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 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 elasticity of demand (PED)= % change in quantity demanded /% change in price of the good.

        % change in quantity demanded = ((New quantity-old quantity)/old quantity)) x 100

Initial quantity =120    Initial price = $ 4

New quantity = 80   New price $ 6

% change in quantity demanded = ((New quantity-old quantity)/old quantity)) x 100

% change in quantity demanded= ((80-120)/120)) x100

                                                         =( -40/120) x100

                                                      = 33.33%

               % change in price = ((New price-old price)/old price)) x 100

% change in price= ((6-4)/4)) x100

                                                         =(2/4) x100

                                                       = 50%

Price elasticity of demand = 33.33%/50%= 0.67

PED is inelastic as it is <1.

b)

Income elasticity of demand

Income elasticity of demand=

% change in quantity demanded/% change in consumers income

New quantity=1 pound                 New Income:$22,000

Old quantity = 2 pounds                Old Income= $20,000

% Change in quantity demanded = ((1-2/1)x100= (-1/1)x100 = -100 %

% Change in income = ((22,000 – 20,000)20,000))x100= (2000/20,000) x100=10%

Income elasticity of demand = -100%/10%=-10. Hamburger is an inferior good as the sign is negative.

When the quantity demanded decreases in response to an increase and increases in response to decrease in the consumer income, the income elasticity of demand is negative and the product is an inferior good.