For each of the following scenarios, decide whether you agree or disagree and explain your answer.
a. If the elasticity of demand for cocaine is −.2 and the Drug Enforcement Administration succeeds in reducing supply substantially, causing the street price of the drug to rise by 50%, buyers will spend less on cocaine.
b. Every year Christmas tree vendors bring tens of thousands of trees from the forests of New England to New York City and Boston. During the last two years, the market has been very competitive; as a result, price has fallen by 10 percent. If the price elasticity of demand was −1.3, vendors would lose revenues altogether as a result of the price decline.
c.If the demand for a good has unitary elasticity, or elasticity is −1, it is always true that an increase in its price will lead to more revenues for sellers taken as a whole.
a. I agree with the statement. According to the given information, the elasticity of demand for cocaine is -0.2. If the supply of cocaine is substantially reduced by the Drug Enforcement Administration, causing the street price to rise by 50%, buyers will face a higher price for cocaine. Since the price elasticity of demand is negative, a price increase will lead to a proportionally smaller decrease in quantity demanded. Therefore, even though the price has increased, the decrease in quantity demanded will not be enough to offset the higher price, resulting in buyers spending less on cocaine.
To calculate the change in quantity demanded, you can use the formula:
% Change in Quantity Demanded = (Elasticity of Demand) * (% Change in Price)
In this case, the % Change in Price is 50% (given), and the Elasticity of Demand is -0.2 (given). Therefore:
% Change in Quantity Demanded = -0.2 * 50% = -10%
b. I disagree with the statement. The given information states that the price of Christmas trees has fallen by 10%. If the price elasticity of demand is -1.3, it means that a 1% decrease in price will result in a 1.3% increase in quantity demanded. Hence, in this scenario, the price decrease of 10% would likely lead to an increase in quantity demanded.
To calculate the change in quantity demanded, you can use the formula:
% Change in Quantity Demanded = (Elasticity of Demand) * (% Change in Price)
In this case, the % Change in Price is -10% (given), and the Elasticity of Demand is -1.3 (given). Therefore:
% Change in Quantity Demanded = -1.3 * (-10%) = 13%
So, contrary to the statement, vendors would not lose revenues altogether, but instead, they would attract more customers due to the price decline.
c. I disagree with the statement. The statement assumes that when the demand for a good has unitary elasticity (elasticity of -1), an increase in its price will always lead to more revenues for sellers as a whole. However, this is not necessarily true.
When demand has unitary elasticity (elasticity of -1), a price increase will result in an equal proportionate decrease in quantity demanded. In this case, the increase in price will be compensated by the decrease in quantity demanded, resulting in the same level of revenue for sellers. Therefore, seller revenues will remain the same, not increase.
To understand the relationship between price, elasticity, and revenue, you can use the formula:
Total Revenue = Price * Quantity
When price increases and quantity decreases proportionally, the effect on revenue is ambiguous, and it depends on the elasticity of demand rather than assuming a guaranteed increase.
Therefore, the statement is not always true, and an increase in price may not necessarily lead to more revenues for sellers taken as a whole when the demand has unitary elasticity.