PBUY
Chapter
3 : DEMAND THEORY
I. Demand Function
Demand
function can be of different forms. In this topic, we will focus on linear
demand function. A basic linear demand function is in the form of
Qx = a - b1Px + b2Py + b3Y
From this
demand function, we can see that quantity demanded for good x depends on
factors like price of good x (Px), price of good y (Py)
and income (Y), where a, b1, b2 and b3 are constant values.
For many
purposes, it is useful to focus on the relationship between quantity demanded and
the price of good or service while holding other variables constant. Hence, the
demand function can be written as
Qx = a - b1Px
This demand
function can be rewritten so that P becomes the subject or in other words, the
conventional way of writing the demand curve function:
Qx = a - b1Px
b1Px = a - Qx
Px = (a/
b1) - (1Qx / b1)
Example: Qx = 20 - 2Px
2Px = 20 - Qx
Px = 20/2 - 1/2Qx
Px = 10 - 0.5Qx
II. The Market Demand
If
you are given individual demand functions and you want to develop the market demand function, you need to
add those individual demand functions.
Give three
individual demand :
Q1 = a1 - b1P1
Q2 = a2 - b2P2
Q3 = a3 - b3P3
To get
market demand, we must make the following assumption:
Let Pm = P1 = P2 = P3 where Qm
= Q1 + Q2 + Q3
Example:
The
followings are individual demand functions for books for three individuals.
Q1 = 25 - 2.50P1
Q2 = 35 - 0.25P2
Q3 = 20 - 1.25P3
The market
demand function, assuming that there are only three individuals in the market,
so we let Pm = P1 = P2 =
P3 where
Qm = Q1 + Q2 + Q3
Qm = (25 -
2.50P1) +
(35 - 0.25P2
) +
(20 - 1.25P3
)
Qm = (25
- 2.50Pm) + (35
- 0.25Pm) + (20
- 1.25Pm )
Qm = 80
- 4Pm
III. Total, Marginal and Average Revenue
a) Total
Revenue, TR = Price,
P x Quantity, Q
Example:
P = 8.5 - 0.5Q
TR = P x Q
TR = 8.5Q - 0.5Q2
(Total
Revenue function must be in the form of Q)
b) Marginal
Revenue, MR = dTR/dQ
Example:
TR = 8.5Q - 0.5Q2
MR = dTR/dQ = 8.5 - Q
c) Average
Revenue, AR = TR/Q
Example:
TR = 8.5Q - 0.5Q2
AR = TR/Q = 8.5 - 0.5Q
IV. Elasticity
a) Price elasticity of demand
It measures the responsiveness of
demand when price changes.
Ed = dQ x P
dP Q
Ed > 1 à elastic (sensitive to price change)
Ed < 1 à inelastic (not very sensitive to price
change)
Ed = 1 à unitary elastic (proportionately sensitive
to price change)
Ed = 0 à perfectly inelastic (not sensitive to
price change)
Ed = ∞ à perfectly elastic (very sensitive to price
change)
Example :
Given Q = 60
– 4P + 10Y and initial values P = 2.5 and Y = 5
Ed
= Q x P
P
Q
Find Q and
Q :
P
Q = –
4
P
and Q =
60 – 4P + 10Y
Q = 60 – 4(2.5) + 10(5)
Q = 100
Ey
= (– 4 )
x 2.5_
100
Ey = 0.1
, since 0 < Ed < 1 à Demand is inelastic
Elasticity
Vs Total Revenue
Change
in Price Elasticity Change In
TR
1. P ↓ Elastic
Demand TR ↑
2. P ↑ Elastic
Demand TR ↓
3. P ↑ or ↓ Unitary
Elastic Demand TR(no change)
4. P ↓ Inelastic
Demand TR ↓
5. P ↑ Inelastic
Demand TR ↑
(Note:
Further explanation on the relationship between Ed and TR , please refer to study manual, page 104 –
105.)
b) Income Elasticity
It measures the responsiveness of
demand to changes in income.
Ey = dQ x Y
dY Q
Ey < 0 à the good is an inferior good
Ey > 1 à the good is a luxury good
0 < Ey ≤ 0 à the good is a necessity good
Example :
Given Q = 60
– 4P + 10Y and initial values P = 2.5 and Y = 5
Ey = Q x Y
Y
Q
Find Q and
Q :
Y
Q =
10
Y
and Q =
60 – 4P + 10Y
Q = 60 – 4(2.5) + 10(5)
Q = 100
Ey
= (10) x 5_
100
Ey = 0.5
, since 0 <
Ey ≤ 0 it is
a necessity good
c) Cross Elasticity
It measures
the responsiveness of demand to changes in price of other goods.
Ec = dQx x Py
dPy Qx
Ec > 0 à the two products x and y are substitutes
Ec < 0 à the two products x and y are complements
Ec = 0 à there is no relationship between the two products.
Example :
Given Qx =
20 – 4Px + 5Py + 10Y and initial values Px = 2.5, Py = 3 and Y = 2
EC = Qx x Py0
Py
Qx0
Find Qx and
Q :
Py
Qx =
5
Py
and Q =
20 – 4P + 5Py + 10Y
Q = 20 – 4(2.5) + 5(3) +
10(2)
Q = 45
EC = (5
) x
3_
45
Ey = 0.33
, since Ec > 0 , products x and y are substitutes
Exercise:
1. The demand equation faced by DuMont
Electronics for its personal computers is given
by P = 10,000 – 4Q.
a) Derive
the total revenue function.
b) Derive
the marginal revenue function.
c) At
what price and quantity will marginal revenue be zero?
d) At
what price and quantity will total revenue be maximized?
e) If
price, P = RM6,000, calculate the price elasticity of demand for the product.
2. Golden Bake is involved with the
production of pies. Its demand function has been estimated as follows:
Qb = -28.60 + 0.24A
+ 45.20Ps – 38.80Pb
Qb =
the demand for Golden Bake pies.
A = Advertising expenditure
Ps = the price of competitor’s pie per unit
Pb = the price of Golden-Bake’s pie per unit
a) Derive
the conventional demand curve function in the form of Q = a – bP, given that Ps
= 0.85 and A = 210.
b) Derive
the total revenue function.
c) Calculate
the sales-revenue maximizing price for Golden Bake.
d) What
is the maximum total revenue it can earn?
(APR
2002/ECO555/510/465/550)
3. Demand for softback managerial economics
text is given by Q = 20,000 – 300P. The book is initially priced at RM30.
a) Compute
the point price elasticity of demand at P = RM30.
b) If
the objective is to increase total revenue, should the price be increased or decreased? Explain.
life priced,do not fight,peace no war
Tiada ulasan:
Catat Ulasan