Question

1. LYFEN is considering adding another fruit-based product for which the demand has been estimated by the function Q = 7500 – 500PF +7I + 100PB, where PF is the price of LYFEN's proposed product, I is per capita income, and PB is the price of a similar product from one of the competing companies. Assume the initial values of PF, I, and PB are 60, ¥9,500, and 40. Given this information, answer the following based on your calculations of appropriate elasticities.
   1. What effect would a price increase have on the total revenues earned from the proposed product? (10%)
   2. What would you expect to occur to sales given an increase in personal income? (10%)
   3. What is the potential impact if the competing seller raises its price? (10%)

Answer 1

Q = 7,500 - 500PF + 7I + 100PB

Plugging in given values,

Q = 7,500 - (500 x 60) + (7 x 9,500) + (100 x 40)

Q = 7,500 - 30,000 + 66,500 + 4,000

Q = 48,000

(1)

Own-price elasticity of demand = (Q/PF) x (PF/Q) = - 500 x (60/48,000) = - 0.625

It means that as price of the good increases by 1%, quantity demanded decreases by 0.625%, therefore total revenue will increase.

(2)

Income elasticity of demand = (Q/I) x (I/Q) = 7 x (9,500/48,000) = 1.38

It means that as income increases by 1%, sales increases by 1.38%. A positive income elasticity means the good is normal, and income elasticity above 1 means that it is a luxury good.

(3)

Cross-price elasticity = (Q/PB) x (PB/Q) = 100 x (40/48,000) = 0.0833

It means that as price of the similar product increases by 1%, sales increases by 0.0833%. A positive cross-price elasticity means that the goods are substitutes.