Question

Explain the Total expenditure method and Geometric method of measuring price elasticity of demand.

Write a short note:

Geometric method of measuring price elasticity of demand.

Answer the details:

Explain the Ratio method and Geometric method of measuring Elasticity of Demand.

Answer 1

1. Total Expenditure Method: This method was developed by Prof. Marshall. In this method, the total amount of expenditure before and after the price change is compared.
   Here the total expenditure refers to the product of price and quantity demanded.
   Total expenditure = Price × Quantity demanded
   In this connection, Marshall has given the following propositions:
   A) Relatively elastic demand (Ed >1): When with a given change in the price of a commodity, total outlay increases, the elasticity of demand is greater than one.
   B) Unitary elastic demand (Ed = 1): When the price falls or rises, total outlay does not change or remains constant, the elasticity of demand is equal to one.
   C) Relatively inelastic demand (Ed < 1): When with a given change in the price of a commodity, total outlay decreases, and the elasticity of demand is less than one. 
2. Geometric Method: Prof. Marshall has developed another method to measure the elasticity of demand, which is known as the point method or geometric method. The ratio method and total outlay methods are unable to measure the elasticity of demand at a given point on the demand curve.
   At any point on the demand curve, the elasticity of demand is measured with the help of the following formula:
   `"Point elasticity of demand (Ed)" = "Lower segment of demand curve below a given point (L)"/"Upper segment of demand curve above a given point (U)"`
   The demand curve may be either linear or non-linear as shown below:
   A) Linear Demand Curve: When the demand curve is linear i.e. a straight line, we extend the demand curve to meet the Y axis at ‘A’ and X axis at ‘B’. Price elasticity of demand at ‘X’ axis is zero and ‘Y’ axis is infinite. The elasticity of demand will be different at each point.
   
   Let us assume that AB is a demand curve and its length is 8 cm. Point elasticity at various points on a linear demand curve can be measured as follows:
   1) At point P, the point elasticity is measured as:
   P = `"PB"/"PA" = 4/4 = 1`
   Thus, at point P, demand is unitary elastic (ed = 1).
   2) At point P₁, the point elasticity is measured as:
   P₁ = `("P"_1"B")/("P"_1"A") = 2/6 = 0.33`
   Thus, at point P₁, demand is relatively inelastic (ed < 1).
   3) At point P₂, the point elasticity is measured as:
   `"P"_2 = ("P"_2"B")/("P"_2"A") = 6/2 = 3`
   Thus, at point P₂, demand is relatively elastic (ed > 1).
   4) At point A, the point elasticity is ∞ (perfectly elastic demand).
   5) At point B, the point elasticity is zero (perfectly inelastic demand.)
   B) Non-linear demand curve: When the demand curve is non-linear i.e. convex to origin, to measure the price elasticity of demand, we have to draw a tangent ‘AB’ touching the given point on the demand curve and extend it to meet ‘Y’ axis at point ‘A’ and ‘X’ axis at point ‘B’.
   Ed = `"Lower segment of the tangent below a given point"/"Upper segment of the tangent above a given point" = "L"/"U"`
   
   If EB = EA (Ed = 1) - Unitary elastic demand
   EB > EA (Ed > 1) - Relatively elastic demand
   EB < EA (Ed < 1) - Relatively inelastic demand
3. Ratio or Percentage method: The ratio method was developed by Prof. Marshall. According to this method, the elasticity of demand is measured by dividing the percentage change in demand by the percentage change in price. The percentage method is also known as the Arithmetic method. Price elasticity is measured as:
   Ed = `"Percentage change in Quantity demanded"/"Percentage change in Price"`
   Ed = `(%Delta"Q")/(%Delta"P")`
   Mathematically, the above formula can be presented as under.
   Ed = `(Delta"Q")/"Q" ÷ (Delta"P")/"P"`
   ∴ Ed = `(Delta"Q")/"Q" xx "P"/(Delta"P")`
   Q = Original quantity demanded
   ΔQ = Difference between the new quantity and original quantity demanded.
   P = Original price
   ΔP = Difference between the new price and original price