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Price Elasticity of Demand 

 

 

The following was implemented in Maple by Marcus Davidsson (2009)

davidsson_marcus@hotmail.com
 

 

 

 

 

 



We basically have two different types of demand function:
 



1) A constant price elasticity demand function           2) A non-constant price elasticity demand function 

 

 

 

 

 

We can plot the two versions as follows: 

 

 

 

 

Demand Curve with Constant
Price Elasticity of Demand (Iso-Elastic)  

Demand Curve with Non Constant
Price Elasticity of Demand  (Linear Demand Curve) 










 

Plot_2d  
 

 

 

 

 










 

Plot_2d  
 

 

 

 

 

 

 

Now the price elasticity of demand for the two demand functions are defined as:  

 

 

 

 

 

Price Elasticity of Demand  

Demand Curve with Constant Price Elasticity of Demand (Iso-Elastic)  

Demand Curve with Non Constant Price Elasticity of Demand (Linear Demand Curve) 

 

 

 

Formula 

 

 




 

 

 

Typesetting:-mprintslash([`assign`(Q, `*`(a, `*`(`^`(P, epsilon))))], [`*`(a, `*`(`^`(P, epsilon)))])
Elasticity = epsilon (1)
 

 

 




 

 

 

Typesetting:-mprintslash([`assign`(Q, `+`(a, `*`(b, `*`(P))))], [`+`(a, `*`(b, `*`(P)))])
Elasticity = `/`(`*`(b, `*`(P)), `*`(`+`(a, `*`(b, `*`(P))))) (2)
 

 

 

Interpretation 

 

 

If we increase price with 1% then demand will decrease with %  

 

 

If we increase price with 1% then demand will decrease with %  

 

 

 

 

 

We now confirm the above reasoning by some simulations: 

 

 

 

 

We start with the demand curve with constant price elasticity of demand 

 

 

































 

 

 

 

 

`Price Last Period` = 92.51775187
`Demand Last Period` = 1.080873648

Plot_2d Plot_2d

 
 

 

 

 

 

 

 

 

We can now illustrate the demand curve with non-constant price elasticity of demand 

 

 

 

 

































 

 

 

 

 

`Price Last Period` = 92.51775187
`Demand Last Period` = 7.48224813

Plot_2d Plot_2d

 
 

 

 

 

 

 

We can also show that the percentage change on quantity demanded due to a 1% change in price is indeed equal to the 

 

price elasticity of demand as follows: 

 

 

 
































 

 

 

 

 

`Price Last Period` = 92.51775187
`Demand Last Period` = 7.48224813

Plot_2d Plot_2d

 
 

 

 

 

 

 

 

We can further illustrate the demand curve with constant price elasticity as follows: 

 

 

 

 

 

Demand Curve with Constant Price Elasticity of Demand (Iso-Elastic)  

 

CodeEditor-Buttonrestart:  

 

 

           
          Elasticity Parameter ε  =  Embedded component
 

 

Embedded component 

 

 

Embedded component 

 

 

 

 

   
 

 

 

We can further illustrate the demand curve with non constant price elasticity as follows: 

 

 

 

 

                                            

Demand Curve with Non Constant Price Elasticity of Demand (Linear Demand Curve)     

 

CodeEditor-Buttonrestart:  

      

         
  Slope Parameter b  =  Embedded component 

 

 

        Embedded component 

 

      

 

Embedded component