ENVECON 162 Lecture Notes - Lecture 8: Groundwater Model
4 May 2018
School
Department
Course
Professor
Economics of Water Resources
Spring 2018
Lecture 8: Optimal Groundwater Management Part I
Groundwater Model
The groundwater model is an inherently dynamic problem. This is because economic
agents are always making tradeoffs between different time periods pumping water today
can limit or change options tomorrow.
❖ Definitions
▪ Let be our index for time
▪ is the amount of water extracted at time
▪ is the amount of groundwater in storage at time
▪ is the benefit (profit) function measured in dollars
▪ is the cost function measured in dollars
▪ is the interest rate
▪ is the total recharge in time
▪
Objective Function
For any time period , the objective function is written as follows:
The economic agent is interested in finding the optimal and for all time periods from
to infinity. In order to sum benefits over time, we have to discount net benefits for all time
periods using as the discount rate.
The infinite-horizon objective function is therefore written as follows:
Equation of Motion
The primary constraint in the groundwater model is a physical constraint referred to as the
equation of motion. The equation of motion describes how storage is depleted and filled up.
The equation of motion is written as follows:
▪
water extracted and the total recharge time
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