To calculate the elasticity of demand for product Y based on the change in price of product X, we use the…

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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

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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 ( $E_{XY}$ ) is:

E_{XY} = \frac{\frac{Q_{Y2} - Q_{Y1}}{(Q_{Y2} + Q_{Y1})/2}}{\frac{P_{X2} - P_{X1}}{(P_{X2} + P_{X1})/2}}

From the table:
Initial Price of X ( $P_{X1}$ ) = 140
Final Price of X ( $P_{X2}$ ) = 150
Initial Demand for Y ( $Q_{Y1}$ ) = 15,000
Final Demand for Y ( $Q_{Y2}$ ) = 19,000

Calculate the percentage change in the price of X.
$\% \Delta P_X = \frac{P_{X2} - P_{X1}}{(P_{X2} + P_{X1})/2} = \frac{150 - 140}{(150 + 140)/2} = \frac{10}{290/2} = \frac{10}{145}$
Calculate the percentage change in the quantity demanded of Y.
$\% \Delta Q_Y = \frac{Q_{Y2} - Q_{Y1}}{(Q_{Y2} + Q_{Y1})/2} = \frac{19,000 - 15,000}{(19,000 + 15,000)/2} = \frac{4,000}{34,000/2} = \frac{4,000}{17,000} = \frac{4}{17}$
Calculate the cross-price elasticity of demand.
$E_{XY} = \frac{\% \Delta Q_Y}{\% \Delta P_X} = \frac{\frac{4}{17}}{\frac{10}{145}}$ $E_{XY} = \frac{4}{17} \times \frac{145}{10} = \frac{4 \times 145}{17 \times 10} = \frac{580}{170}$ $E_{XY} = \frac{58}{17}$ $E_{XY} \approx 3.41176$
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 $\text{3.41}$ .

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

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Step-by-step solution

Calculate the percentage change in the price of X.

Calculate the percentage change in the quantity demanded of Y.

Calculate the cross-price elasticity of demand.

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