Relationship between AR, MR and Price Elasticity of Demand
As we know that 𝑄 = 𝑓(𝑃)
Where, 𝑄 =Quantity Demand and 𝑃 = Price
And also we know that,
(1) 𝑃𝑟𝑖𝑐𝑒 𝐸𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦 𝐸 = × (Percentage method)
(2) 𝑃𝑟𝑖𝑐𝑒 𝐸𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦 𝐸 = × (Mid-point method)
Now,
𝑇𝑜𝑡𝑎𝑙 𝑅𝑒𝑣𝑒𝑛𝑢𝑒 (𝑇𝑅) = 𝑃 × 𝑄
𝑑𝑇𝑅 𝑑(𝑃 × 𝑄) 𝑑𝑄 𝑑𝑃 𝑑𝑃
𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑅𝑒𝑣𝑒𝑛𝑢𝑒 (𝑀𝑅) = = =𝑃× +𝑄× =𝑃+𝑄×
𝑑𝑄 𝑑𝑄 𝑑𝑄 𝑑𝑄 𝑑𝑄
𝑄 𝑑𝑃 1 1
=𝑃 1+ × =𝑃 1+ =𝑃 1+
𝑃 𝑑𝑄 𝑃 𝑑𝑄 𝑑𝑄 𝑃
× ×
𝑄 𝑑𝑃 𝑑𝑃 𝑄
𝟏 𝟏
𝑴𝑹 = 𝑷 𝟏 + =𝑷 𝟏−
𝒆 𝒆
As we know that 𝑄 = 𝑓(𝑃)
Where, 𝑄 =Quantity Demand and 𝑃 = Price
And also we know that,
(1) 𝑃𝑟𝑖𝑐𝑒 𝐸𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦 𝐸 = × (Percentage method)
(2) 𝑃𝑟𝑖𝑐𝑒 𝐸𝑙𝑎𝑠𝑡𝑖𝑐𝑖𝑡𝑦 𝐸 = × (Mid-point method)
Now,
𝑇𝑜𝑡𝑎𝑙 𝑅𝑒𝑣𝑒𝑛𝑢𝑒 (𝑇𝑅) = 𝑃 × 𝑄
𝑑𝑇𝑅 𝑑(𝑃 × 𝑄) 𝑑𝑄 𝑑𝑃 𝑑𝑃
𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑅𝑒𝑣𝑒𝑛𝑢𝑒 (𝑀𝑅) = = =𝑃× +𝑄× =𝑃+𝑄×
𝑑𝑄 𝑑𝑄 𝑑𝑄 𝑑𝑄 𝑑𝑄
𝑄 𝑑𝑃 1 1
=𝑃 1+ × =𝑃 1+ =𝑃 1+
𝑃 𝑑𝑄 𝑃 𝑑𝑄 𝑑𝑄 𝑃
× ×
𝑄 𝑑𝑃 𝑑𝑃 𝑄
𝟏 𝟏
𝑴𝑹 = 𝑷 𝟏 + =𝑷 𝟏−
𝒆 𝒆
