Question

Problem IV. The Entertainment Warehouse, Inc. is a leading retailer of home theater systems. Demand for home theater systems is sensitive to changes in national income. Entertainment retailing is highly competitive, so retail demand for home theater systems is also very price-sensitive. During the past year, the Entertainment Warehouse sold 550,000 home theater systems at an average retail price of $4,000 per unit. This year, GDP per household is expected to fall from $58,800 to $53,200 as the nation enters a steep recession. Without any price change, the Entertainment Warehouse expects current-year sales to fall to 450,000 units.

A. Calculate the implied arc income elasticity of demand.

B. Given the projected fall in income, the sales manager believes that current volume of 550,000 units could only be maintained with a price cut of $500 per unit. On this basis, calculate the implied arc price elasticity of demand.

C. Holding all else equal, would a further decrease in price result in higher or lower total revenue? Explain your answer

Answer 1

Ans. Initial quantity of home theatres sold, Q1 = 550000

Initial price level, P1 = $4000

Initial GDP per household, Y1 = $58800

New sales, Q2 = 450000

New GDP per households, Y2 = $53200

New price level, P2 = $3500

a) Arc income elasticity of demand = [(Q2-Q1)/(Q2+Q1)] / [(Y2 - Y2)/(Y2 + Y1)] = [(450000-550000)/(550000+450000)] / [(53200-58800)/(53200+58800)] = 2

b) Arc price elasticity of demand = [(Q1-Q2)/(Q2+Q1)]/[(P2-P1)/(P2+P1)] = [(550000-450000)/(550000+450000)]/[(3500-4000)/(3500+4000)] = -1.5

c) The price elasticity greater than 1, shows that the demand is elastic. So, a 1% increase in price leads to a decrease in quantity demanded by 1.5%. This means that increasing price further will decrease the total revenue.

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