
$5
$5
6.67
4
5.00
3
$5
3.33
2
1.671
0 0
MUY
PY



PX
4
3
2
MUX
PX
=
MUY
PY
.
5
1
Demand
That
portion
of demand
between $3 and $5
is mapped!
1
2
3
.



4
5
$5
12
$5
6
$5
4
At PX = $5,
ceteris paribus,
3 units of X are
purchased.
6
7
2
1.6
0
QX/ut
25
Demand
 By continuing to change the price of
good X (and holding all other
variables constant) the rest of the
demand for good X can be mapped.
 All price and quantity combinations
on the demand curve for X are
equilibrium points, or points of
maximized utility for the consumer.
26
By changing the price of the good and holding all
Other variables constant, the demand for the good
can be mapped.
The demand function
is a schedule of the
PX
quantities that
individuals are willing
5
and able to buy at a
4
schedule of prices
3
during a specific
2
period of time,
ceteris paribus.
1
1
2
3
4
5
6
7
QX/t
27
The demand function has a negative slope because of the
income and substitution effects.
Income effect: As the price of a good that you buy increases
and money income is held constant, your real income decreases
and you can not afford
to buy as much as you
PX
could before.
Substitution effect: As
the price of one good rises
relative to the prices of
other goods, you will
substitute the good
that is relatively cheaper
for the good that is
relatively more expensive.
5
4
3
2
1
1
2
3
4
5
6
7 QX/t
28
Elasticity
 Elasticity - measure of responsiveness
 Measures how much a dependent variable
changes due to a change in an
independent variable
 Elasticity = %Δ X / %Δ Y
• Elasticity can be computed for any two
related variables
29
Price Elasticity of Demand
 Can be computed at a point on a demand function or as
an average [arc] between two points on a demand
function
 ep, h, e are common symbols used to represent price
elasticity of demand
 Price elasticity of demand, ε, is related to revenue
• “How will a change in price effect the total revenue?”
is an important question.
30
Price Elasticity of Demand
 The “law of demand” tells us that as the price of
a good increases the quantity that will be
bought decreases but does not tell us by how
much.
 The price elasticity of demand, ε, is a measure
of that information
 “If you change price by 5%, by what percent
will the quantity purchased change?
31
Price Elasticity of Demand
ε 
ε=
At a point on a demand
function this can be
calculated by:
%DQ
%DP
QQ
2 2--Q
Q1 1= D Q
Q1
PP22-- PP11 = D P
P1
=
DQ
Q1
DP
P1
=(ΔQ/ΔP) x (P1/Q1)
32
using our formula,
For a simple demand function: Q = 10 - 1P
price
quantity
$0
10
$1
9
$2
8
$3
7
$4
6
$5
5
$6
4
$7
3
$8
2
$9
1
$10
0
ep
0
-.11
-.25
-.43
-.67
-1.
-1.5
-2.3
-4.
-9
undefined
Total
Revenue
ε =
DQ
P1
D P * Q1
the slope is -1, price is 7
P71
DQ
ε = (-1) * Q1 = -2.3
3
DP
at a price of $7, Q = 3
Calculate
Q=1
ε
at P = $9
ε = (-1)
9
1
= -9
Calculate ε for all other
price and quantity
combinations.
33
For a simple demand function: Q = 10 - 1P
price
quantity
$0
10
$1
9
$2
8
$3
7
$4
6
$5
5
$6
4
$7
3
$8
2
$9
1
$10
0
ep
0
-.11
-.25
-.43
-.67
-1.
-1.5
-2.3
-4.
-9
undefined
Total
Revenue
0
Notice that at higher prices
the absolute value of the price
elasticity of demand, ε, is
greater.
Total revenue is price times
quantity; TR = PQ.
Where the total revenue [TR]
is a maximum, ε  is equal
to 1
9
16
21
24
25
24
In the range where ε< 1, [less
than 1 or “inelastic”], TR increases as
price increases, TR decreases as P
decreases.
21
16
9
0
In the range where ε> 1,
[greater than 1 or “elastic”], TR
decreases as price increases, TR
increases as P decreases.
34
Graphing Q = 10 - P,
TR is a maximum
where ep is -1 or TR’s
slope = 0
Price
When ε is -1 TR is a maximum.
When | ε | > 1 [elastic], TR and P
move in opposite directions. (P has
a negative slope, TR a positive slope.) 10
The top “half” of the demand
function is elastic.
| ε | > 1 [elastic]
ε = -1
When | ε | < 1 [inelastic], TR and P
move in the same direction. (P and TR 5
both have a negative slope.)
Arc or average ε is the average
elasticity between two point [or prices]
point
ε is the elasticity at a point or price.
TR
|ε|<1
inelastic
5
10 Q/t
The bottom “half” of the demand
Price elasticity of demand describes function is inelastic.
how responsive buyers are to change
in the price of the good. The more “elastic,” the more responsive to DP.
35
Use of Price Elasticity
 Ruffin and Gregory [Principles of Economics,
Addison-Wesley, 1997, p 101] report that:
|ε| of gasoline is = .15 (inelastic)
long run |ε| of gasoline is = .78 (inelastic)
short run |ε| of electricity is = . 13 (inelastic)
long run |ε| of electricity is = 1.89 (elastic)
• short run
•
•
•
 Why is the long run elasticity greater than short
run?
 What are the determinants of elasticity?
36
Determinants of Price Elasticity
 Availability of substitutes
• greater availability of substitutes makes a good more
elastic
 Proportion of budget expended on good
• higher proportion – more elastic
 Time to adjust to the price changes
• longer time period means more adjustments possible
and increases elasticity
 Price elasticity for “brands” tends to be
more elastic than for the category
37