Lecture 6 - Water valuation in crop farming
Lecturer:
Wim van Veen, msc. economist.
Amsterdam Centre for World Food Studies
School of Business and Economics, Vrije Universiteit Amsterdam
w.c.m.van.veen@vu.nl
This lecture uses a stylized mathematical optimization model to analyze the value of water in crop farming. In the model, the farmer maximizes net revenue by optimally allocating area, labor and water to the different crops, at given total land resources and given output prices, while taking into account the prevailing production functions. In the optimal solution, water has a (positive) shadow price that indicates the increase in net revenue if one additional cubic meter of water would be available. Hence, this shadow price is a good measure of the value of water to the farmer.
The shadow price is not constant but depends on the parameters in the mathematical program. In the lecture, we will focus on this dependency and study how the value of water changes under different conditions. Also, the impact of water quality will be assessed. The lecture consists of a slide presentation, numerical assignment and a concluding discussion in which the participants report on the assignment. The lecture may also serve as a starting point for a joint empirical application to a specific district later in the OKP project.
Contents of the slide presentation
The slide presentation will address:
- the concept of the water shadow price
- crop-specific shadow prices (merely based on crop yield functions)
- farm shadow prices (with behavior and constraints of farmers)
- the structure of the stylized farm model
- the optimal (Kuhn-Tucker) conditions for solving the model
- the impact of the production (yield) function on the shadow price of water
- the impact of water quality on its shadow price
- the impact of constraints (area, labor, water itself) on the shadow price of water
Numerical assignments
First, a brief explanation of constrained optimization in Excel will be given. Then, a pre-programmed crop farm optimization model will be made available to the course participants (also in Excel). With this numerical example, they are asked to study the impact of changes in model parameters (e.g. prices, yield coefficients, resources) on the shadow prices of water, and prepare a succinct report on the outcomes.
Exercises:
Lecture 6 - Text_exercises.pdf
Slides:
Lecture 6 - Water valuation in crop farming_ concepts and application.pdf