How does elasticity impact market efficiency? I am wondering how the price elasticity of demand (or supply) impacts market efficiency. A more specific question - can we say that in a monopolized market elasticity will be low, and that in a competitive market the competition allows the elasticity of demand to increase? Said another way, a lack of competition places a ceiling on the elasticity of demand, when there is good competition, the elasticity is not bound and reaches the correct market equilibrium value.

Can a regulator use low elasticity as evidence there is a lack of competitiveness?

Can an increase to price elasticity of demand increase consumer surplus while reducing producer surplus?

Would be great to hear some layman thoughts,a s well as references to academic literature (I didn't find much on the topic in my search).
Good question

If we examine edge cases of full elasticity, then we get:
supply or demand with zero impact of quantity on price: no matter the quantity, price will remain the same

Looking at elastic demand, that mean that for suppliers the MC function will arrive to the particular demand price. No special change in efficiency

Looking at elastic supply, that means that the consumer surplus will derive from the fixed price

Based on theory, there will be no loss of efficiency (a certain quantity that will be lost) when adding taxes or subsidies

The common real case of full elasticity, is for imported or exported goods, where the world market's equilibrium for the product imported /exported is unaffected by local market
In this case, either consumers get cheaper prices for products, comparing to a similar product manufactured locally 
or get extra prices for local goods sold abroad