Question

Using the midpoint formula for calculating elasticity of demand, if the price decreased from $16 to $10, what would be the elasticity of demand if the quantity demanded changed from 8 to 12 units? Interpret your results

Answer 1

The demand for a commodity changes with respect to its price. The price elasticity of demand is the responsiveness of the quantity demanded of a good or service due to the change in its price, keeping other factors ( like, income, price of related goods, etc.) of demand constant.

Price elasticity of demand = percentage change in quantity demand / percentage change in price

For calculating elasticity of demand by midpoint formula, we have to calculate the percentage change in quantity demand, and the percentage change in price.

Percentage change in quantity demand = [(Q₂ - Q₁)/{(Q₂ + Q₁)/2}]*100

Percentage change in price =  [(P₂ - P₁)/{(P₂ + P₁)/2}]*100

Where ,  Q₁ = original quantity demand

  Q₂ = new quantity demand after price change

   P₁ = original price

P₂ = New price

In the given question,

P₁ = $16

P2 = $10

Q₁ = 8

Q₂ = 12

Elasticity of demand(E_d) = {(12-8)/(12+8)/2} / {(10-16)/(10+16)/2}

Or, E_d = (4)/(20/2) /((-6)/26/2}

Or, E_d = 4/10 / -6/13

Or, E_d = - 0.4 / 0.46

Or, E_d = - 0.869

Or, E_d = - 0.87 (approx.)

Taking modulus

| E_d | = 0.87 (approx.)

E_d <1

As price elasticity of demand at this range (P₂/Q₂ ----- P₁/Q₁) is less than one, it means that at this range, price elasticity of demand is inelastic.

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