ENVECON 162 Lecture Notes - Lecture 5: Farm Water, Production Function, Fixed Cost
4 May 2018
School
Department
Course
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Economics of Water Resources
Spring 2018
Lecture 5:
Farm Water Use
-run) profit function is defined by:
❖
This profit function can also be written as follows:
❖
➢ is the amount of applied water; represents the irrigation technology.
➢ is a measure of land quality; represents the irrigation effectiveness of
technology .
➢ is the price of the crop; is the crop-water production function which
depends on the amount of effective water, .
➢ is the price of water; represents the fixed cost of implementing technology .
Once the farmer solves for the optimal amount of applied water for each passible
technology, the farmer can then choose the profit-maximizing technology.
The farm water use problem can be solved in two steps using backwards induction:
❖ First, calculate the optimal for each technology .
❖ Next, compare profits across each possible technology and then finish by choosing the
technology that maximizes profits.
Step 1: Calculating Optimal
For Each Technology
Applied water is chosen to maximize short-run profit given a previous choice of
technology:
❖
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Economics of Water Resources
Spring 2018
is the applied water level that solves this equation. It represents the optimal applied
water given a choice of technology and land quality .
: this relationship states that the optimal level of applied water equates the
value of the marginal product of effective water to its price.
This optimality condition implies that the water demand curve slopes downwards. In other
words, a higher implies a higher
.
Step 2: Finding the Optimal Technology
Suppose we have two irrigation technologies, and :
❖ represents the traditional technology.
❖ represents the modern technology.
We need to calculate and compare profits for both technologies to determine which
technology yields higher profits:
❖
➢ We plug the values for into the above expression to find .
Using the Caswell-Zilberman Model to Predict Irrigation Technology Adoption
Often in economics, we want to know how a change in an exogenous variable will affect
optimizing behavior relative to the status quo.
For the farm water use problem, we can use the Caswell-Zilberman model to predict how
differences in land quality affect the likelihood of adopting the modern technology
irrigation. This is known as comparative statics.
To perform such a comparative statics exercise, we need to know how profits under the
traditional and modern irrigation technologies change with land quality:
❖ First, we start by differentiating profits with respect to land quality, :
➢
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Document Summary
This profit function can also be written as follows: Lecture 5: land quality and farmers" choice of irrigation technology. A farmer"s conditional (cid:4666)short-run) profit function is defined by: (cid:1853) is the amount of applied water; represents the irrigation technology. Is a measure of land quality; (cid:4666)(cid:4667) represents the irrigation effectiveness of technology . (cid:1868) is the price of the crop; (cid:1858)(cid:4666)(cid:1857)(cid:4667) is the crop-water production function which depends on the amount of effective water, (cid:1857). (cid:1874) is the price of water; represents the fixed cost of implementing technology . Once the farmer solves for the optimal amount of applied water for each passible technology, the farmer can then choose the profit-maximizing technology. The farm water use problem can be solved in two steps using backwards induction: Next, compare profits across each possible technology and then finish by choosing the. Applied water is chosen to maximize short-run profit given a previous choice of technology: technology that maximizes profits.
