1. A Summer Research Experience for Undergraduates Program in China
Preparing Resource and Environmental Managers with International Understandings and Merits (PREMIUM)
A Summer Research Experience for Undergraduates Program in China
May 16 - July 8, 2005
Application Deadline: March 5

2. Static Efficiency, Dynamic Efficiency and Sustainability
Wednesday, January 26

3. Represent the demand for a resource as: P = 8 – 0.4 q
Quantity $
Marginal willingness to pay is equal to marginal benefit – would be willing to pay for an additional quantity the amount by which that quantity would increase benefits. Marginal willingness to pay = demand.
This line is found using the equation shown. Can fill in values for P and calculate Q.
Demand = marginal willingness to pay = Marginal Benefit (MB)

4. P = q q P 8 1
7.6 2
7.2 3
6.8 4
6.4 5 6

5. Assume a constant marginal cost of extraction = $2.00
(Marginal cost = supply) $ MB
Demand MC
Quantity
Efficient allocation occurs where MB = MC, q = 15 units

6. Static Efficiency MB = MC
Criteria for allocation in a given time period, with no consideration of future time periods
Efficiency: no one can be made better off without making someone else worse off

7. $ MC
MB>MC
MC>MB MB Q

8. What are the net benefits of the efficient allocation?$ MB
Demand MC
Quantity
Efficient allocation occurs where MB = MC, q = 15 units

9. TB = ½(6x15) + (2x15) = 45+30 = 75 TC = (2x15) = 30 $ NB MB MC
NB = TB – TC = ½(6x15) = 45 NB
To calculate net benefits – that area under the MB curve less that area under the MC curve.
Quantity

10. This graph illustrates marginal net benefits: MB-MC$
MNB
An alternative way to view this is to graph marginal net benefit. Then total net benefit is that area under the MNB curve. MNB = MB-MC.
Quantity
Total NB = ½(6x15) = 45

11. Dynamic Efficiency
When the concern is efficient allocation of a nonrenewable resource over multiple time periods
MNB0 = PV MNB1 = PV MNB2 = … = PV MNBt
t represents time period

12. With only 20 units of the resource available, what is the present value of total net benefits if effective demand is met in the first period, with no consideration of the second period?
Only two time periods in this example
For present value calculations, r=.10

13. Period t0 $ MB MC Quantity
Given a two period world, with no attention to the future, quantity extracted in the first period is 15. NB = 45.
What is the implicit discount rate? It is infinite, since the future is not being considered.
It is not zero. A zero discount rate implies that the decision in period 0 does not affect the decision in period 1, so that each time period involves the same decision. But in this example, period 1 is being ignored even though it will be affected by the decision made in period 0.
Quantity

14. Period t0 $ MB MC
Quantity
NB = Area = ½(6x15) = 45

15. Period t1 $ MB MC Quantity
Given that there are only 20 units of the resource available, extraction of 15 units in the first period leaves only 5 units for the second period. NB to the second period = 25.
Quantity

16. Period t1 $ MB MC
Quantity
NB = Area = ½(2x5) + (4x5) = 25

17. Present Value of NB for t1 = 25/(1+r)
= 25/1.1
= $22.73
PV Total net benefit for two periods =
$45 + $22.73 = $67.73
What are the total net benefits? Have to discount second period benefits. Using 10%, PV TNB = $67.73.

18. With only 20 units of the resource available, what is the present value of total net benefits if the resource is allocated equally across two time periods?
(q0 = q1)

19. Period t0 $ MB MC Quantity
What if objective is fairness, so an equal amount is allocated to each time period? NB is $40, since the area of net benefits lost is ½ of (2x10).
What is the implicit discount rate here? It is zero. There is recognition that the decision in period 0 affects period 1, and the decision is made to treat each period that same. That means that the outcome in period 1 is as valuable as the outcome in period 0 – so no discounting is applied.
Quantity

20. Period t0 $ MB MC
Quantity
NB = Area = ½(4x10) + (2x10) = 40

21. Period t1 $ MB MC Quantity NB = Area = ½(4x10) + (2x10) = 40
The same is true for the second period.
Quantity
NB = Area = ½(4x10) + (2x10) = 40

22. Present Value of NB for t1 = 40/(1+r)
= 40/1.1
= $36.36
PV Total net benefit for two periods =
= $40 + $36.36 = $76.36
However, to accurately calculate total net benefits for two periods, must discount second period.
PV TNB = $76.36.

23. Find the dynamically efficient quantities for q0 and q1.
Find the efficient allocation of the resource over the two periods (dynamic efficiency).
Find the dynamically efficient quantities for q0 and q1.
Recall, for dynamic efficiency (to maximize PV of total net benefits), MNB0 = PV MNB1

24. MNB0 = PV MNB1
MNB = MB - MC
MB = 8 – 0.4q
MB – MC = (8 – 0.4q) – 2 = 6 – 0.4q
MNB = 6 – 0.4q

25. MNB0 = PV MNB1
6 - .4q0 = (6 - .4q1)/1.1
q0 + q1 = 20
6 - .4q0 = (6 - .4[20-q0])/1.1
1.1(6 - .4q0)= (6-8+.4q0)
q0 = (-2 +.4q0)
8.6=.84q0
q0 =
q1 = 9.762

26. This graph illustrates marginal net benefits: MB-MC=MNB$
MNB
Quantity

27. Period t0 $ MNB0 Quantity MNB = MB – MC = 6 – 0.4q
What would outcome be if dynamic efficiency is the objective?
Recall, dynamic efficiency requires that MNB0 = PV MNB1.
This graph shows marginal net benefit for the first period.
Quantity
MNB = MB – MC = 6 – 0.4q

28. Period t1 $ PV MNB1 Quantity Present value calculation: 6/1.1 = 5.45
This graph illustrates marginal net benefit for the second period. With a discount rate of 10%, this reduces the MNB of 6 to So the whole MB line is shifted down.
How do you determine where MNB0 = PV MNB1?
Present value calculation: 6/1.1 = 5.45

29. $ 7 6
5.45 5
MNB0
MNB1 4 3 2 1 t0 5 10 15 t1 15 10 5 q0
Quantity q1

30. MNB0 = 6 – 0.4(10.238) =
MNB1 = [6 – 0.4(9.762)]/1.1
= /1.1 =

31. $ q0 Quantity q1 MNB0 MNB1 MNB=1.9048 5.45 t0 t1 7 6 5 4 3 2 1 5 10 155 10 15 t1 15 10 5 q0
Quantity q1

32. To calculate total benefits, total costs, and net benefits:
P0 = q0
P0 = (10.238)
P0 = 3.905
P1 = q1
P1 = (9.762)
P1 = 4.095

33. Period t0 $ MB MC Quantity
3.905 MC
Graphically, the quantity allocated for period 0 is shown above. This graph can help calculate the NB for period 0. However, we need to know the $ at Q=
P = 8-0.4(10.238) = 8 – = 3.905
Quantity
10.238
NB = ½(4.095x10.238) + (1.905x10.238) = 40.46

34. Period t1 $ MB MC Quantity NB = ½(3.905x9.762) + (2.095x9.762) = 39.51
4.095 MB MC
NB for the second period are calculated the same way.
9.762
Quantity
NB = ½(3.905x9.762) + (2.095x9.762) = 39.51

35. Present Value of NB for t1 = 39.51/(1+r)
= 39.51/1.1
= $35.92
Total net benefit for two periods = $
= $76.38
To solve for total net benefits, the returns to period 1 must be discounted. So PV NB = $76.39.
Note that this exceeds PV NB from equal allocation ($76.36).

36. Comparing allocations:
Maximize NB to period 0
TNB = $67.73
q0 = q1
TNB = $76.36
Dynamically efficient allocation
TNB = $76.38

37. Sustainability Environmental sustainability Strong sustainability
Do not reduce total stock of natural capital
Strong sustainability
Do not reduce productivity (value) of natural capital stock
One type of natural capital may substitute for another
Weak sustainability
Do not reduce productivity of capital
May substitute manufactured capital for natural capital

38. With equal distribution
NB0 = $40
NB1 = $40
With efficient distribution
NB0 = $40.46
NB1 = $39.51
With sharing, keep NB0 = $40, invest 10%, send to t1
.46(1.1) = .506
NB1 = $ = $40.02

39. Marginal User Cost MNB0 = 6 – 0.4(10.238) = 1.905
= /1.1 = 1.905
The value of the last unit extracted in t0
Foregone benefit for t1
Opportunity cost of choosing to extract the last unit used in t0

40. User Cost and Natural Resource Rent
P = MEC + MUC
$3.905 = $
Period t0 $
Rent MB
3.905
User Cost
Wages, etc. MC
Quantity
10.238

41. MUC increases at the rate of discount 2.095 = 1.1(1.905)
P = MEC + MUC
$4.095 = $
MUC increases at the rate of discount
2.095 = 1.1(1.905)
Period t1 $
Quantity MB MC
9.762
4.095
Rent
User Cost

42. Reading assignment for Wed. Feb. 2:
Hartwick and Olewiler, on ANGEL
and
Field, Ch. 6