How do I estimate price elasticity in a non-linear price setting? Non-linear prices are seen in utilities (electricity, water etc.) where the price per unit is determined by quantity purchased.
So a price tier would look something like this:
0 - 500 units: $2 per unit
501-1000 units: $1.5 per unit
1001 - 5000 units: $1 per unit
I would like to estimate elasticity coefficients using historical sales, where different sales volumes are observed at different price schedules.
In a linear setting, I'd estimate elasticity using something like this:
log(Demand) = Beta1*log(Price per unit) + Error
where Beta1 would be the elasticity.
However, in a non-linear setting, there is an interaction between price per unit and quantity. What would be an appropriate functional form for such a situation?