Some publishing companies make money from reprinting classic novels such as Romeo and Juliet, The Great Gatsby and Animal Farm. The publisher knows that a reprinted novel sells, on average, 2000 copies in Australia at a price of $6.99. They also estimate the point elasticity of demand for reprinting classic novels to be 4 (in absolute terms). The publisher decides to sell a comparable reprinted edition of Robinson Crusoe for $6.49. Which of the following statements are true: The point price elasticity of demand for the reprinted novel must be inelastic along the entire demand curve. A 1% decrease in the price of a reprinted novel will lead to a 4% decrease in the quantity demanded. The estimated quantity of Robinson Crusoe novels sold at a price of $6.49 is 2,572 (nearest whole number). The estimated quantity of Robinson Crusoe novels sold at a price of $6.49 is 2,006 (nearest whole number).
Question
Some publishing companies make money from reprinting classic novels such as Romeo and Juliet, The Great Gatsby and Animal Farm. The publisher knows that a reprinted novel sells, on average, 2000 copies in Australia at a price of 6.49. Which of the following statements are true:
The point price elasticity of demand for the reprinted novel must be inelastic along the entire demand curve.
A 1% decrease in the price of a reprinted novel will lead to a 4% decrease in the quantity demanded.
The estimated quantity of Robinson Crusoe novels sold at a price of $6.49 is 2,572 (nearest whole number).
The estimated quantity of Robinson Crusoe novels sold at a price of $6.49 is 2,006 (nearest whole number).
Solution
The first statement is false. The point price elasticity of demand being 4 (in absolute terms) means that the demand is elastic, not inelastic. Elasticity measures the responsiveness of quantity demanded to a change in price. If the absolute value of the elasticity is greater than 1, as it is in this case, the demand is elastic.
The second statement is also false. A point price elasticity of demand of 4 means that a 1% decrease in price will lead to a 4% increase in quantity demanded, not a decrease.
For the third and fourth statements, we need to calculate the estimated quantity of Robinson Crusoe novels sold at a price of $6.49.
Given that the original price is 6.49, the percentage change in price is ((6.99 - 6.49) / 6.99) * 100 = 7.15%.
Since the elasticity of demand is 4, the percentage change in quantity demanded is 4 * 7.15% = 28.6%.
The original quantity demanded was 2000 copies. So, the new quantity demanded is 2000 + (2000 * 28.6%) = 2572 copies.
Therefore, the third statement is true and the fourth statement is false.
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