To calculate the elasticity of demand for product Y based on the change in price of product X, we use the cross-price elasticity of demand formula. The term "loss elasticity" is not standard, so we assume it refers to cross-price elasticity, which measures how the demand for one good changes in response to a price change in another good. We will use the arc elasticity (midpoint) formula for accuracy with discrete changes.
The formula for cross-price elasticity of demand (EXY) is:
EXY=(PX2+PX1)/2PX2−PX1(QY2+QY1)/2QY2−QY1
From the table:
Initial Price of X (PX1) = 140
Final Price of X (PX2) = 150
Initial Demand for Y (QY1) = 15,000
Final Demand for Y (QY2) = 19,000
Step 1: Calculate the percentage change in the price of X.
%ΔPX=(PX2+PX1)/2PX2−PX1=(150+140)/2150−140=290/210=14510
Step 2: Calculate the percentage change in the quantity demanded of Y.
%ΔQY=(QY2+QY1)/2QY2−QY1=(19,000+15,000)/219,000−15,000=34,000/24,000=17,0004,000=174
Step 3: Calculate the cross-price elasticity of demand.
EXY=%ΔPX%ΔQY=14510174
EXY=174×10145=17×104×145=170580
EXY=1758
EXY≈3.41176
The cross-price elasticity of demand for product Y is approximately 3.41. The positive value indicates that products X and Y are substitutes.
The loss elasticity of demand of product Y is 3.41.
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