Dynamic Efficiency and Mineral Resources

Monday, Feb. 27

Mineral extraction decisions

Private property rights Owner will extract that amount of

resource that maximizes her net returns over time.

Rent – accrues to owner of resource because of scarcity

Natural Resource Rent

Quantity

Period t0

0

1

2

3

4

5

6

7

8

9

0 5 10 15 20

MB

MC

$

10.238

3.905

Rent

Wages, etc.

In our previous example (two-period, social planner model), rent was viewed as all returns going to society.

Formal definition of rent:

Returns to a resource in excess of what is required to bring the resource into production. e.g. any earning above extraction

cost for minerals In formal sense, must have a

market and a PRICE to have rent.

Natural resource rent to resource owner

Quantity

Period t0

0

1

2

3

4

5

6

7

8

9

0 5 10 15 20

MB

MC

$

10.238

3.905

Rent (producer surplus)Wages, etc.

When a resource is privately owned, the owner earns rent. The remaining surplus accrues to consumers.

Consumer surplus

Dynamic efficiency and mineral extraction In a well-functioning market, a mineral

owner’s incentives lead to a rate of extraction that satisfies: MNB0 = PVMNB1 = … = PVMNBt

This maximizes the present value of rents to the owner of the resource.

Rents to owner reflect user costs to society If owner doesn’t make decision based on

earning rent, then opportunity costs of current use are ignored.

Marginal rent to resource owner is equal to marginal user cost to society

Quantity

Period t0

0

1

2

3

4

5

6

7

8

9

0 5 10 15 20

MB

MC

$

10.238

3.905

MUC = 1.905

Marginal rent = 1.905

Total rent = 1.905*10.238=

59.41

MEC + MUC = P

Exercise – how a market allocation of a depletable resource responds to various factors

Illustrate dynamically efficient extraction rate and marginal user costs

How does the availability of a renewable substitute affect extraction rate? (A more sustainable solution?)

How do increasing marginal extraction costs affect extraction rate?

Can investment of rents also address sustainability?

In a two-period world: MNB0 = PBMNB1 MB = 8 - .4q MEC = $2, r=.1 Total Q = 20 = q0+

q1

Solve for qs 2 equations, 2

unknowns

In an unlimited time frame:

MNB0 = PBMNB1 =…= PVMNBt

MB = 8 - .4q MEC = $2, r=.1 Total Q = 20 = q0+

q1+…+ qt

Solve for qs t equations, t

unknowns

Computer algorithms use iterative process to solve for qs.