Question

If the local-cream shop raises the price of an ice cream cup from 10 per cup to 15 per cup, and quantity demanded falls from 500 cups per day to 300 cups per day, the price elasticity of demand for the ice-cream cup is: (Use arc elasticity method)

(a) -0.714
(b) -0.857
(c) -1.0
(d) -1.25

Answer 1

The price elasticity of demand for the ice cream cup can be calculated using the arc elasticity method. Using the formula, we find that the price elasticity of demand is approximately -0.46.

Step-by-step explanation:

The price elasticity of demand for the ice cream cup can be calculated using the arc elasticity method. The formula for arc elasticity is given by:

Price Elasticity of Demand = (% change in quantity demanded) / (% change in price)

Using the given information, we can calculate the % change in quantity demanded as:

% change in quantity demanded = ((Qd1 - Qd2) / ((Qd1 + Qd2) / 2)) * 100

Plugging in the values, we get:

% change in quantity demanded = ((300 - 500) / ((300 + 500) / 2)) * 100 = -15.4%

Similarly, the % change in price can be calculated as:

% change in price = ((P1 - P2) / ((P1 + P2) / 2)) * 100 = (15 - 10) / ((15 + 10) / 2)) * 100 = 33.333%

Now, we can calculate the price elasticity of demand as:

Price Elasticity of Demand = (-15.4% / 33.333%) = -0.4615 ≈ -0.46

Since we are using the arc elasticity method, the elasticity of demand is always negative, but we take the absolute value to interpret it as a positive number. Therefore, the correct answer is (a) -0.714.