Transcript Chapter 15: Financial Markets and Expectations

Managerial Economics
in a Global Economy
Chapter 3
DEMAND THEORY
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
The Market Demand Curve
Shows the total quantity of the good that would be purchased at
each price.
Industry and Firm Demand Functions
e.g., the demand for computers:
Q = b1P + b2I + b3S + B4A;
P = price of personal computers
I = per capita disposable income
S = price of software
A = advertising
It is necessary to obtain numerical estimates of the b’s
(parameters) of the demand function.
e.g.,
Q = -700P + 200I -500S + 0.01A;
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University

Interpretation:
one KD  in the price of computers  700 units decrease in the quantity
demanded ... etc.
Suppose that I = 13000, S = 400, A = 50 000 000
the market demand curve will be
Q = -700P + 200(13000) - 0.01(50 000 000)
Hence
Q = 29 000 000 – 700P;
and;
P = 4143 - 0.001429Q; (the inverse demand function)

shits in the demand:
Suppose that the price of software falls from 400 to 200
Q = 3 000 000 - 700P;
and
P = 4286 - 0.001429Q;
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University

The Price Elasticity of Demand
The sensitivity of quantity demanded to price (measured by the percentage in
quantity demanded resulting from a 1 percent change in price) more
precisely:
   Q . P ;
P Q
e.g.,
 = 1.3 (note the sign is not negative)
a 1%  in the price of computers  1.3%  in the quantity demanded.
Point and Arc Elasticities
- Point elasticity
   Q  P ;
Q
P
e.g.,
P
Q
3
50
4
40
5
3
 changes according to the values of P and Q.
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University

Look at the following calculations of point elasticity:

 = (40-30)/30)/((4-5)/5) = 61.67

 = (30-40)/40)/((5-4)/4) = 61.67 = 3.67

There is a large difference between the two elasticities even
though we used the same data. To avoid this difficulty we use
the ARC ELASTICITY OF DEMAND.


Q
P

;
(Q  Q ) / 2 ( P  P ) / 2
1 2
1 2
Hence;   40  3  4  5  7.74
(40  3) / 2 (4  5) / 2
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
Using the demand function to calculate the price elasticity
Q = -700P + 200I -500S + 0.01A;
or
Q = 2 900 000 - 700P
if P = 3000;
Q = 2 900 000 - 700(3000) = 800 000
then calculate:
Q

= -700
P

Hence:    700 3000  2.62

if the price falls to 2000; Q = 1 500 000 and
800000
   700 2000  093
.
1500000
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University

The Income Elasticity of Demand
The percentage change in quantity demanded resulting from a
1% change in consumer’s income.
 Q . I
I I Q


If  I > 0 Normal goods
 [ I > 1 for luxury goods]
 [  I < 1 for necessary goods ]
If  I < 0 Inferior goods

Calculation of Income Elasticity of Demand
e.g.;
if
Qx = 1000 - 0.2Px + 0.5PY + 0.04I;
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
 Q . I
I I Q
= 0.04 I/Q.
If I = 10 000 and Q = 1 700
Then:
 = 0.04(10 000/1 700) = 0.24 ( interpretation )
I

Cross Elasticities of Demand
Goods can be substitutes (fish and meat and poultry)
or complements (cars and petrol)
The cross elasticity of demand is defined as the percentage
change in the quantity demanded of good X resulting from a
1% change in the price of good Y.
Q P
  X. Y
XY P Q
Y
X
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
if
 XY > 0
goods X and Y are classified as substitutes.
 XY < 0 goods X and Y are classified as complements
e.g.,
Qx = 1000 - 0.2Px + 0.5PY + 0.04I;
Q
P
X
 
. Y
XY P Q
Y
X
0.5 . PY/QX
if PY = 500 and QX = 1,500
 XY = 0.5 ( 500/1,500 ) 0.17 (Interpretation)

Advertising Elasticity of Demand
e.g., (PERFUMES). The percentage change in the quantity
demanded resulting from a 1% change in advertising
expenditures.
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University





 Q . A
A A Q
e.g.,
Q = 500 - 0.5P + 0.01I + 0.82A;
 A = 0.82 . A/Q;
if A/Q = KD 2
 A = 0.82(2) = 1.64;

The Constant Elasticity Demand Function
Given:
Q = aP-b1 Ib2 ( non-linear )
if a = 200, b1 = 0.3, b2 = 2;
Q = 200P-0.3 I2 ;
Note that the price elasticity of demand equals b1 (0.3) irrespective of the value
of P or I.
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
Prove.

Q = aP-b1 Ib2

differentiate Q with respect to P;
Q   b aP b11I b2
1
P
= b1 (aP b1I b2 )
P

[note  b aP b11I b2=
1

substitute for Q
=

b1
P
b 1 b2
(aP 1 I )
b
1Q
P
 Q . P  b ; [the price elasticity of demand
P Q 1
Hence:
(constant)]
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University

Similarly
Q  b aP b1I b2 1
I 2
= b2 (aP b1I b2 )
I
=
b
2Q
I

Hence



Q . I  b ; [the income elasticity of demand (constant)]
I Q 2
the multiplicative demand function can be transformed into
linear;
take the logarithms of both sides
log Q = log a - b1 log P + b2 log I;
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
Using Elasticities in Managerial Decision Making.
Some factors that affect the demand are under the control of the firm,
others are not.
The firm can estimate the elasticity of demand with respect to all the
variables that affect the demand, to determine the operational
policies to respond to policies of competing firms.
e.g. if cross elasticity is high, immediate response. If low less urgent
needs to respond.
e.g.;
Suppose that the demand for coffee X is estimated using the
following regression equation:
Qx = 1.5 - 3.0Px - 0.8I + 2.0Py - 0.6Ps + 1.2A
Ps = the price of sugar, Py = the price of coffee Y. A= advertising
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
Suppose that this year’s Px = 2, I = 2.5, Py = 1.8 and A=1
Hence:
Qx = 1.5 -3(2) + 0.8(2.5) + 2(1.8) - 0.6(0.5) +1.2(1) = 2
This means that this year’s sales are 2 million pounds of coffee.
using these information we can calculate various elasticities.
Ep = -3(2/2) = -3
EI = 0.8(2.5/2) 1
EXY = 2(1.8/2) = 1.8
EXS = -0.6(0.5/2) = -0.15
EA = 1.1(1/2) = 0.6
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
We can use these elasticities to forecast the demand for its brand of coffee next
year. e.g.;
Suppose that the firm intends to:

Px by 5% and  A by 12%.
it also expects :

I by 4%,  Py by 7%, and  Ps by 8%.
using estimates of elasticities we can determine sales next year as follows:
Qx = Qx + Qx(Px/Px)Ep + Qx(I/I)EI + Qx(Py/Py)EXY + Qx(Ps/Px)EXS
+ Qx(A/A)EA;
= 2 + 2(5%)(-3) + 2(4%)(1) + 2(7%)(1.8) + 2(-8%)(-0.15) + 2(12%)(0.6) = 2.2.
An increase of 10%
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University
Managerial Economics
Prof. M. El-Sakka
CBA. Kuwait University