Arc income elasticity Deluxe Carpeting a leading manufacturer of carpeting sold

Question

Arc income elasticity Deluxe Carpeting a leading manufacturer of carpeting sold 28 million square yards of carpeting at a price of $16 per yard. This year, GNP per capita is expected to fall from $19,000 to $17,000 as the nation enters a recession. Deluxe expects that current-year sales to fall to 20 million square yards. a. Calculate the implied arc income elasticity of demand. b. Given a price elasticity coefficient of -2.5, to what level would price have to be lowered to maintain sales at a level of 28 million square yards? ***Please show ALL work*** Thank you!

Explanation / Answer

E= delta Q / delta I X    I2 +I1 / (Q1 + Q2)

=(20-28) /(17000-19000)   x (17000+19000) / (20-28) =3  

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Without a price decrease, sales this year would total 20 million units. Therefore, it is appropriate to estimate the arc price elasticity from a (before-price-decrease) base of 20 million units:

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Lower. Because carpet demand is in the elastic range, EP = -2.5, an increase (decrease) in price will result in lower (higher) total revenues

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