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bez when demand function have price on y-axis, its mean that price have the inverse relation to the demand, in other words price lead to demand curve.

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Q: Why price on y-axis in demand function?
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Is the price elasticity constant along the demand curve?

Price elasticity of demand is equal to the instantaneous slope of the demand curve, or the slope of the tangent line at any point on the demand curve. So if the demand curve is represented by a straight downward sloping line, then yes, price elasticity of demand is equal to the slope of the demand curve. Otherwise, the slope at any point on the curve is changing, and you can find the it by taking the derivative of the demand curve function, which will find the Price elasticity of demand at any single point. Thus, the Price Elasticity of Demand changes at different points on the demand curve.