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 http://forestry.msu.edu/China/Premium.htm

Static Efficiency, Dynamic Efficiency and Sustainability Wednesday, January 26

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)

P = 8 - 0.4q q P 8 1 7.6 2 7.2 3 6.8 4 6.4 5 6

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

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

$ MC MB>MC MC>MB MB Q

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

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

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

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

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

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

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

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

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

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.

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)

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

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

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

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.

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

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

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) 6.6-.44q0 = (-2 +.4q0) 8.6=.84q0 q0 = 10.238 q1 = 9.762

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

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

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 5.45. So the whole MB line is shifted down. How do you determine where MNB0 = PV MNB1? Present value calculation: 6/1.1 = 5.45

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

MNB0 = 6 – 0.4(10.238) = 1.9048 MNB1 = [6 – 0.4(9.762)]/1.1 = 2.9052/1.1 = 1.9048

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

To calculate total benefits, total costs, and net benefits: P0 = 8 - .4q0 P0 = 8 - .4(10.238) P0 = 3.905 P1 = 8 - .4q1 P1 = 8 - .4(9.762) P1 = 4.095

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=10.238. P = 8-0.4(10.238) = 8 – 4.095 = 3.905 Quantity 10.238 NB = ½(4.095x10.238) + (1.905x10.238) = 40.46

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

Present Value of NB for t1 = 39.51/(1+r) = 39.51/1.1 = $35.92 Total net benefit for two periods = $40.46+35.92 = $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).

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

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

With equal distribution NB0 = $40 NB1 = $40 With efficient distribution NB0 = $40.46 NB1 = $39.51 With sharing, keep NB0 = $40, invest $.46 @ 10%, send to t1 .46(1.1) = .506 NB1 = $39.51 + .51 = $40.02

Marginal User Cost MNB0 = 6 – 0.4(10.238) = 1.905 = 2.0952/1.1 = 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

User Cost and Natural Resource Rent P = MEC + MUC $3.905 = $2.00 + 1.905 Period t0 $ Rent MB 3.905 User Cost Wages, etc. MC Quantity 10.238

MUC increases at the rate of discount 2.095 = 1.1(1.905) P = MEC + MUC $4.095 = $2.00 + 2.095 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

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