# Price and cross price Elasticity of demand [closed]

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?

## closed as off-topic by Giskard, Brythan, Herr K., Kitsune Cavalry♦Nov 9 '18 at 1:03

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• Hint: check an example, e.g. linear demand. – afreelunch Nov 4 '18 at 15:43

$$P_XX+P_YY=M$$

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.

Sketch your answer for the demand function $$x = -p_x/p_y$$.