A local pizzeria sells 500 large pepperoni pizzas per week at a price of $20 each. Suppose the owner of the pizzeria tells you that the price elasticity of demand for his pizza is -2, and he asks you for advice. He wants to know two things. First, how many pizzas will he sell if he cuts his price by 10%? Second, how will his revenue be affected?

(1) He would sell 600 pizzas if he cuts his price by 10%

(2) His revenue would increase by 8% ($800)

Step-by-step explanation:

(1) Price elasticity of demand = % change in quantity demanded /% change in price

price elasticity of demand = -2

Initial price = $20

New price = $20 - (10% × $20) = $20 - $2 = $18

Change in price = new price - initial price = 18 - 20 = -2

% change in price = -2/20 × 100 = -10%

% change in quantity demanded = price elasticity of demand × % change in price = -2 × -10% = 20%

Let the new quantity demanded be y

% change in quantity demanded = (y-500)/500

0.2 = (y-500)/500

y-500 = 0.2×500

y-500 = 100

y = 100+500 = 600

If he reduces his price by 10%, he would sell 600 pizzas.

(2) If he sells each pizza $20, quantity demanded is 500

Revenue = 500 × $20 = $10,000

If he cuts his price by 10%, his new price would be $180 and new quantity demanded is 600

Revenue = 600 × $18 = $10,800

If he cuts his price by 10% his revenue would increase by $800 ($10,800 - $10,000 = $800)