Price Elasticity of Demand

Price elasticity of demand is a measure of the responsiveness of quantity demanded to changes in the price of a good. The formula for price elasticity of demand is:

Price Elasticity of Demand = % Change in Quantity Demanded / % Change in Price

Calculating Price Elasticity of Demand

To calculate the price elasticity of demand in this case, we need to know the percent change in quantity demanded and the percent change in price.

Given that the price of the good falls by 40% and the quantity demanded increases by 50%, we can calculate the percent change in quantity demanded and the percent change in price as follows:

% Change in Quantity Demanded = (New Quantity Demanded - Old Quantity Demanded) / Old Quantity Demanded x 100%
% Change in Quantity Demanded = (50 - 100) / 100 x 100%
% Change in Quantity Demanded = -50%

% Change in Price = (New Price - Old Price) / Old Price x 100%
% Change in Price = (-40 - 0) / 0 x 100%
% Change in Price = -40%

Substituting the Values

Substituting these values into the formula for price elasticity of demand, we get:

Price Elasticity of Demand = % Change in Quantity Demanded / % Change in Price
Price Elasticity of Demand = -50% / -40%
Price Elasticity of Demand = 1.25

Interpreting the Result

The price elasticity of demand is 1.25, which means that the demand for the good is relatively elastic. This means that a small change in price will lead to a relatively large change in quantity demanded. In this case, a 40% decrease in price led to a 50% increase in quantity demanded, which is consistent with the idea of elastic demand.

Price of goods falls by 40%
therefore= %∆p = 40
quantity demanded increases by 50%
therefore = %∆q = 50
elasticity of demand is calculated as
E = %∆q/%∆p = 50/40 = 5/4 = 1.25
1.25 >1
the demand of the commodity is relatively elastic.