Answer to Question #156752 in Microeconomics for [e-mail]

Question

 A pizzeria lowers the price of its most popular pizza, the Margherita, from $5 to $4.50. As such, the weekly quantity demanded of the pizzas increases from 60 to 72. 

a) Calculate the Price Elasticity of Demand for pizzas.

b) Calculate the change in total revenue that the pizzeria will experience following the decrease in price.

c) Illustrate and explain the change in revenue using an appropriate diagram. Was the firm sensible to lower the price of the pizza? Explain.

Answer 1

a) By the definition of the Price Elasticity of the Demand, we get:

$$PED=\dfrac{\%\Delta\ in\ Quantity\ Demanded}{\%\Delta\ in\ Price}=\dfrac{20\%}{10\%}=2.$$

Since the PED>1, the demand for the pizza is elastic.

b) Let's calculate the total revenue before and after the price change:

$$TR_1=P_1Q_1=\$5\cdot60=\$300,$$ $$TR_2=P_2Q_2=\$4.50\cdot72=\$324.$$

Finally, we can calculate the change in total revenue that the pizzeria will experience following the decrease in price:

$$\Delta TR=TR_2-TR_1=\$324-\$300=\$24.$$

c) Let's draw the diagram:

In our case, before the lowering the price, the pizza seller was earning revenue equal to "revenue box b" plus "revenue box b". After lowering the price, the pizza seller loses "revenue box a" because the price of the pizza decreases to $4.50, but gains "revenue box c" because the quantity demanded increases to 72 pizzas. Since the "revenue box c" ($12\cdot\$4.5=\$54$) is clearly greater than "revenue box a" ($60\cdot\$0.5=\$30$), the pizza seller's total revenue increases by$24. Thus, the firm is sensible to lower the price of Margherita.