Sailright Inc. manufactures and sells sailboards. Management believes that the p

Question

Sailright Inc. manufactures and sells sailboards. Management believes that the price elasticity of demand is -3.0. Currently, boards are priced at $500 and the quantity demanded is 10,000 per year. Show all work in your answers.
A. If the price is increased to $600, how many sailboards will the company be able to sell each year?
B. The cross-price elasticity of demand between Sailright and its closest competitor is +2.25 and income elasticity of demand is +1.5. If income increases by 5% and its competitor reduces its prices by 10%, how much would Sailright have to change its prices to keep its total sales unchanged? Assume that price elasticity of demand is still -3.0.

Explanation / Answer

A. ep= dQ/dP *(P/Q) where ep is the price elasticity, P is the price , Q is the quantity

now -3 = dQ/dP*(500/10000)

dQ/dP = -60

now when price is increased to $600 then dP = 600-500 = $100

hence dQ = -60*100 = 6,000

hence the company will be able to sell (10000-6000) = 4,000 sailboards.

since the price increses quantity decreases.

B. ec = 2.25 this means they are substitutes of each other

ei = 1.5

now due to the increase in income by 5% the percentage increase in quantity of sailboards will be 1.5*5 = 7.5%

competior reduces its price by 10% due to which the percentage decrease in quantity of sailboards will be 10*2.25=22.5%

now the increase in demand is 7.5% and decrease in demand is 22.5%. hence net decline in the demand of salboards would be 15% = 0.15*10,000 = 1500. so it has to decrease the price of the sailboards so that his decline of 1500 sailboards would cover up.

obviously to keep the total sales unchanges at 10,000 units it must decrease its price.

now dQ/dP = -60

dP = dQ/60 = 1500/60 = $25

hence he should reduce his price by $25 and now sell the salboard at $475 to keep its total sales unchanged.

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