AssignmentWater Economics and Policy for Integrated Water Resource Management

Problem #1A small town accommodates 1000 households, all connected to a water supply network. It is assumed that all households behave according to one same demand function. It is also assumed that all fully pay their water bills. Water is currently supplied at Pc = $10 per 1000m3(current price). Overall current supply of domestic water is 1,000,000 m3 per year (assumed to be the demand Qd).

- Question #1: what is the annual consumption per household (averge)?

The annual consumption per household

- Question #2: what is the annual revenue of the water utility (service provider) (excluding costs)?

The annual revenue

A survey reveals that households would be willing to pay upto 200 $ per 1000 m3 in order to satisfy their basic needs in domestic water (such is the price of large bottles of drinking water supplied by vendors).

- Question #3: what is the logarithmic demand function (for all households as one sector)?The logarithmic demand function is

Let P1=10 Q1 = 1,000 And P2= 200 Q2 = 0Substitue P and Q in such equation, when Q2 = 0, a = P2 = 200

Therefore,

Remark: Units of P is $ / 1,000 m3 and Q is x103 m3

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- Question #4: similary, what is the exponentail marginal benefit function (or WTP curve)?

The exponentail marginal benefit function is From Question #3, a = 200 and b = 333.8082Therefore, Remark: Units of P is $ / 1,000 m3 and Q is x103 m3

Figure 1 Demand Function Curve

Qd = -333.81Ln(P) + 1768.63

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Figure 2 Marginal Benefit Function Curve

P = 200e(Q/-333.81)

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- Question #5: what is the total benefit of domestic consumer (households), also called consumer surplus CS?

Figure 1 Demand Function Curve

Qd = -333.81Ln(P) + 1768.63

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To find the consumer surplus as shown in the figure above, let us integrate the area under the curve between the limits 10 and 200.

Given a supply equation:

- Question #6: Considering demand and supply equations, calculate the market clearing price of water (also called equilibrium price Pe)?

Demand equation = Marginal benefit equation

Supply equation = Marginal cost equation

Let MB = MC, the intersection point of these two equations is equilibrium price, PeTherefore, Pe = 17.3 $/1,000 m3

Qe = 817.7 x103 m3

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Figure 3 Market Equilibrium Point

P = 200e(Q/-333.81)

MC = 0.015Qs + 5

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- Question #7: Compare Pe with Pc, and comment on the difference. How would a shift from Pc to Pe alter demand Qd and Cs?

From previous question, Pc = 10 $/1,000m3 Qc=1,000 x103 m3

Pe= 17.3 $/1,000m3 Qe= 817.7 x103 m3

The Pe is greater than Pc but the supplied water will be less than demand. So that, water price is increased from Pc to Pe and the supplied water will be less than demand. Such that, CS will be changed.

CS is decreased from 53,423.60 to 46,852.1 $/1,000m3, decrease 6,571.50 $/1,000m3.

- Question #8: Calculate the net benefit of supplier (or producer surplus PS) and CS under two prices scenarios.

Scenario 1, water price = 10$/1,000m3.PS = area above the supply curve, limited by price

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Pe = 17.3

Qe = 817.7

CS = area below the Demand curve, limited by price

Scenario 2, water price = 17.3$/1,000m3 (equilibrium price)PS = area above the supply curve, limited by price

CS = area below the Demand curve, limited by price

- Question #9: what is the total economic value (CS + PS) of domestic water as supplied and used in SmallTown, under current circumstances (P and Qw)

Scenario 1, water price = 10$/1,000m3.Total economic value = 833.33 + 53,423.60 = 54,256.93 $

Scenario 2, water price = 17.3$/1,000m3 (equilibrium price)Total economic value = 50,28.86 + 46,852.10 = 51,880.96 $

- Question #10: calculate price elasticity of demand ε around Pc (use current price and an alternative price of 11 $ per 1,000 m3 to calculate ε)

From

For P = 11 $/100m3,

Price elasticity of demand ε is -0.332, means 1% of increasing price make 0.332% decrease in demand quantity. Nevertheless, if 1% of price is deceased, 0.332 % of demand quantity will increase.

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Problem #2: SmallTown authorities wish to develop a waste water plant and plan to impose a tax of $2 per 1,000 m3 used, to be added to the current price Pc.

- Question #11: What will be the consequences of such a decision on consumer demand? On CS?

The new current price is Pc = 10 + 2 = 12 $/1000m3.

Therefore,

Determine consequence on consumer surplus CS

- Question #12: consequences on the total revenue from tax?Total revenue from tax

- Question #13: consequences on PS and CS? On total economic value of the supply system?

Determine Producer Surplus

Determine Consumer Surplus

Total economic value of the supply systemPS + CS = 3,286.99 + 51,486.27 = 54,773.26 $

When tax is added to the price of water, Consumer demand is decreased to 939.14 x1,000m3, CS is decreased 1,937.29 $ while PS is increased from 833.33 $ to 3,286.99 $. Furthermore, total economic vlaue is also increased 516.36$.

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Problem #3: The small town municipality plans to develop a greenhouse based horticultural projects producing high value products (orchids) using the same municipal water. Since overall resources is limited to 1,000,000 m3 and already serves domestic users, choices are to be made.The horticultural product will use 100,000 m3 per annum, supplied free of charge by supply utility. Crop budget unfolds as follows

Average farm-gate price of products (orchids) = $1 eachTotal yearly production = 8,000 unitsTotal production costs = $ 2,000

- Question #14: what is the total value of water (as a product input) of the project?Total value of water

- Question #15: The supplier still has to supply 1,000,000 m3 but only 900,000 m3 are paid for (10$/1,000m3). What is the revenue of the supplier?

Total benefit of supply

Total cost of supply

Therefore, net revenue of supplier

- Question #16: Calculate the total economic value of the domestic supply system under these new conditions (CS+PS) and compare with the total economic value of the horticultural project. Compare scenarios and comment.

Determine Consumer Surplus CS = area below the Demand curve, limited by price

Determine Producer Surplus PS = area above the supply curve, limited by price

Total economic value

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CS + PS = 53,248.91 + 833.33 = 54,082.24 $

In conclusion, the total economic value of domestic supply system is greater than total value economic value of the horticultural project. The total economic value of this alternative compares with the alternative without horticultural project, the quantity which is supplied for domestic reduced but the value of this alternative is bigger than total value of the alternative without horticultural project.

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