DEMAND FUNCTION AND DEMAND CURVE

1
DEMAND FUNCTION AND DEMAND CURVE Note The
students may refer to Managerial Economics by
E.J.Dauglas for details    
2
DEMAND FUNCTION REFERS TO THE RELATIONSHIP THAT
EXISTS BETWEEN THE QUANTITY DEMANDED OF A
PARTICULAR PRODUCT AND ALL DETERMINANTS OF
DEMAND.THE DEMAND CURVE REFERS TO THE
RELATIONSHIP THAT EXISTS BETWEEN THE QUANTITY
DEMANDED OF A PARTICULAR PRODUCT AND THE PRICE OF
THAT PRODUCT WITH ALL OTHER INFLUENCING FACTORS
HELD CONSTANT.   THUS, THE DEMAND CURVE IS A
SUBSET OF DEMAND FUNCTION WHERE CETERIS PARIBUS
APPLIES ALL THE INDEPENDENT VARIABLES EXCEPT
PRICE. THE DETERMINANTS OF DEMAND FOR A
PRODUCT Qx ƒ (Px, Ax, Dx, Ox, Ic, Tc, Ec, Py,
Ay, Dy, Oy, G, N, W, .)   STRATEGIC
CONSUMER COMPETITOR
OTHER VARIABLES VARIABLES VARIABLES
VARIABLES   CONTROLLABLE UNCONTROLLABLE
VARIABLES VARIABLES
3
WHERE Qx IS THE QUANTITY DEMANDED OF PRODUCT X,
PER PERIOD Px IS THE PRICE OF PRODUCT X Ax
IS ADVERTISING/PROMOTION FOR PRODUCT X Dx IS
DESIGN/STYLE/QUALITY OF PRODUCT X Ox IS OUTLETS
FOR DISTRIBUTION OF PRODUCT X Ic IS INCOMES
OF CONSUMERS/CUSTOMERS/CLIENTELE Tc IS TASTES
AND PREFERE ICE PATTERNS OF CUNSUMERS Ec IS
EXPECTATIONS OF CONSUMERS REGARDING FUTURE
PRICES, ETC. Py IS PRICES OF RELATED GOODS
(SUBSTITUTES, COMPLEMENTARIES) Ay IS
ADVERTISING/PROMOTION FOR RELATED GOODS Dy IS
DESIGN/STYLE/QUALITY OF RELATED GOODS Oy IS
COMPETITOR DISTRIBUTION OUTLETS G IS
GOVERNMENT POLICY, INDUSTRIAL STRATEGY N IS
NUMBER OF PEOPLE IN THE ECONOMY W IS WEATHER
CONDITIONS
4
FORM OF DEMAND FUNCTION COULD BE A)
ADDITIVE B) MULTIPLICATIVE
A) Qx ? ?1Px ?2Py ?3Ax ?4Ay ?5Ic
?6Tc ?7Ec ?8N (1)
B) Qx ? Px?1 Py?2 N3 O?4 (2)
Log QX Log ? ?1 Log Px ?2 Log Py ?3 Log
N ?4 Log O (3)
EXAMPLE SUPPOSE THE ESTIMATED DEMAND
FUNCTION IS AS FOLLOWS
Qx 5030 - 3,806 Px 1,458 Py 256.6 Ax -
32.3 Ay 0.18 Ic (4)
GIVEN THIS PREDICT THE SALE VOLUME/LEVEL
WHEN Px 8, Py 6, Ax 168 (THOUSAND) Ay
182 AND Ic 12875
SUBSTITUTING THESE VALUES IN THE ABOVE EQUATION
QUANTITY DEMANDED OF THE PRODUCT WILL BE 22,879.1
UNITS.
5

• THE DEMAND CURVE FOR THE MARKET CAN BE DERIVED
  FROM
• THE DEMAND FUNCTION.
•  
• DEMAND CURVE IS A SPECIAL SUBCASE OF THE DEMAND
  FUNCTION.
• CETERIS PARIBUS APPLIES TO ALL INDEPENDENT
  VARIABLES EXCEPT THE PRICE OF THE PRODUCT IN
  QUESTION.

CONSIDER THE EARLIER DEMAND FUNCTION i.e.. Qx
? ?1Px ?2Py ?3Ax ?4Ay ?5Ic ?6Tc
?7Ec ?8N (5) LET ALL OTHER VALUES INCLUDING
THE ? REMAIN CONSTANT AND WE AGGREGATE THEM TO A
SINGLE TERM i.e. A AND EXPRESS THE DEMAND
FUNCTION AS   Qx A ?1Px Where A ? ?2Py
?3Ax ?4Ay ?5Ic ?6Tc ?7Ec ?8N  IN
SUCH A SITUATION Qx A ?1Px IS THE DEMAND
CURVE (6)
6
CONVENTIONAL USE OF DEPENDENT AND INDEPENDENT
VARIABLES IN GRAPHICAL ANALYSIS IS TO REPRESENT
THE DEPENDENT VRIABLE (Y) ALONG THE VERTICAL AXIS
AND THE INDEPENDENT VARIABLE (X) ALONG THE
BORIZONTAL AXIS.
BUT IN ALL GRAPHICAL ANALYSIS RELATING TO Px AND
Qx, THE ORDER IS REVERSED i.e. PRICE IS
PRESENTED ALONG THE VERTICAL AXIS AND Qx ALONG
THE HORIZONTAL AXIS. (AFTER ALFRED MARSHALL)
LET Px a b1Qx (7)   WE HAD THE DEMAND
CURVE AS Qx A ?1Px (8)   OR Px -
A/?1 1/?1 Qx   ? a - A/?1 AND ?1
1/?1
7
CONSIDERING THE INVERSE RELATIONSHIP BETWEEN Qx
AND Px IN 8, THE SIGN OF a INEqn 7 WILL BE A
POSITIVE ONE AND THAT OF b, WILL BE A NEGATIVE
ONE.   EXAMPLE THE NUMERICAL EXAMPLE Eqn (4)
WITH VALUES OF THE INDEPENDENT VARIABLES

• (5030) OTHER TERMS EXCEPT Px WILL GIVE A
  53,328.7
• THUS, THE DEMAND CURVE WILL BE Qx 53,328.7 -
  3,806.2 Px
•  
• OR CONVERTING THE UNITS IN TO- '000 Qx 53.3287
  - 3.8062 Px
•  
• TO GET Px a bQx WE HAVE Px 14.011 -
  0.26273 Qx

8
THE DEMAND CURVE FOR X CAN BE REPRESENTED IN A
DIAGRAM AS FOLLOWS
Y
D
PRICE
D
O
X
DEMAND
LAW OF DEMAND   LAW OF DEMAND STATES THAT AS
PRICE IS RAISED THE CONSUMER DEMANDS
PROGRESSIVELY LESS OF A PRODUCT, AND CONVERSELY,
AS PRICE IS REDUCED THE CONSUMER DEMANDS
PROGRESSIVELY MORE OF A PRODUCT, CETERIS
PARIBUS.
9

• ? THE LAW OF DEMAND IS AN EMPIRICAL LAW,
  MEANING THAT IT IS COMMONLY OBSERVED IN
  PRACTIVE.
• ? IT IS EXPRESSED GRAPHICALLY AS A NEGATIVELY
  SLOPING LINE RELATING PRICE TO UNITS OF
  QUANTITY DEMANDED.
• ? THE ACTUAL DATA THAT UNDERLIE THE DEMAND CURVE
  DEPENDS ON INDIVIDUALS REACTION TO CHANGE IN
  PRICE.
• INDIVIDUAL DEMAND CURVE MAY NOT BE THE SAME
• DEPENDS ON SEVERAL FACTORS FOR INDIVIDUAL
• REACTION. (CURVATURE OF I.C.s.)

MOVEMENT ALONG A DEMAND CURVE AND SHIFT IN THE
DEMAND CURVE CAN BE SHOWN IN THE FOLLOWING
DIAGRAMS.
10
MOVEMENT ALONG THE DEMAND CURVE SHIFT IN THE
DEMAND CURVE
 
PX
PX
D
D
PRICE
PRICE
P2
P1
D
D
Q2
Q1
QX
DEMAND
QX
Q1
Q2
DEMAND