Question

Determine the price elasticity of demand, the cross-price elasticity of demand or the income elasticity in the following scenarios.

a. Consider the market for coffee. Suppose the price rises from $4 to $6 and quantity demanded falls from 120 to 80. What is price elasticity of demand? Is coffee elastic or inelastic?

b. John’s income rises from $20,000 to $22,000 and the quantity of hamburger he buys each week falls from 2 pounds to 1 pound. What is his income elasticity? Is hamburger a normal or inferior good?

c. The price of apples rises from $1.00 per pound to $1.50 per pound. As a result, the quantity of oranges demanded rises from 8,000 per week to 9,500. What is the cross-price elasticity of apples? Are these goods substitutes or complements?

Answer 1

(a) Price of coffee rises from $4 to $6, as a result the quantity demanded falls from 120 to 80.

% change in price of coffee = [(6 -4) / 4]*100 = 50

% change in quantity demand = [(80 - 120)/120]*100 = -33.33

Price elasticity of demand = (% change in quantity demand for coffee / % change in price of coffee)

=> Price elasticity of demand = (-33.33 / 50)

=> Price elasticity of demand = -0.67

The absolute value of price elasticity of demand for coffee is 0.67, which is less than one. It means demand for coffee is inelastic.

-------------------------

(b) John’s income rises from $20,000 to $22,000 and the quantity of hamburger he buys each week falls from 2 pounds to 1 pound.

% change in income = [(22000 - 20,000)/ 20,000]*100 = 10

% change in demand of hamburger = [(1-2) /2]*100 = -50.

Income elasticity = (% change in demand for hamburger / % change in income)
=> Income elasticity = (-50 / 10)

=> Income elasticity = -5.

Since, the income elasticity is negative, implies hamburger is an inferior good.

---------------------

(c) The price of apples rises from $1.00 per pound to $1.50 per pound. As a result, the quantity of oranges demanded rises from 8,000 per week to 9,500.

% change in price of apple = [(1.50 - 1) / 1]*100 = 50

% change in demand for oranges = [(9500 - 8000)/ 8000]*100 =18.75

Cross price elasticity = (% change in demand for oranges / % change in price of apple)

=> Cross price elasticity = (18.75 / 50)

=> Cross price elasticity = 0.375

Since, the cross price elasticity between oranges and apple is positive, implies apple and oranges are substitute goods.