# How to explain the claim mathematically: The effect considered local, and locally, the elasticity is approximately constant if the demand is "smooth"?

My book has considered the effects of supply and demand changes on price (specifically the equilibrium price and quantity themselves) when the supply and demand themselves have constant elasticity and then go on to claim this statement

When the effect considered is local, and locally, the elasticity is approximately constant if the demand is "smooth".

As a mathematician and a beginner in micro-economics, I fail to understand this statement from a rigorous viewpoint. How do you prove this mathematically?

• The quoted sentence isn't even grammatically correct. Please check again. Commented Sep 2 at 9:29
• @VARulle Huh? I copied and pasted the author's statement. It reads: When the effects of demand considered is local, the elasticity is approximately constant if the demand is "smooth". Commented Sep 2 at 9:35
• I'm pretty sure it doesn't. "Effects" is plural, so the "is" doesn't fit. And apart from this, this sentence is different from the one quoted in your question. Commented Sep 2 at 9:44
• It'd help if you include the name of the book and page reference from which you quoting. Commented 23 hours ago