Market Demand
99
Market Demand
A. To get market demand, just add up individual demands.
1. add horizontally
2. properly account for zero demands; Figure 15.2.
PRICE
20
15
PRICE
Agent 1's
demand
20
PRICE
Agent 2's
demand
20
15
15
10
10
10
5
5
D1 (p 1)
A
D1 (p 1) + D2 (p 2)
5
D2 (p 2)
x1
Market demand =
sum of the two
demand curves
x1 + x2
x2
B
C
Figure 15.2
Market Demand
100
B. Often think of market behaving like a single individual.
1. representative consumer model
2. not true in general, but reasonable assumption for
this course
C. Inverse of aggregate demand curve measures the
MRS for each individual.
D. Reservation price model
1. appropriate when one good comes in large discrete
units
2. reservation price is price that just makes a person
indifferent
3. defined by u(0; m) = u(1; m p1 )
Market Demand
Agent A's
demand
pA*
Agent B's
demand
.....
pA*
p B*
.....
p B*
xA
A
.....
101
Demand
market
.....
xB
B
xA + xB
C
Figure 15.3
4. see Figure 15.3.
5. add up demand curves to get aggregate demand
curve
Market Demand
102
E. Elasticity
1. measures responsiveness of demand to price
2.
p
dq
= q dp
3. example for linear demand curve
a) for linear demand, q = a bp, so =
bp=q =
bp=(a bp)
b) note that = 1 when we are halfway down
the demand curve
c) see Figure 15.4.
4. suppose demand takes form q
5. then elasticity is given by
= Ap b
b
p
bAp
b
1
= q bAp
= Ap b = b
6. thus elasticity is constant along this demand curve
7. note that log q = log A b log p
8. what does elasticity depend on? In general how
many and how close substitutes a good has.
Market Demand
103
PRICE
|ε| = ∞
|ε| > 1
a/2b
|ε| = 1
|ε| < 1
|ε| = 0
a/2
QUANTITY
Figure 15.4
F. How does revenue change when you change price?
1. R = pq , so R = (p + dp)(q + dq ) = pq + pdq +
qdp + dpdq
2. last term is very small relative to others
3. dR=dp = q + p dq=dp
4. see Figure 15.5.
5. dR=dp > 0 when jej < 1
Market Demand
104
PRICE
q∆p
p + ∆p
∆p∆q
p
p∆q
q + ∆q
q
QUANTITY
Figure 15.5
G. How does revenue change as you change quantity?
1. marginal revenue = MR = dR=dq = p +
q dp=dq = p[1 + 1=].
2. elastic: absolute value of elasticity greater than 1
3. inelastic: absolute value of elasticity less than 1
4. application: Monopolist never sets a price where
jj < 1 --- because it could always make more
money by reducing output.
Market Demand
105
H. Marginal revenue curve
1. always the case that dR=dq = p + q dp=dq .
2. in case of linear (inverse) demand, p = a
bq,
MR = dR=dq = p bq = (a bq) bq = a 2bq.
I. Laffer curve
1. how does tax revenue respond to changes in tax
rates?
2. idea of Laffer curve: Figure 15.8.
TAX
REVENUE
Maximum
tax revenue
Laffer curve
t*
1
TAX RATE
Figure 15.8
Market Demand
106
3. theory is OK, but what do the magnitudes have to
be?
4. model of labor market, Figure 15.9.
BEFORE
TAX
WAGE
S
Supply of labor
if taxed
S'
Supply of labor
if not taxed
Demand
for labor
w
L
L'
LABOR
Figure 15.9
5. tax revenue
= T = twS
(w(t))
(1 t)w
6. when is dT=dt < 0?
where
w(t) =
Market Demand
107
7. calculate derivative to find that Laffer curve will
have negative slope when
dS w > 1 t
dw S
t
is :50, would need
8. so if tax rate
labor supply
elasticity greater than 1 to get Laffer effect
9. very unlikely to see magnitude this large