The price elasticity of demand for imported whiskey is estimated to be -0.20 over a wide interval of prices. The federal government decides to raise the import tariff on foreign whiskey, causing its price to rise by 20 percent. Will sales of whiskey rise or fall, and by what percentage amount?
To determine the change in sales of whiskey after the price increase, we need to consider the price elasticity of demand. The price elasticity of demand measures how sensitive the quantity demanded is to a change in price.
Given that the price elasticity of demand for imported whiskey is -0.20, a negative value indicates that it is an inelastic good. This means that a change in price will result in a proportionately smaller change in quantity demanded.
With a price increase of 20 percent due to the import tariff, we can calculate the expected change in quantity demanded:
% Change in Quantity Demanded = Price Elasticity of Demand * % Change in Price
Using the given price elasticity of demand (-0.20) and the 20 percent price increase, we can calculate the percentage change in quantity demanded:
% Change in Quantity Demanded = -0.20 * 20
% Change in Quantity Demanded = -4%
The negative sign indicates that the quantity demanded will decrease. Therefore, sales of whiskey will fall by approximately 4 percent.
To determine the percentage change in sales of whiskey, we need to use the price elasticity of demand formula. The formula for price elasticity of demand is:
Price Elasticity of Demand = (% Change in Quantity Demanded) / (% Change in Price)
Given that the price elasticity of demand for imported whiskey is estimated to be -0.20, we can use this information to calculate the percentage change in quantity demanded.
First, we know that the price of imported whiskey has increased by 20 percent. We can now calculate the percentage change in quantity demanded by rearranging the formula:
Price Elasticity of Demand = (% Change in Quantity Demanded) / 20%
-0.20 = (% Change in Quantity Demanded) / 20%
Now, let's isolate the percentage change in quantity demanded:
(% Change in Quantity Demanded) = -0.20 * 20%
(% Change in Quantity Demanded) = -0.04
This means that the quantity demanded of imported whiskey will decrease by 4 percent.
To summarize, the sales of imported whiskey will fall by 4 percent due to the 20 percent increase in price resulting from the raised import tariff.