GroundwaterGroundwater can be viewed as both an exhaustible resource and as arenewable resource:Groundwater as an exhaustible resource--Aquifer that is not being replenishedRelevant Economic FactorsPumping CostsCP = pumping cost per unit of waterCP = hi Ui dUi = unit price of energy service (fuel, electricity)hi = energy source requirement per unit of liftd = well depth.Increase in energy price:(1) Reduces pumping with existing equipment.(2) May lead to modernization of pumps.(3) Likely to reduce groundwater demand.(4) Will lead to adoption of modern technologies.Groundwater as an Exhaustible Resource (cont.)Public vs. Private Conflicts in Groundwater UseConflicts arise when individual pumps are not regulated or metered:open access => over-extractionSW = social cost of groundwater pumpingSW = CP + CS + CECP = pumping costCS = user cost (cost of exhaustibility of the water stock; shadowprice of the resource stock constraint)CE = open access cost associated with common pool problem(increased cost of pumping associated with reduction inwater level as stock is depleted).The user cost increases as:• Interest rate is lower.• Water stock is smaller.• Alternative water sources are costlier at present or future.Open access costs increase as:• the area of aquifers is smaller and lift costs are larger.Inefficient resource use may occur when:• Water users are myopic or their interest rate is larger than the socialrate.• There are many resource users.Corrective Policies:• Tax based on crop and technology choices.• Regulation restricting crop/technology choices.• Subsidy of conservation technologies.• Limitations on pumping capacity per acre.Groundwater as a Renewable ResourceRain and deep percolation can renew the groundwater stock.The model:The equation of motion for the groundwater stock is:St+1 = St− Xt+ δXt+ RtSt+1 = water stock at period t + 1Xt= pumping in the previous periodδ = deep percolation of water pumped onto fieldRt= replenishment by rain.In the long run average water pumping has to be equal to averagerainfall in order to sustain optimal water stocks. Actual water use mayvary from year to year to reflect:• Variation in water conditions and• Variation in output price.Every steady-state level of the state variable, S, is associated with adifferent groundwater table, which will influence the choice of theoptimal well depth. Determining of optimal, sustainable, average welldepth involves assessing the:• Risk of prolonged droughts (which is used to set lower bounds).• Increase in average pumping cost as average depth increases.• Benefits from mining excessive water un-sustainably in early periodsin order to reach the average sustainable well depth.Groundwater as a Renewable Resource (cont)The theory of renewable resources suggests that when water isreplenished, and optimal sustainable depth is lower than the initial watertable, the optimal water pumping strategy consists of two phases:(i) Mining of excessive stock until sustainable depth is reached; and then(ii) Pumping of water at the rate of replenishment (Rt) for theremainder of time.InitialdepthIntiallevelGroundwater as a Renewable Resource (cont)Modeling Problems• Deep percolation may lead to reduction of water quality due toleaching of nitrates, phosphates and pesticides.• There is a time lag between rain, water use and replenishment.• Rain is randomly distributed.Other Issues:the stock of groundwater is stochastic due to natural variability inrainfall.When we solve for the optimal well depth, we implicitly assume that allfarms are the same, even though water uses over a groundwater sourcewill vary greatly based on cropping patterns, and irrigation technology.A few decades ago, the Mississippi River Basin was dredged by theconservation corps., then in 1994 there was a huge flood. This raisesquestions such as:• Should the government build a levy to protect farmland fromflooding?• Or should these lands be allowed to revert back to wetlands?Conjunctive UseDefinition: The simultaneous use of groundwater and surface water.A Model of Conjunctive Use:there are three types of events occurring with equal probability:W - Wet Seasons; N - Normal Seasons; D - Dry SeasonsS = the level of surface water = a with probability 1/3 2a with probability 1/3 3a with probability 1/3.Assume water stock is infiniteCost of surface water: m$/AFCost of groundwater: n$/AFm < nLet: B(A) be the benefit from water and applied water be denoted by:A = S + GS = amount of surface water applied,G = amount of groundwater applied.Conjunctive Use (cont) A = S+G SW = 3a SN = 2a SD = a D1 D2 VD = n VS = m VN1 a b c e f g d h j VN2 kThe idea of conjunctive use is to combine the management of surfaceand groundwater using groundwater supplies as storage. Total wateravailable is the sum of groundwater and surface water, but surfacewater is used first (because it is cheaper) and groundwater reserves areused only to stabilize variability in the annual supply of surface water.The optimal water use strategy can be found by solving:MaxSD,GD,SNGN,SW,GW13B SD+ GD( )+ B SN+ GN( )+ B SW+ GW( )− m SD+ SN+ SW( )− n GN+ GD+ GW( ){ }where the FOCs for a dry year are:(1) dLdSD=13BSD− m = 0(2) dLdGD=13BGD− n = 0, and similar for wet and normal years.Conjunctive Use (cont)When surface water and groundwater are of homogeneous quality, it isnot optimal to use both surface and groundwater at the same time. =>use all surface water first, since it is the cheaper source, and then usegroundwater only when we run out of surface water. The optimal choices (when benefits are based on Demand = D1)Year Groundwater Surface Water Water PriceDry ef ab VD = nNormal 0 ac VN1Wet 0 adVs = mThe optimal choices (when benefits are based on Demand = D2):Year Groundwater Surface Water Water PriceDry eh ab VD = nNormal gh ac VD = nWet 0 aj VN2If groundwater price declines with stock, and stock can be adjusted,there will be a steady state where groundwater is used in dry years;where excess water is added in wet years, so that avg. groundwaterlevel is stabilized at the desirable steady-state level.the price of groundwater is determined by the appropriate steady-statesolution. If demand is high (D2), groundwater is used in 2 out of 3 ofthe possible seasons at an annual average level of:eh gh+2The other 33% of the time, in wet years, the rate of groundwaterreplenishment is only at level hk (the surface