Question

1.

Today Tomorrow

Price of Coke 1.90 2.10

Quantity of Pepsi 297 303

a. Write down the formula for the cross-price elasticity of demand?

b. Calculate the cross-price elasticity Pepsi with respect to Coke?

c. From part b, are Coke and Pepsi substitutable goods or complementary? Explain intuitively.

d. If Q=200-4P, find P and Q when price elasticity of demand e=1.

Answer 1

1. (a) The cross price elasticity of demand is the percentage change in quantity of a product for a unit percent increase in price of another product. It would be as .

(b) For the given values, we have or or as the cross price elasticity of demand.

(c) Since cross price elasticity is positive (), the goods are substitute goods. The cross elasticity would basically mean in this case that for a unit percent increase in price of Coke, the quantity demanded of Pepsi increased by 0.2%. This further means that, as price of Coke increases, the quantity demanded of Coke must decrease, and as that happens the quantity demanded of Pepsi increases. Two goods are substitute if decrease in demand for one good increases the demand for the other good.

(d) The elasticity would be as or or or or , and since is the inverse demand, we have . For price elasticity of demand be (-)1, we have or or or or , and . Hence, for $25 of P and 100 units of Q, the price elasticity of demand is 1.