The Market
Molly W. Dahl
Georgetown University
Econ 101 – Spring 2009
1
Economic Modeling

Construct a model
 Choose

simplifications
Solve the model
 Come
up with a prediction
 Set S = D, etc.

Evaluate the model
 Was
it too simple?
 Do we learn anything about the real world?
2
Modeling the Apartment Market
How are apartment rents determined?
 Suppose

 apartments
are close or distant, but
otherwise identical
 distant apartments rents are exogenous
(determined outside the model) and known
 many potential renters and landlords
3
Modeling the Apartment Market
Who will rent close apartments?
 At what price?
 Will the allocation of apartments be
desirable in any sense?


How can we construct an insightful model
to answer these questions?
4
Economic Modeling
Assumptions

Two basic assumptions:
 Rational
Choice: Each person tries to choose
the best alternative available to him or her.
 Equilibrium: Market price adjusts until
quantity demanded equals quantity supplied.
5
Modeling Apartment Demand
Demand: Suppose the most any one
person is willing to pay to rent a close
apartment is $500/month. Then
p = $500  QD = 1.
 Suppose the price has to drop to $490
before a 2nd person would rent. Then
p = $490  QD = 2.

6
Modeling Apartment Demand
The lower is the rental rate p, the larger is
the quantity of close apartments
demanded
p   QD .
 The quantity demanded vs. price graph is
the market demand curve for close
apartments.

7
Market Demand Curve for
Apartments
8
Market Demand Curve for
Apartments
p
QD
9
Modeling Apartment Supply

Supply: It takes time to build more close
apartments so in this short-run the quantity
available is fixed (at say 100).
10
p
Market Supply Curve for
Apartments
100
QS
11
Competitive Market Equilibrium
“low” rental price  quantity demanded of
close apartments exceeds quantity
available  price will rise.
 “high” rental price  quantity demanded
less than quantity available  price will
fall.

12
Competitive Market Equilibrium

Quantity demanded = quantity available
 price will neither rise nor fall
 so
the market is at a competitive equilibrium.
13
Competitive Market Equilibrium
p
pe
100
QD,QS
14
Competitive Market Equilibrium





Q: Who rents the close apartments?
A: Those most willing to pay.
Q: Who rents the distant apartments?
A: Those least willing to pay.
So the competitive market allocation is by
“willingness-to-pay”.
15
Comparative Statics

What is exogenous in the model?
 price
of distant apartments
 quantity of close apartments
 incomes of potential renters.

What happens if these exogenous
variables change?
16
Comparative Statics
Suppose the price of distant apartment
rises.
 Demand for close apartments increases
(rightward shift), causing

a
higher price for close apartments.
17
Market Equilibrium
p
pe
100
QD,QS
18
Market Equilibrium
p
Higher demand
pe
100
QD,QS
19
Market Equilibrium
p
Higher demand causes higher
market price; same quantity
traded.
pe
100
QD,QS
20
Comparative Statics
Suppose there were more close
apartments.
 Supply is greater, so

 the
price for close apartments falls.
21
Market Equilibrium
p
pe
100
QD,QS
22
Market Equilibrium
p
Higher supply
pe
100
QD,QS
23
Market Equilibrium
p
Higher supply causes a
lower market price and a
larger quantity traded.
pe
100
QD,QS
24
Comparative Statics
Suppose potential renters’ incomes rise,
increasing their willingness-to-pay for
close apartments.
 Demand rises (upward shift), causing

 higher
price for close apartments.
25
Market Equilibrium
p
pe
100
QD,QS
26
Market Equilibrium
p
Higher incomes cause
higher willingness-to-pay
pe
100
QD,QS
27
Market Equilibrium
p
Higher incomes cause
higher willingness-to-pay,
higher market price, and
the same quantity traded.
pe
100
QD,QS
28
Market Equilibrium
p
pe
100
QD,QS
29
Budget Constraints
Molly W. Dahl
Georgetown University
Econ 101 – Spring 2009
30
Consumption Choice Sets
A consumption choice set is the
collection of all consumption choices
available to the consumer.
 What constrains consumption choice?

 Budgetary,
time and other resource
limitations.
31
Budget Constraints
A consumption bundle containing x1
units of commodity 1, x2 units of
commodity 2 and so on up to xn units of
commodity n is denoted by the vector (x1,
x2, … , xn).
 Commodity prices are p1, p2, … , pn.

32
Budget Constraints
Q: When is a bundle (x1, … , xn) affordable
at prices p1, … , pn?
 A: When
p1x1 + … + pnxn  m
where m is the consumer’s (disposable)
income.

33
Budget Constraints

The bundles that are only just affordable
form the consumer’s budget constraint.
This is the set
{ (x1,…,xn) | x1  0, …, xn  and
p1x1 + … + pnxn = m }.
34
Budget Constraints
The consumer’s budget set is the set of
all affordable bundles;
B(p1, … , pn, m) =
{ (x1, … , xn) | x1  0, … , xn 0 and
p1x1 + … + pnxn  m }
 The budget constraint is the upper
boundary of the budget set.

35
x
2
m /p2
Budget Set and Constraint for Two
Commodities
Budget constraint is
p1x1 + p2x2 = m.
m /p1
x1
36
x
2
m /p2
Budget Set and Constraint for Two
Commodities
Budget constraint is
p1x1 + p2x2 = m.
m /p1
x1
37
x
2
m /p2
Budget Set and Constraint for Two
Commodities
Budget constraint is
p1x1 + p2x2 = m.
Just affordable
m /p1
x1
38
x
2
m /p2
Budget Set and Constraint for Two
Commodities
Budget constraint is
p1x1 + p2x2 = m.
Not affordable
Just affordable
m /p1
x1
39
x
2
m /p2
Budget Set and Constraint for Two
Commodities
Budget constraint is
p1x1 + p2x2 = m.
Not affordable
Just affordable
Affordable
m /p1
x1
40
x
2
m /p2
Budget Set and Constraint for Two
Commodities
Budget constraint is
p1x1 + p2x2 = m.
the collection
of all affordable bundles.
Budget
Set
m /p1
x1
41
x
2
m /p2
Budget Set and Constraint for Two
Commodities
p1x1 + p2x2 = m is
x2 = -(p1/p2)x1 + m/p2
so slope is -p1/p2.
Budget
Set
m /p1
x1
42
Budget Constraints

For n = 2 and x1 on the horizontal axis,
the constraint’s slope is -p1/p2. What
does it mean?
p1
m
x2 =  x1 
p2
p2
43
Budget Constraints

For n = 2 and x1 on the horizontal axis,
the constraint’s slope is -p1/p2. What
does it mean?
p1
m
x2 =  x1 
p2
p2

Increasing x1 by 1 must reduce x2 by
p1/p2.
44
Budget Constraints
x2
Slope is -p1/p2
-p1/p2
+1
x1
45
Budget Constraints
x2
Opp. cost of an extra unit of
commodity 1 is p1/p2 units
foregone of commodity 2.
-p1/p2
+1
x1
46
Budget Constraints
x2
Opp. cost of an extra unit of
commodity 1 is p1/p2 units
foregone of commodity 2. And
the opp. cost of an extra
+1
unit of commodity 2 is
-p2/p1
p2/p1 units foregone
of commodity 1.
x1
47
Budget Sets & Constraints;
Income and Price Changes

The budget constraint and budget set
depend upon prices and income. What
happens as prices or income change?
48
How do the budget set and budget
constraint change as income m
x2
increases?
Original
budget set
x1
49
Higher income gives more choice
x2
New affordable consumption
choices
Original and
new budget
constraints are
parallel (same
slope).
Original
budget set
x1
50
How do the budget set and budget
constraint change as income m
x2
decreases?
Original
budget set
x1
51
How do the budget set and budget
constraint change as income m
x2
decreases?
Consumption bundles
that are no longer
affordable.
New, smaller
budget set
Old and new
constraints
are parallel.
x1
52
Budget Constraints - Income
Changes

Increases in income m shift the
constraint outward in a parallel manner,
thereby enlarging the budget set and
improving choice.
53
Budget Constraints - Income
Changes
Increases in income m shift the
constraint outward in a parallel manner,
thereby enlarging the budget set and
improving choice.
 Decreases in income m shift the
constraint inward in a parallel manner,
thereby shrinking the budget set and
reducing choice.

54
Budget Constraints - Income
Changes
No original choice is lost and new choices
are added when income increases, so
higher income cannot make a consumer
worse off.
 An income decrease may (typically will)
make the consumer worse off.

55
Budget Constraints - Price
Changes
What happens if just one price decreases?
 Suppose p1 decreases.

56
How do the budget set and budget
constraint change as p1 decreases from
x2
p1’ to p1”?
m/p2
-p1’/p2
Original
budget set
m/p1’
m/p1
”
x1
57
How do the budget set and budget
constraint change as p1 decreases from
x2
p1’ to p1”?
m/p2
New affordable choices
-p1’/p2
Original
budget set
m/p1’
m/p1
”
x1
58
How do the budget set and budget
constraint change as p1 decreases from
x2
p1’ to p1”?
m/p2
New affordable choices
-p1’/p2
Original
budget set
Budget constraint
pivots; slope flattens
from -p1’/p2 to
-p1”/p2
-p ”/p
1
m/p1’
2
m/p1
”
x1
59
Budget Constraints - Price
Changes

Reducing the price of one commodity
pivots the constraint outward. No old
choice is lost and new choices are added,
so reducing one price cannot make the
consumer worse off.
60
Budget Constraints - Price
Changes

Similarly, increasing one price pivots the
constraint inwards, reduces choice and
may (typically will) make the consumer
worse off.
61
The Food Stamp Program
Food stamps are coupons that can be
legally exchanged only for food.
 How does a commodity-specific gift such
as a food stamp alter a family’s budget
constraint?

62
The Food Stamp Program
Suppose m = $100, pF = $1 and the price
of “other goods” is pG = $1.
 The budget constraint is then
F + G =100.

63
The Food Stamp Program
G
F + G = 100; before stamps.
100
100
F
64
The Food Stamp Program
G
F + G = 100: before stamps.
100
100
F
65
The Food Stamp Program
G
F + G = 100: before stamps.
100
Budget set after 40 food
stamps issued.
40
100 140
F
66
The Food Stamp Program
G
F + G = 100: before stamps.
100
Budget set after 40 food
stamps issued.
The family’s budget
set is enlarged.
40
100 140
F
67
The Food Stamp Program

What if food stamps can be traded on a
black market for $0.50 each?
68
The Food Stamp Program
G
F + G = 100: before stamps.
Budget constraint after 40
food stamps issued.
Budget constraint with
black market trading.
120
100
40
100 140
F
69
The Food Stamp Program
G
F + G = 100: before stamps.
Budget constraint after 40
food stamps issued.
Black market trading
makes the budget
set larger again.
120
100
40
100 140
F
70
Shapes of Budget Constraints
Q: What makes a budget constraint a
straight line?
 A: A straight line has a constant slope and
the constraint is
p1x1 + … + pnxn = m
so if prices are constants then a
constraint is a straight line.

71
Shapes of Budget Constraints
But what if prices are not constants?
 E.g. bulk buying discounts, or price
penalties for buying “too much”.
 Then constraints will be curved or kinked.

72
Shapes of Budget Constraints Quantity Discounts

Suppose p2 is constant at $1 but that
p1=$2 for 0  x1  20 and p1=$1 for x1>20.
73
Shapes of Budget Constraints Quantity Discounts

Suppose p2 is constant at $1 but that
p1=$2 for 0  x1  20 and p1=$1 for x1>20.
Then the constraint’s slope is
- 2, for 0  x1  20
-p1/p2 =
- 1, for x1 > 20
and the constraint is
{
74
Shapes of Budget Constraints with a
Quantity Discount
x2
m = $100
Slope = - 2 / 1 = - 2
100
(p1=2, p2=1)
Slope = - 1/ 1 = - 1
(p1=1, p2=1)
20
50
80
x1
75
Shapes of Budget Constraints with a
Quantity Discount
x2
m = $100
Slope = - 2 / 1 = - 2
100
(p1=2, p2=1)
Slope = - 1/ 1 = - 1
(p1=1, p2=1)
20
50
80
x1
76
Shapes of Budget Constraints with a
Quantity Discount
x2
m = $100
100
Budget Constraint
Budget Set
20
50
80
x1
77
Shapes of Budget Constraints with a
Quantity Penalty
x2
Budget
Constraint
Budget Set
x1
78