<p><span class="math-container">$P_XX+P_YY=M$</span></p>

<p>Differentiating w.r.t. <span class="math-container">$P_X$</span>,</p>

<p><span class="math-container">$\frac{\partial X }{\partial P_X}P_X+X+\frac{\partial Y}{\partial P_X}P_Y=0$</span></p>

<p>Divide the whole term by <span class="math-container">$X$</span>, considering <span class="math-container">$X\neq 0$</span></p>

<p><span class="math-container">$\varepsilon _X+1+\frac{\partial Y}{\partial P_X}\frac{P_Y}{X}=0$</span></p>

<p><span class="math-container">$\varepsilon _X=1$</span>(Given) </p>

<p><span class="math-container">$2+\frac{\partial Y}{\partial P_X}\frac{P_X}{Y}(\frac{P_Y}{X}\frac{Y}{P_X})=0$</span></p>

<p>Here, <span class="math-container">$$P_X,P_Y,X,Y&gt; 0$$</span>(ASSUMPTION)</p>

<p>Therefore, Cross- Price elasticity is <span class="math-container">$-2$</span> (some positive no.) and not $0.
So, this statement is not true. </p>

CC BY-SA 4.0
2018-11-08T10:05:49.053Z
2018-11-08T10:05:49.053Z
Henam
<p>Sketch your answer for the demand function <span class="math-container">$x = -p_x/p_y$</span>.</p>

CC BY-SA 4.0
2018-11-06T20:01:03.277Z
2018-11-06T20:01:03.277Z
Marcelo Gelati
<p>The question is: Prove or disprove, if the price elasticity of a demand of a good is unitary then the cross price Elasticity of demand of that good is zero.</p>

<p>Any hints on how to approach this? </p>

<elasticity>
Price and cross price Elasticity of demand
Sumukh Sai
# Price and cross price Elasticity of demand

(Asked by: username_0 on 2018-11-04)

The question is: Prove or disprove, if the price elasticity of a demand of a good is unitary then the cross price Elasticity of demand of that good is zero.

Any hints on how to approach this?

**Tags:** elasticity

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## 2 answers

### Answer by username_1 on 2018-11-08. Score: 1 | Accepted answer

$P\_XX+P\_YY=M$

Differentiating w.r.t. $P\_X$,

$\frac{\partial X }{\partial P\_X}P\_X+X+\frac{\partial Y}{\partial P\_X}P\_Y=0$

Divide the whole term by $X$, considering $X\neq 0$

$\varepsilon \_X+1+\frac{\partial Y}{\partial P\_X}\frac{P\_Y}{X}=0$

$\varepsilon \_X=1$(Given)

$2+\frac{\partial Y}{\partial P\_X}\frac{P\_X}{Y}(\frac{P\_Y}{X}\frac{Y}{P\_X})=0$

Here, $$P\_X,P\_Y,X,Y> 0$$(ASSUMPTION)

Therefore, Cross- Price elasticity is $-2$ (some positive no.) and not $0.
So, this statement is not true.


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### Answer by username_2 on 2018-11-06. Score: -2

Sketch your answer for the demand function $x = -p\_x/p\_y$.


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