AE 5108: WATER RESOURCE ECONOMICS 1 FIRST SEMISTER 2006/2007

1. AE 5108: WATER RESOURCE ECONOMICS 1FIRST SEMISTER 2006/2007 LECTURE NO. 3 & 4 • L. No 3: MARGINAL ANALYSIS • What is Marginal Analysis ? • How may it be used in W. Resource Economics? L. No. 4: Marginal Analysis & Econ. Decision Making

2. L. No. 3: MARGINAL ANALYSIS FRAMEWORK MA constitute one of the most pervasive concepts of economic decision making. Resource allocation decisions are typically expressed in terms of marginal conditions to attain an optimal solution. In the MA framework, resource allocations are made by Comparing the M Benefits of a change in the level of activity with the M Cost of the Change. A Change is Desirable as long as the MB > MC Y x PY > X x PX Optimal level is reached at MB = MC.

3. Substitution among Ys or Xs due to price movements is advisable if the MR of the substitution is higher. Activity should be reached where Marginal Net Benefit (MNB) = MB – MC = 0 Y = f (X); MPX = Y / X The use of M Analysis in Optimization Problem in Tabular, Graphic & Algebraic Framework Total, Marginal & Average Products Relationships • The first derivative (dY / dX) of Y = f ‘(X) • The limit of the ratio Y / X as X approaches to 0

4. Marginal Analysis Start at producing zero. Should you produce one unit? Yes, if marginal revenue > marginal cost. Given one can profitably be produced, what about a second unit? Yes, if MR greater than or equal to MC. Continue this iterative process until you get to the point where MR (price) = MC. Stop. After that, producing one more will generate MR < MC.

5. Water Supply Example: MC schedule that illustrates the Law of Diminishing Marginal Returns. As quantity supplied increases by one unit, the associated MC increases.

6. Water Supply Curve The firm’s MC curve is it’s supply curve, since it shows the relationship between price and quantity supplied

7. Optimal Water Supply Level Largest available profit where P = MC

8. The Firm’s MC Curve is it’s Supply Curve. So, why should we care about all of this cost curve analysis? Because in an unregulated competitive market external costs are not accounted for in the firm’s marginal cost, which means that the firm’s supply decision ignores external costs. Marginal Social Cost = Marginal private cost (borne by the firm, passed along to consumers via market price) + Marginal external cost (uncompensated costs borne by the environment and society)

9. The supply curve based on marginal private cost. The supply curve based on marginal social cost. Marginal social cost Marginal private cost

10. The Production Function (PF) The PF express the max. quantity of product that can be produced from different quantities of one or bundle of inputs, with all other inputs held constant and the technology remains the same. Law of Diminishing Return (LDR) As additional units of a input are used in combination w one or more fixed inputs, e Marginal Physical Product will eventually begin to decline. LDR indicates that at some point it becomes no longer profitable to make additional application of inputs to fixed items. Add variable resource to a fixed resource as long as the added return is greater than the added cost.

11. Water Production Functions for Irrigated Agriculture WPFs are basic in the optimal allocation of water among soil types, farms and uses • WRF are sought to estimate • the best farm organization & water use • the yield increases expected • the relevant charges form water users The productivity of W differ among e different soils & it will differ when it is applied at different levels. • Decision rulefor optimal use of W depend on • the knowledge of the WPF relative to soils, env. variables & management variables. • the stochastic nature of the water supply

12. Simple Response Function Yi =ai Wi -bi Wi2 ; Y1 =a1 W1 –b1 W12 ; Y2 =a2 W2 –b2 W22 Marginal productivitydYi/dWi = ai Wi -2bi Wi With a maximum output the marginal productivity of water is the same on all land areas, even they differ in productivity, & their WPF. The goal in incorporating soil & env. variables is to allow prediction of yield response to irri. Level over a wide range of soil, climate, & locational conditions. Dynamics of Water Response Simple WPF do not consider time of applications Time of irri. & plant growth interact w other moisture & soil characteristics to affect plant stress, wilting, & yield. Thus a complex of response to W applications

13. Dynamics of crop yield response to time & amount of Irrigation d c Yield b a t0 t1 t2 t3 Time • Water response functions are complex functions • in their dynamic nature • in their interactions w other biological inputs- F,S • in conformance w their surrounding soil & climate

14. Production Functions & Economic Applications Y3 B Frontier PF Yield Y2 Increase A A1 Hypothetical PF for Yield – W relationships A0 Y1 O X1 X2 Water added PF are used in many economic analysis By definition, a PF embodies technical efficiency. i.e: a specified set of inputs cannot be recombined to produce a larger output. Consequently, production should occur on the “frontier” of a production possibility surface. OX1 input is expected to produce OY2 A producer operate along OA, have e access to technology & successfully adopt it. Move OA to OB

15. The Crop Water Response Relation - Yield & Water Increasing Decreasing Negative Returns Returns Returns MPP & APP per m3 AP MP A B C D PWP FC WL Ep = 0 Z Ep =1 Stage I Ep>1 Crop Yield Kg/ha Stage III Ep<0 Stage II 0 < Ep <1 TP Water reaching crop m3ha 0 A B C D

16. Demand for Irrigation Water - Derived from the VMP • The scope for increase in Opportunity Cost of Irri. W • Increased field IE • Substitution: Labour for water • Choice of Crops: Short age, • High Yield Crops • Complementary inputs; Ferti MVP/M3 Rs. B C P MVP2 MVP1 Quantity of Water m3 Farmers Decision Related to Irrigation:- Crop Price, WaterCost, Risk, Expected Yield, Water Availability

17. DECIDING UPON THE LEVEL OF INPUTS Profit will be maximized when: VMPW (MPW xPY) = MC ( PW) 2. MPW = PW / PY (Inverse PriceRatio) 3. TR (Y x PY)–TC( FC + VC) Marginal Value Product (MVP) Change in the total value of the product resulting from on unit change in input. MVP = [d (Y x PY) / d W)] Value of Marginal Product (VMP) The value of the change intotal production resulting from one unit change in input. VMP = (dY/dW) x PY =MPW x PY It isimp. not to confuse MVP w VMP & MC w MIC

18. Economic Optimization How Much Input (W) to Use? VMPW (MPW xPY) = W x PW / W = MIC ( PW) MIC = ( TIC / W) = ( W x PW / W) = PW Decision Rule: If VMP > MIC increase Input < MIC decrease Input How much output to produce? MR = PY = MC = W PW / Y = PW / MP MC = ( TIC / Y ) = ( W x PW) / Y) = PW/MPW Decision Rule: If MR > MC increase Output < MC decrease Output

19. Prod. Function Relationships & Optimal Y* and W* • W Y AP MP TVP MR* VMP MIC MC • (YxPY) (PY) (Pw) (Pw/MPw) • 0 20 - 200 10 • 1 30 30 10 300 10 100 250 25 • 2 80 40 50 800 10 500 250 12.5 • 3 150 50 70 1500 10 700 250 8.3 • 4 160 40 10 1600 10 400 250 25 • 160 32 0 1600 10 320 250 *Marginal Revenue (MR) = dTR / dY = d(PY x Y) / dY If PY is constant then MR = d(PY x Y) / dY = K = PY Y* = 140 and X* = 2.5

20. L NO. 4. Economics of Water Resource Allocation Water is Replenishable but Depletable Resource. Global level Water Supply > Water Demand. Water Scarcity & “Water Blindness”. Current Use > Replenishable = Irreversible SURFACE WATER Renewable – Flow, Earth’s Hydrologic Cycle. Less Intergenerational Effects in Allocation. Efficient Allocation: MVPA = MVPB = MOCW = PW Transfer Equalize MNBS & Increase SNBS

21. Marginal Net Benefit (MNB) S0 S2 S1 MNBB Aggregate MNB MNBA MNB = VMP (D. Curve) – MC = Scarcity Rent (SR) MNBA = MNBB = SR ; Maximize Social Benefit Rs MNBS2 MNBS1 MNBS0 A0 B0 W When W is not scare at S0 SR = 0 = MNBA = MNBB When W is scare SR is +ve MNBA = MNBB at S1 At S2 MNBA < MNBB

22. The Efficient Pricing of Water RS RS D- Urban A D- Rural B P* 0 R0 W W’ W* U0 Effi. market equilibrium; MVPU =MVPR at P* Rural Consume W*W Urban Consume 0W* Any Deviation leads to loss in welfare

23. The Allocation of Water Between A & B Equal Users MVP A MVP B Rs MVP / m3 P 0 A’ SW E F B’S W The Allocation of Water Bet. A & B Un Equal Users Rs MVP / m3 Economic Rent Economic Rent P 0 A’ SW F B’S W

24. Sources of Inefficiencies In Allocation MC of Water C A Rs. Demand of Low Income Group P* Aggregate Demand for Water B O WL Water PW is set atAgg.Demand and MC affect the Poor P* CWL O a large share of the low income group. PW = 0, Fairness / Equity Principles Water Transfers are Restricted W as a Public Good – Non Exclusive & Joint Use

25. GROUND WATER • Fund is accumulated over time • Recharge depends on time and geology • GW is primarily a depletable stock • Fund withdrawals affects the future availability Efficient Allocation of Finite Stock 3 Conditions Optimal Use of Depletable Resource – GW • PW = MPC +MUC + MEC ; RR = MUC + MEC • OC = associated with future unavailability • 2. Constant PVRR for each period of use • PVRR = ( RR x Q ) / ( 1 + r ) t : r = Discount rate • Social optimal extraction • RR rise (g%) = Rate of Interest (r%) • 3. Withdraws should be < Stock

26. Optimal resource allocation (Hotelling) MUC=MUC0ert PW = MC + MUC Rs Reserves MC Consumption Time The PW = MC + MUC, rise with increasing scarcity This Pw will diminish use by leading to substitution As well as increased efficiency & recycling. More exploration when MUC is high The rise would continue until 1. Supply is exhausted 2. MC > MB 3. Find next least alternative at MC

27. Optimal Rate of Resource Use • Optimal use of resource considers time • Time helps to distinguish bet. Renewable & Non R • The link between RR & NRR is very close • Static models fails to capture the trade off bet. • Use & Time. Criteria used is Dynamic efficiency • Max.PV of the NB from the use of resources • When the resource use at time t1 • Increase the degree of scarcity in time t2 • Optimum time path of use must consider MUCt • Allocation of W over time is crucial for GW

28. Production Functions with One Variable Input Y = f (W/ S,F, L, C) f = input – output relationship Cobb-Douglas PF Y = kWb ; Y^ = 25W.3 Average & Marginal Products APW = Y/W = f(W/ S,F,L,C) = 25W-.7 MPW= dY/dW = df(W/ ….)/dW = bkW1-b = 7.5W-.7 • Economically Optimum Input Use-Level • = PYY – PW W = PYf (W/.…) - PW W = PY 25W.3- PW W (d/dW) = PY (dY/dW) – PW = 0 = 7.5PYW-.7- PW = 0 PY= 1.50 & PW=1.35 ; W that Max  = 20.7 M3 & Y= 62

29. Static Demand for a single input – Water MVPW = PW ; W = [bkPY PW-1] 1/(1-b) = [7.5PY PW-1] 1.429 The level of W varies inversely with PW. If PY,k, or b increase D curve shifts to right. Price Elasticity of Demand with respect to PW WPW = % W / % PW= (dW/dPW) (PW/W) = -1 (1-b) The negative sign denotes that if b is less than 1.0, PW & W should move in opposite directions. Price Elasticity of Demand with respect to PY WPW = % W / % PW WPY = (dW/dPY) (PY/W) = 1/ (1-b) The positive sign denotes that PY should increase the use of W.

30. Problems in Large Scale Irrigation Schemes: Insufficient resource provision for O&M Deterioration of Physical structures Unreliable W supplies & unorthodox practice Head and Tail end inefficient water allocation. “rent seeking” activities – unofficial charges for W. Approaches for Overcoming these Problems Technical improvements, control structures etc., Introduction of economic incentives farmer participation – accountable leadership.