Question

Suppose the price of a cup of coffee is $5, and at this price, the quantity supplied is 300 cups of coffee. Now suppose the price of coffee is raised to $7, where at this price, the quantity supplied is 400 cups of coffee. The price elasticity of supply is _________________ and the supply is price _________________.

Answer 1

The price elasticity of supply is 0.83 and the supply is price inelastic.

Step-by-step 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 =
`(Q_2 - Q_1)/(Q_1) * 100`

% change in price =
`(P_2 - P_1)/(P_1) * 100`

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 =
`(400 - 300)/(300) * 100 = (100)/(300) * 100= 33.33`

% change in price =
`(7 - 5)/(5) * 100 = (2)/(5) * 100= 20`

∴ PES =
`(33.33)/(40) = 0.83`

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.