OPTIMAL AQUIFER MANAGEMENT
4.4 Implementation of Optimal Aquifer Management
to the steady state. For a water depth that is very low, the efficiency gain of groundwater management occurs in a far future so the discounted welfare improvement from optimal management is small.
However, for a water depth close to Ha, according to this model, the efficiency gain from optimal management can be significant as it reallocates groundwater from low-value annuals to high-value permanents. Studies that fail to consider the difference of the two types of crops will take a smooth water demand function and hence miss the efficiency gain from this channel. For example, in Knapp, Weinberg, et al. (2003), they estimated a water demand function using Kern County Water Agency 1998 report, when both annual and permanent crops were farmed in the county and the annual crops were always the marginal crops. The estimated water demand function then only captures the demand elasticity of annual crops and ignores the inflexible water demand from high-value permanent crops. That biases down the estimate of efficiency gain.
The second channel of efficiency gain usually does not add too much to the welfare im- provement of optimal management. Even though the equilibrium recharge is significant and the difference of equilibrium water depth between optimal management and common access regime is large as in Knapp and L. J. Olson (1995), the time required to reach the steady state is so long that the discounted value of the efficiency gain is tiny. This is often the case for large aquifer with plenty of groundwater stock to deplete before water becomes scarce. For small aquifers, water is scarce; therefore, it is important to manage the steady state water depth as the efficiency gain is realized immediately.
also achieve the optimal outcome. I will briefly talk about them when discussing the design of pumping rights.
Defining the property rights of groundwater includes two important aspects: the design of water rights, and an incentive compatible assignment of those rights. I assume that there will be an efficient water market where the agents could trade their water rights (both surface and ground water) without transaction costs. Thus the design of groundwater rights determines whether the market can induce a socially efficient outcome or not. How the water rights are assigned does not affect the efficient allocation according to Coase (1960). However, the assignment of water rights could affect whether the new policy will be approved by the voters.
Design of water rights
The water rights design that has been widely discussed or implemented including one- time groundwater stock rights and operating pumping rights. V. L. Smith (1977) proposes to create water rights for the stock of groundwater to solve the water valuation problem.
According to Chapter 2, such an arrangement does not completely solve the commons problem as the agents tend to use more stock rights in the early period than is efficient because saving the stock rights creates positive externality as it raises the water table which also benefits others. Suppose the rights for natural recharge are negligible for this section5. Proposition 1 states the inefficiency result for stock rights.
Proposition 4.1 If one-time stock rights of groundwater are created and distributed to a large number of pumpers, the total extraction per period will not match the socially optimal volume.
Proof of Proposition 4.1 is in Appendix 4.B. Intuitively, when the return gap between annual and permanent crops is large enough, it takes a long time after annuals no longer
5The issues of distributing the flow rights are similar to the issues of stock rights as the main conflict of interests is always between farmers with access to groundwater and those without.
access groundwater before the permanent crop farmers stop mining the aquifer. AtHa, the marginal value of holding water rights is very small since the scarcity will arise far into the future. Therefore, the price of stock rights will be so tiny that the annual crop farmers will essentially ignore it and continue pumping groundwater untilH approaches toha. As a result, assigning water rights for groundwater stock at once does not solve the commons problem.
To avoid the externality caused by unused water rights, individual farmers must not have discretion to choose extraction. Instead, each period’s available water rights should equal the socially optimal extraction. Such varying water rights already exist and are called operating pumping rights as in Chapter 2. In that chapter, we have discussed how some Southern California basins set their pumping rights per period equal to the recharge to the aquifer. They do not issue pumping rights for the stock of water since their groundwater stock has been severely depleted. In this chapter, we have shown that the optimal aquifer management includes a period of depleting the groundwater stock and then maintaining the steady state water table by setting average pumping to equal average recharge to the aquifer.
As the recharge is assumed to be constant, the operating pumping rights discussed in this chapter are designed for the stock of groundwater:
Operating Pumping Rights: For H ≥ Ha, the pumping rights are 0 in wet years. In dry years, the pumping rights are Lp−SL forH ∈ [Ha,Hs)andRforH = Hs.
Operating pumping rights assign exactly the same number of pumping rights to the farmers per period as the optimal extraction derived in the social planner’s case. When there is a water market without friction, the water use is always efficient, so is the crop decision.
Similar to pumping rights, a varying pumping tax such that the annual crop farmers stop pumping at Ha and the permanent crop farmers stop further depleting the aquifer at Hs generates the same result. Land use control that restricts growing annuals when water depth is beyond Ha may also work. The political issues to implement those policies could be different. In this chapter, we discuss the political conflict raised by water rights assignment.
Incentive compatibility of optimal management The Bathtub Assumption Holds
Because of the heterogeneity among the farmers, the assignment of pumping rights should also be incentive compatible to make sure that the policy is approved by the agents. The following assignment rule is individually incentive compatible when the aquifer satisfies the bathtub condition.
Assignment 1: Pumping rights are shared by all farmers proportional to their land when