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

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 = $\frac{Q_2 - Q_1}{Q_1} * 100$

% change in price = $\frac{P_2 - P_1}{P_1} * 100$

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 = $\frac{400 - 300}{300} * 100 = \frac{100}{300} * 100= 33.33$

% change in price =$\frac{7 - 5}{5} * 100 = \frac{2}{5} * 100= 20$

∴ PES = $\frac{33.33}{40} = 0.83$

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.