Question

Month Income Price Coke Price Pepsi Q^D Coke Q^D Pepsi
Jan 300 2.40 2.40 14 10
Feb 300 3.00 2.40 10 14
Mar 500 2.40 2.40 20 14
Apr 300 3.00 1.20 8 16
Calculate the e D of coke and Income Elasticity Demand of Coke using the midpoint method. Hint: We need to be careful about the data we choose to calculate these. To calculate e D we need a change in price of Coke and quantity demanded for Coke but we need everything else that affects the demand to remain the same. Similarly, to calculate Income Elasticity Demand of coke, need two months such that there is a change in income, but no other changes.
(a) Price Elasticity of Demand (e D) of coke.
i) What are the two months you pick? Why?
ii) Calculate eD of coke.
(b) Income Elasticity of Demand (IED) of Coke.
i) What are the two months you pick? Why?
ii) Calculate IED of coke

Answer 1

Answer:

midpoint method for income elasticity of demand = {ΔQD / [(QD₀ + QD₁)/2]} / {ΔI / [(I₀ + I₁)/2]}

midpoint method for price elasticity of demand = {ΔQD / [(QD₀ + QD₁)/2]} / {ΔP / [(P₀ + P₁)/2]}

a) I will use the information from January and February to calculate the price elasticity of demand of Coke. I cannot use March instead of January because income increased during that month.

QD₀ = 14

QD₁ = 10

P₀ = 2.40

P₁ = 3

PED = {(10 - 14) / [(14 + 10)/2]} / {(3 - 2.4) / [(3 + 2.4)/2]}

PED = {-4 / 12} / {0.6 / 2.7} = -0.3333 / 0.2222 = -1.5 or |1.5| in absolute terms

Coke's PED is elastic since a 1% change in price will result in a larger proportional change in the quantity demanded.

b) I will use the information from January and March to calculate the income elasticity of demand of Coke. These are the two months where income changes but price of Coke remains the same.

QD₀ = 14

QD₁ = 20

I₀ = 300

I₁ = 500

PED = {(20 - 14) / [(14 + 20)/2]} / {(500 - 300) / [(300 + 500)/2]}

PED = {6 / 17} / {200 / 400} = 0.3529 / 0.5 = 0.71

Coke's IED is positive, therefore, Coke is a normal good.