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.
To understand why the vendors would lose revenues altogether as a result of the price decline, we need to consider price elasticity of demand and how it relates to changes in quantity demanded and total revenue.
Price elasticity of demand is a measure of how responsive the quantity demanded of a product is to changes in its price. It is calculated as the percentage change in quantity demanded divided by the percentage change in price. A negative price elasticity of demand indicates an inverse relationship between price and quantity demanded, meaning that as price decreases, quantity demanded increases.
In this case, the price has fallen by 10 percent, and the price elasticity of demand is given as -1.3. This means that for every 1% decrease in price, the quantity demanded would increase by 1.3%.
To determine whether the vendors would lose revenues altogether, we need to analyze the effect of the price decrease on total revenue. Total revenue is calculated as the product of price and quantity demanded.
If the price decreases by 10%, the percentage change in price is -10%. According to the price elasticity of demand (-1.3), the percentage change in quantity demanded would be 1.3 * -10% = -13%.
To calculate the effect on total revenue, we need to consider the combined effect of the price decrease and the change in quantity demanded.
If the percentage change in price is -10% and the percentage change in quantity demanded is -13%, the net effect on total revenue can be calculated as follows:
Net percentage change in total revenue = (percentage change in quantity demanded) + (percentage change in price)
Net percentage change in total revenue = -13% + (-10%)
Net percentage change in total revenue = -23%
A net percentage change in total revenue of -23% implies that total revenue would decrease by 23%. In other words, the vendors would lose 23% of their revenue as a result of the price decline.
Therefore, based on the given price elasticity of demand and the price decrease of 10%, the vendors would indeed lose revenues altogether.
To determine the effect of the price decline on revenues, we can use the price elasticity of demand formula:
Price Elasticity of Demand (Ed) = (% change in quantity demanded) / (% change in price)
Given that the price has fallen by 10 percent, we can calculate the percentage change in price as follows:
% change in price = (change in price / original price) * 100
= (-10 / 100) * 100
= -10 percent
Since the price elasticity of demand (Ed) is given as -1.3, we can now solve for the percentage change in quantity demanded:
-1.3 = (% change in quantity demanded) / (-10)
% change in quantity demanded = -1.3 * -10
= 13 percent
From the above calculation, we can conclude that the quantity demanded would decrease by 13 percent due to a 10 percent price decline. However, the question states that if the price decline results in vendors losing all revenues, we know that the quantity demanded would need to decrease by 100 percent.
Therefore, with a price decline of 10 percent and a price elasticity of demand of -1.3, vendors would not lose all revenues. Instead, they would experience a decrease in quantity demanded of 13 percent.