Elasticity Of Demand

Definition:

Elasticity  means responsiveness.  Thus, elasticity of demand means the responsiveness of demand due to some changes to the factors which influence demand.

There three types of elasticity of demand:

1.     Price Elasticity of Demand  (PED)  - (E_d)

2.     Income Elasticity of Demand (IED) - (E_I)

3.     Cross Elasticity of Demand (CED) - (E_c)

1.   Price Elasticity of Demand  (PED) 

     

     a.  Definition of PED:

It measures the responsiveness of quantity demanded  due to a change in its price.

      b. Formula :                     

          i.   E_d   =      % ∆ in Qty demanded for product A      (Percentage Method)

                             % ∆ in price for product A

               E_d   =     % ∆Q

                             % ∆P

Note:                     The following are the steps to convert from percentage method to proportionate method:

                             ∆Q × 100%

                             q₀ 

                   =       _________                           

                             ∆P × 100%

                             p₀        

                 E_d =          ∆Q× p₀                                     

                                ∆P     q₀

           ii.   E_d  =     ∆Q × p₀                                         (Proportionate Method)

                           ∆P     q₀

                            

                 E_d =        (q₁− q₀)× p₀                                     absolute value

                               (p₁ − p₀)   q₀

                  

            iii.   E_d  =    dQ ×  p₀                                          (Point Method)

                           dP     q₀

            iv.    Ed =      ∆Q × (p1 +  p0)/2                 (Arc Elasticity or average method)

                              ∆P     (q1 + q0)/2  

Note:         All answers must be for PED must be converted by the absolute value to turn it to positive.

Example 1:

           

            If the price of product Y has increased by 10% then the quantity demanded has decreased by 20%. Calculate the price elasticity of demanded when price increases.

                   % ∆P  =    10%

                   % ∆Q =  −20%

                  

                   E_d   = % ∆Q

                             % ∆P

                   E_d   = −20%

                               10%

 

                   E_d   =   −2                                absolute value     

                   E_d   =   2           (Since  1<E_d  < ∞ , the demand is elastic)

           

Example 2:

            Given the price of product X is RM 4 and the quantity demanded is 12 units. When the price of product X increases to RM 5 the quantity demanded is 6 units. Calculate the price elasticity of demanded when price increases.

                   p₀ =  RM4   q₀   =  12

                   p₁ =  RM5   q₁  =  6

                    

                 E_d  =     ∆Q × p₀                                          (Proportionate Method)

                             ∆P     q₀

                            

                 E_d  =      (q₁− q₀) × p₀           

                             (p₁ − p₀)    q₀

                                    =          (6 − 12)  ×  4  

                              (5 − 4)       12

                      =    − 6 ×  1

                                1      3

 

                      =          − 2

                E_d   =  2          (Since  1<E_d  < ∞ , the demand is elastic)

c.  Objective for PED or Degrees of  PED:

Once we have calculated the PED then we need to interpret the coefficient value. For PED coefficient there are degrees of PED :

·        Elastic Demand   ,  (1<E_d  < ∞)  or ( E_d  > 1)

·        Inelastic Demand ,  (0< E_d  < 1) or  ( E_d  < 1)

·        Unitary Elastic Demand ,  ( E_d  = 1)

·        Perfectly Inelastic Demand , (  E_d  = 0)

·        Perfectly Elastic Demand , (  E_d  = ∞)

           

2.       Income Elasticity of Demand (IED)

          a.  Definition of IED:

                   It measures the responsiveness of quantity demanded  due to a change in consumer’s income.

            b. Formula :               

             i.   E_d   =      % ∆ in Qty demanded                     (Percentage Method)

                             % ∆ in Income      

                  E_d   =  % ∆Q         Note : I’m using notation I for Income but the

                             % ∆I                           manual is using Y.

Note:                  The following are the steps to convert from percentage method to proportionate method:

                             ∆Q × 100%

                               I₀ 

                   =       _________                           

                             ∆P× 100%

                               I₀        

                   =        ∆Q× I₀                                          

                             ∆I     q₀

            ii.    E_d  =   ∆Q× I₀                                 (Proportionate Method)

                             ∆I     q₀

                            

                 E_d   =   (q₁− q₀)× I₀                          

                             (I₁ − I₀)   q₀

iii.        E_d  =   dQ× I₀                                (Point Method)

                               dI     q₀
b.  Objective for IED:

          Is to identify the types of good.

                                                  Luxury Goods, if  (E_I  > 1)

                                                    i.e  antique furniture, antique cars

          i.        Normal Goods        Necessity Goods, if  (0< E_I  =< 1)

                                                    i.e   clothings, shoes.

         (Note : As income  increased , the quantity demanded will also increased.)

          ii.       Inferior Goods         (E_I  < 0)

                   (Giffen Goods)

                                                 i.e  low-grade rice, black&white TV, secondhand clothings

         (Note : As income  increased , the quantity demanded will also decreased.)

          iii.      Essential Goods         (E_I  = 0)

                                             i.e   Insulin for diabetic patient

                   (Note : As income  increased , the quantity demanded no changed.)

c.       Example 1 :

          Given the consumer’s income increased by 10% ,  the quantity demanded for houses have increased by 5% . Calculate the income elasticity of demanded for houses when income increases.

                   Given  :       %∆I   =  10%             % ∆Q =  5%

         

          E_I   = % ∆Q          =   5% 

                   % ∆I        10%

          E_I   =   0.5   ( Since 0<E_d=<1 , the good is Necessity good)

         

Example 2:

          Given the following table:

Income ($)	Qty for Good A	Qty for Good B	Qty for Good C
300	20	20	20
400	25	18	20
500	30	15	20
600	35	10	20
700	40	5	20
800	45	0	20

Questions:

          Find the E_I when consumer’s income changes from RM500 to RM600 for good A,B and C respectively. Then determine the type of goods from the above calculation.

Suggested Solutions:

Since we have three (A,B & C) goods, so there should be three calculation to find the E_I  for good A, B & C respectively.

For Good A :        I₀ = RM500 q₀= 30

                             I₁= RM600 q₁ = 35

          E_I   =       ∆Q × I₀                                     (Proportionate Method)

                          ∆I     q₀

                      (35 − 30)      500

                   =                    ×

                     (600− 500)    30

E_I    =   0.833            (Since E_I is  0 < E_I  =< 1, thus the good is a necessity good)

For Good B :        I₀ = RM500 q₀= 15

                             I₁= RM600 q₁ = 10

          E_I   =       ∆Q × I₀                                     (Proportionate Method)

                          ∆I     q₀

                        (10 − 15)       500 

                =                             ×        

                         (600 − 500)      15

          

            E_I   =   −  1.67        (Since E_Iis  E_I  < 0, thus the good is an inferior good)

For Good C :        I₀ = RM500 q₀= 20

                             I₁= RM600 q₁ = 20

          E_I   =       ∆Q × I₀                                     (Proportionate Method)

                          ∆I     q₀

                     (20 − 20)       500 

                =                             ×        

                      (600 − 500)      20

          E_I   =    0    (Since  E_I  is  E_I =  0, thus the good C is an essential good)

3.  Cross Elasticity of Demand (CED)

          a.  Definition of CED:

                   It measures the responsiveness of quantity demanded (i.e  ∆ in Qx)  due to a change in price of related product (∆ in Py).

            b. Formula :               

             i.   E_c   =      % ∆ in Qty  of  X                            (Percentage Method)

                             % ∆ in Price of Y      

                  E_c   =  % ∆Q_x                 

                             % ∆P_y                         

Note:    The following are the steps to convert from percentage method to proportionate method:

                             ∆Q _x × 100%

                               q_x0 

                     =     _________                           

                             ∆P_y × 100%

                              p_y0        

              ii.   E_c   =   ∆Q_x × p_y0                       (Proportionate Method)

                              ∆P_y      q _x0

             iii.   E_c   =   dQ_x × p_y0                        (Point Method)

                              dP_y      q _x0

          c. Objective :

                   It is to establish the relationship between good X and good Y. There are three possibilities of goods:

                   i)  X and Y are substitute goods =>   E_c   =   +(positive value)

Note : As price Py increase, the quantity Qx will also increase.

                   ii) X and Y are complementary goods =>  E_c   = −  (negative value)

                             Note : As price Py increase, the quantity Qx will also decrease.

                   iii) X and Y has no relationship =>   E_c   =   0  (zero value)

                             Note : As price Py increase, there is no effect on Qx.

Examples :

The following table shows the demand for two goods Y and Z, when there is a change in price for good X :

Price of Good X	Qty of Good Y	Qty of Good Z
5	10	5
6	8	8
7	7	10
8	6	14

Questions:

          1. Calculate the CED of good Y when price of good X increased from RM6 to   RM7 per unit.

          2. Calculate the CED of good Z when price of good X increased from RM6 to   RM7 per unit.

Suggested Solutions: 

1.      p_x0  = 6     q _y0  =  8

          p_x1  = 7     q _y1  =  7

          E_c   =        ∆Q _y × p_x0                                      (Proportionate Method)

                       ∆P_x     q _y0

             

                       (7 − 8)          6

                =                             ×        

                        (7 − 6)          8

          E_c   =   −  0.75   (Since  E_c  is  E_c < 0 , thus as P_x  increased the Q _y  will                       decreased which mean Good X & Y are complementary goods)

2.       p_x0  = 6     q _z0  =  8

           p_x1  = 7     q _z1  = 10

          E_c   =        ∆Q _z × p_x0                                      (Proportionate Method)

                       ∆P_x      q_z0

                       (10 − 8)         6

                =                             ×        

                          (7 − 6)        8

           E_c   =    1.5      (Since  E_c  is  E_c > 0 , thus as P_x  increased the Q _y  will                                  increased which mean Good X & Z are substitute goods)