In a recent study it has been estimated that the own price elasticity of demand
ID: 2441611 • Letter: I
Question
In a recent study it has been estimated that the own price elasticity of demand for a special type of U.S. manufactured automobile tires is - .75, while the income elasticity of demand is 1.1 and the cross price elasticity of demand with respect to foreign imports is 1.4. The current sales volume for the U.S. manufactured tires is 5 million units per year. It is anticipated that the price of the foreign imports will rise by 5%.
(a) Assuming that average income of the target group of customers will not change, calculate the number of tires that the tire manufacturers will be able to sell if they plan to increase their own price by 3%.
Explanation / Answer
Solution:
Given the following as per question
price elasticity of demand = - .75
income elasticity of demand is 1.1
cross price elasticity of demand with respect to foreign imports is 1.4
current sales volume ( demanded ) = 5 million units = 5000000 lakhs units
average income of the target group of consumers in the U.S. will grow by 4%
the price of the foreign imports will rise by 5%
Sales Volume rise by 8.4% = 5420000 ( 5000000 + 8.4% of 5000000)
Price Elasticity of Demand = % Change in Quantity Demanded / % Change in Price
E(p)= dQ/dP*p/Q
-.75= 5420000/5% * p/500000
thus p = -16.26
Income Elasticity of Demand = % change in quantity demanded / % change in income
E(y)= dQ/dY*Y/Q
y=0.13
Original Sales = 5000000
New Sales = 5420000
% change in quantity demanded =420000/5000000 = 0.084
Original Price = -16.26
New Price = -16.26*5% +(-16.26) = -17.073
% Change in Price = -0.813 (-17.073 - (-16.26)) = -0.813
Price Adjustment when sales volume rises by 8.4% = 0.084/-0.813
= -0.103
Thus price will change from -.75 to -0.103
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