Answer:
The price elasticity of supply is 0.83 and the supply is price inelastic.
Explanation:
The price elasticity of supply is the ration of the percentage change in the quantity of a product supplied to the percentage change in price. It is used to measure essentially the degree to which the quantity of a good or service supplied change with a change in price. Mathematically, Price elasticity of supply (PES) is:
PES = (% change in the quantity ) ÷ (% change in price)
% change in quantity = [tex]\frac{Q_2 - Q_1}{Q_1} * 100[/tex]
% change in price = [tex]\frac{P_2 - P_1}{P_1} * 100[/tex]
where :
Q₂ = New quantity supplied = 400 cups of coffee
Q₁ = Initial quantity supplied = 300 cups of coffee
P₂ = new price = $7
P₁ = initial price = $5
∴ % change in quantity = [tex]\frac{400 - 300}{300} * 100 = \frac{100}{300} * 100= 33.33[/tex]
% change in price =[tex]\frac{7 - 5}{5} * 100 = \frac{2}{5} * 100= 20[/tex]
∴ PES = [tex]\frac{33.33}{40} = 0.83[/tex]
Finally, the following rules hold for PES:
PES < 1 = inelastic
PES > 1 = elastic
PES = 1 = unitary
PES = 0 = perfectly inelastic
PES = ∞ = perfectly elastic
Hence since our answer is 0.83, the PES is inelastic for a cup of coffee, meaning that the degree of price change is of a more greater proportion that the change in quantity supplied.
