Problem III

The demand for tennis rackets can be characterized by the following point elasticities: price elasticity = 1.5, cross-price elasticity with tennis club membership fees= 2.0, and income elasticity = 3.0. Indicate whether each of the following statements is true or false, and explain your answer.

1. A price increase for tennis rackets will decrease both the number of units demanded and the total revenue of sellers.
2. The cross-price elasticity indicates that a 2% reduction in the price of tennis rackets will cause a 4% increase in tennis club membership demand.
3. Tennis rackets are cyclical normal goods.
4. Falling tennis club membership fees will definitely increase revenues received by sellers
5. of both tennis rackets and tennis club memberships.
6. A 2% price reduction in tennis racket prices would be necessary to overcome the effects
7. of a 1.5% decline in income.

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.

1. Calculate the implied arc income elasticity of demand.
2. Given the projected fall in income, the sales manager believes that current volume of
3. 550,000 units could only be maintained with a price cut of $500 per unit. On this basis,
4. calculate the implied arc price elasticity of demand.
5. Holding all else equal, would a further decrease in price result in higher or lower total
6. revenue? Explain your answer.