# Price Elasticity Estimation with a non-linear price schedule

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?