<p>Not necessarily. </p>

<p>For example if the utility function is <span class="math-container">$U=\min\{x,y\}$</span>, then the demand function for x is given by <span class="math-container">$D=\frac{M}{P_x+P_y}$</span>.</p>

<p>The own price elasticity of demand for x is: <span class="math-container">$-\frac{M}{(P_x+P_y)^2} \frac{P_x}{x}$</span>.</p>

<p>The cross price elasticity of demand for x is: <span class="math-container">$-\frac{M}{(P_x+P_y)^2} \frac{P_y}{x}$</span>.</p>

<p>If these elasticities are evaluated at <span class="math-container">$P_x=P_y=p$</span>, then for any value of x, you have the same elasticities. </p>

CC BY-SA 4.0
2018-10-07T13:59:11.167Z
2018-10-07T15:25:40.473Z
2018-10-07T15:25:40.473Z
erik
<p>Is the cross price elasticity of demand between two goods always lower in magnitude than the price elasticities of demand of each good?</p>

<supply-and-demand><elasticity>
Cross price elasticity of demand vs Price elasticity of demand
Jason
# Cross price elasticity of demand vs Price elasticity of demand

(Asked by: username_0 on 2018-10-06)

Is the cross price elasticity of demand between two goods always lower in magnitude than the price elasticities of demand of each good?

**Tags:** supply-and-demand, elasticity

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## 1 answers

### Answer by username_1 on 2018-10-07. Score: 3

Not necessarily.

For example if the utility function is $U=\min\{x,y\}$, then the demand function for x is given by $D=\frac{M}{P\_x+P\_y}$.

The own price elasticity of demand for x is: $-\frac{M}{(P\_x+P\_y)^2} \frac{P\_x}{x}$.

The cross price elasticity of demand for x is: $-\frac{M}{(P\_x+P\_y)^2} \frac{P\_y}{x}$.

If these elasticities are evaluated at $P\_x=P\_y=p$, then for any value of x, you have the same elasticities.


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