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Lecture 21 & 22

The efficient allocation of a resource

at one point in time,

the case of surface water.

A new equimarginal condition

• First –

• Second –

• Third - The MNB to every user should be equal

at the efficient allocation.

A single farmer

3

Tons

Q - water

Yield

2

A single farmer

4

$

Q - water

Revenue

A single farmer

5

$

Q - water

Revenue

Cost

A single farmer

6

$

Q - water

Revenue

Cost

Profit

3

A single farmer

7

$

Q - water

Revenue

Cost

Profit

A single

farmer

(marginal)

8

$

Q - water

Revenue

Cost

Profit

$

Q - water

MarginalRevenue

M. Cost

A single

farmer

(marginal)

9

$

Q - water

Revenue

Cost

Profit

$

Q - water

MR

MCMNR

4

A single

farmer

(marginal)

If Marginal

Net Rev. >0

then Profits

can be

increased by

using more

water

10

$

Q - water

Revenue

Cost

Profit

$

Q - water

MR

MCMNR

A single

farmer

(marginal)

11

$

Q - water

Revenue

Cost

Profit

$

Q - water

MarginalRevenue

M. CostProfit

A single

farmer

(marginal)

Profits are

maximized

when

MNR=0

12

$

Q - water

MR

M. CostMNR

$

Q - water

MNR

5

A single

farmer

As long as

there is at

least Q*

gallons of

water,

profits can

be

maximized

13

$

Q - water

MNR

Q*

A single

farmer

Suppose there

isn’t enough

water.

Profits cannot

be maximized.

The marginal

value of water

will not be

driven to zero.

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$

Q - water

MNR

Q

A single

farmer

Suppose

there isn’t

enough

water.

The positive

marginal

value of

water is

called

“marginal

scarcity rent”

15

$

Q - water

MNR

Q

6

Two Identical Farmers

Suppose there are 2 identical farmers, both who would like to use Q* gallons of water

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$

Q - water

MNR

Q*

$

Q - water

MNR

Q*

Farmer # 1Farmer # 2

Two Identical Farmers

If there is less than 2xQ*, then there won’t be enough water for both

farmers to maximize their profits. We have an allocation problem.

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$

Q - water

MNR

Q*

$

Q - water

MNR

Q*

Farmer # 1Farmer # 2

Two Identical Farmers

If there is exactly Q* gallons and Farmer 1, uses it all, then the profits

will be as shown

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$

Q - water

MNR

Q*

$

Q - water

MNR

Q*

Farmer # 1Farmer # 2

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Two Identical Farmers

If Farmer 1 gives a little bit of his water to Farmer 2, then profits change as shown and total

profits goes up.

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$

MNR

Q*

$

Q - water

MNR

Q*

Farmer # 1Farmer # 2

decrease increase

Two Identical Farmers

As long as the marginal net revenue to Farmer #2 is greater than that to Farmer #1, then

total profits will be increased by moving water from 1 to 2.

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$

MNR

Q*

$

Q - water

MNR

Q*

Farmer # 1Farmer # 2

decrease increase

Two Identical Farmers

The efficient allocation is achieved when the MNR to Farmer #1 is equal to the MNR of

water to Farmer #2.

In this case, because the farmers are identical this occurs where there water use is equal,

but in general that will not hold.

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$

MNR

Q /2*

$

MNR

Farmer # 1Farmer # 2

Q /2*

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Marginal Scarcity RentAs in the single-user case, because of the limited nature of the

resource, at the optimum the marginal scarcity rent will not be zero.

This tells us how much society would benefit if we could obtain a little

more of the resource.

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$

MNR

Q /2*

$

MNR

Farmer # 1Farmer # 2

Q /2*

Team Exercise: Answer

• Al and Betty both share a water supply. For Al the cost to use water is

essentially free because he lives downstream of the supply. Betty, has to

pump water, meaning every unit she uses costs her $1

10

8

6

4

2

00 10 20 30 40 50

MBA

MBB

$/unit

units of water used

• 1) What is the marginal net benefit to Al of

the 20th unit that he uses?

(pick the nearest answer)

A. =0

B. =1

C. =2

D. =3

E. =4

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• 2) What is the marginal net benefit to Betty of

the 20th unit that she uses?

A. =0

B. =1

C. =2

D. =3

E. =4

• 3) Suppose Betty already has a right to 20 units of

water. How much would she be willing to pay per

unit for a marginal increase in her water rights?

A. =0

B. =1

C. =2

D. =3

E. =4

• 4) Suppose there is 100 units of water available. What would be the

efficient allocation of water between Al and Betty?

A. A=30, B=70

B. A=40, B=60

C. A=50, B=50

D. A=60, B=40

E. None of the above

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• 5) Suppose there are only 15 units of water available

in the reservoir. How much would Al use and how

much would Betty use in the efficient allocation?

A. A=0, B=15

B. A=5, B=10

C. A=10, B=5

D. A=15, B=0

E. None of the above

•

• 6) Suppose there are 30 units of water available. How much

would Al use and how much would Betty use in the efficient

allocation?

A. A=0, B=30

B. A=10, B=20

C. A=20, B=10

D. A=30, B=0

E. None of the above

•

• 7) Suppose there are 30 water rights and Al owns all 30. What

would be the increase in net benefits that could be achieved if

Al decides to sell a portion of his rights to Betty instead of

keeping all of the rights to himself?

Shade in the appropriate area on your graph

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Riparian vs. Prior Appropriation

• Riparian rights:

– If you have access to a waterway, you can extract

what you need. You are not allowed to sell water

to others

• Prior appropriation:

– Rights are specified to individuals in terms of the

quantity of water they can extract. These rights

can be sold. Those with the oldest rights, more

seniority, have more certainty that they will get

their water in the event of a drought.

Team Answer

• Which system of water rights allocation is

more likely to lead to an efficient allocation

and why?

• When do riparian rights tend to be more

efficient (i.e. maximizing net benefits at

minimal cost).

• Don’t forget about transaction costs.

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Where is the failure of exclusivity under Riparian Rights going to be a problem?

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Where is transferability under PriorAppropriation going to have the greatest value?

Municipal Water Pricing

• Which system(s) will satisfy the 3rd

equimarginal condition, the MNB to every

user should be equal at the efficient

allocation?

A. Uniform rate structure

B. Declining block rate structure

C. Inverted block rate structure

D. Seasonal rate structure

Municipal Water Pricing

• Which system(s) will satisfy the 1st

equimarginal condition, MB = MC?

A. Uniform rate structure

B. Declining block rate structure

C. Inverted block rate structure

D. Seasonal rate structure

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15

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• 8) Suppose that the river has 30 units of water in it, and Al

and Betty use all of it, efficiently allocating the water

between the two of them. However, this leaves no water

for fish in the river. Would this be socially efficient?

• 8) Suppose that the river has 30 units of water in it, and Al

and Betty efficiently use all of it. However, this leaves no

water for fish in the river. Would this be socially efficient?

• How would you adjust the water policy to

achieve an efficient allocation?

Review

• Public Goods

– A public good is non-rival and non-exclusive.

• Externalities

– An externality occurs when the benefits or costs

associated with use or ownership accrue to

someone other than the owner.

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The nature of water

• Is water a private good or a public good?

• Are there externalities associated with the use

of water quantity (not quality)?

• When, if ever, are these true for water?

• When, if ever, is there a justification for public

intervention in the supply of water?

Brazos River & Senior Rights

Prepare to debate either side

• Pro: By taking away water rights from the

senior rights holders, net benefits to society

increased.

• Con: By taking away water rights from the

senior rights holders, social efficiency was

diminished.

• http://www.youtube.com/watch?v=rlctTUwn

Gm8

• Suppose we want to know if it would be

economically efficient to build the pipeline.

What would we need to know?

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Scope of work

• Carry out a study to assess whether it would be

economically efficient to build the pipeline from

the Missouri River to the Colorado River.

• Step 1:

– Identify benefits of the project.

– Identify costs of the project.

• Step 2: Estimate the dollar value of the benefits

• Step 3: Estimate the dollar value of the costs