Question

If a 12% increase in the price of grapefruit juice causes a 22% decrease in the quantity of grapefruit juice demanded. On the other hand, there is a 14% increase in the quantity demanded for Ron Don Q; Calculate:

a) the price elasticity of demand for grapefruit juice and rum.

b) Calculate the cross elasticity of demand between grapefruit juice and Don Q Rum.

Answer 1

Elasticity of demand is nothing but the percentage change in quantity demanded due to one percent change in price. The elasticity of demand may be splitted in to three categories; one is own price elasticity of demand , other two are cross price elasticity of demand and income elasticity of demand. Own price elasticity of demand and cross price elasticity of demand are discussed by following way

• Own Price Elasticity of demand refers to the percentage change in quantity demanded of the particular product due to one percent change in price of that product. The given formula of the own price elasticity of demand is ; own price elasticity of demand Ep= percentage change in quantity demanded / percentage change in price.
• Cross Price Elasticity of demand refers to the percentage change in quantity demanded of any commodity due to one percent change in price of the other commodity. The formula of cross Price elasticity is given as follow; The cross price elasticity of demand E xPy= percentage change in quantity demanded/ percentage change in price of other commodity

Consider, an increase 12% in price of grapefruit juice.

This is cause of decrease 22% of quantity demanded of grapefruit juice.

a) Now calculate the price elasticity of demand of grapefruit juice. To calculate the elasticity of own price elasticity ,the given formula is

Ep = Percentage change in quantity demanded/ percentage change in price

Percentage change in price of grapefruit juice be 12%

Percentage change in quantity demanded of grapefruit juice be 22%

Put the values ,in the formula.

Ep = 22/12= 1.83

The price elasticity of grapefruit juice be given as 1.83.

b) The cross price elasticity of demand shows the percentage change in own commodity due to price of the other commodity

By increase in price of grapefruit juice by 12% , the quantity demanded of Don Q Rum increases by 14%

So the cross price elasticity of grapefruit juice and Don Q Rum is given by the formula

E_{​​​​​​Gp Rq} = Percentage change in quantity demanded of Don Q Rum / Percentage change in price of Grapefruit juice

Now put the value of in given formula.

E_{​​​​​​Gp Rq} = 14/12= 1.17

Cross Price elasticity of demand of grapefruit juice and Don Q Rum is given as 1.17.

The own price elasticity be shown that, as the price increases of grapefruit juice , the quantity demanded of of demand of grapefruit juice decreases.

For the cross price elasticity , as the price of grapefruit juice increases, the quantity demanded of Don Q Rum also increases.