The demand for mini cassette players can be characterized by the following point

Question

The demand for mini cassette players can be characterized by the following point elasticities: price elasticity = -2, cross-price elasticity with AA Alkaline batteries = -1.5, and income elasticity = 3. Indicate whether each of the following statements is true or false, and explain your answer. A. A price increase for cassette players will decrease both the number of units demanded and the total revenue of sellers. B. The cross-price elasticity indicates that a 2% reduction in the price of cassette players will cause a 3% increase in battery demand. C. Demand for cassette players is price elastic and they are cyclical normal goods. D. Falling battery prices will definitely increase revenues received by sellers of both cassette players and batteries. E. A 3% price reduction in cassette players would be necessary to overcome the effects of a 2% decline in income.

Explanation / Answer

(A) TRUE

Absolute value of price elasticity is 2 which is more than 1, so demand is elastic. With elastic demand, an incease in price reduces quantity demanded & reduces total revenue.

(B) TRUE

A cross price elasticity of - 1.5 means that as price of cassette players fall by 1%, quantity of battery increases by 1.5%. So, as price of cassette players fall by 2%, quantity of battery increases by 2 x 1.5% = 3%

(C) TRUE

Income elasticity is positive, so it is a normal good.

(D) TRUE

Refer part (A). Plus, absolute value of cross price elasticity is also higher than 1, so fall in price of cassette players will increase total revenue for battery.

(E) FALSE

% Change in price = % Change in quantity demanded / Price elasticity of demand

As income falls by 1%, quantity demanded falls by 3%. As quantity demanded falls by 3%, price must increase by (3% / 2) = 1.5%

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