Static Efficiency Dynamic Efficiency and Sustainability Wednesday January
Static Efficiency, Dynamic Efficiency and Sustainability Wednesday, January 25
Represent the demand for a resource as: P = 8 – 0. 4 q $ Demand Quantity Demand = marginal willingness to pay = Marginal Benefit (MB)
P = 8 - 0. 4 q q 0 5 P 8 6 10 15 20 4 2 0
Represent the demand for a resource as: P = 8 – 0. 4 q $ (5, 6) Demand (15, 2) Quantity
Assume a constant marginal cost of extraction (Marginal cost = supply) = $2. 00 $ MB Demand. MC Quantity Efficient allocation occurs where MB = MC, q = 15 units
Static Efficiency n n n 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 MB=MC Q
What are the net benefits of the efficient allocation? $ MB Demand. MC Quantity Efficient allocation occurs where MB = MC, q = 15 units
TB (area under MB curve)=½(6 x 15) + (2 x 15)=45+30=75 TC (area under MC curve) = (2 x 15) = 30 $ NB MB MC Quantity NB = TB – TC = ½(6 x 15) = 45
This graph illustrates marginal net benefits: MB-MC = (8 -0. 4 q)-2 = 6 -0. 4 q = MNB $ MNB Quantity Total NB (area under MNB curve) = ½(6 x 15) = 45
Dynamic Efficiency n n When the concern is efficient allocation of a nonrenewable resource over multiple time periods MNB 0 = PV MNB 1 = PV MNB 2 = … = PV MNBt n 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? n n Only two time periods in this example For present value calculations, r=. 10
Period t 0 $ MB MC Quantity
Period t 0 $ MB MC Quantity NB = Area = ½(6 x 15) = 45
Period t 1 $ MB MC Quantity
Period t 1 $ MB MC Quantity NB = Area = ½(2 x 5) + (4 x 5) = 25
NB for t 0 = $45 Present Value of NB for t 1 = 25/(1+r) = 25/1. 1 = $22. 73 PV Total net benefit for two periods = $45 + $22. 73 = $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? (q 0 = q 1)
Period t 0 $ MB MC Quantity
Period t 0 $ MB MC Quantity NB = Area = ½(4 x 10) + (2 x 10) = 40
Period t 1 $ MB MC Quantity NB = Area = ½(4 x 10) + (2 x 10) = 40
NB for t 0 = $40 Present Value of NB for t 1 = 40/(1+r) = 40/1. 1 = $36. 36 PV Total net benefit for two periods = = $40 + $36. 36 = $76. 36
Find the efficient allocation of the resource over the two periods (dynamic efficiency). Find the dynamically efficient quantities for q 0 and q 1. Recall, for dynamic efficiency (to maximize PV of total net benefits), MNB 0 = PV MNB 1
1) 2) 3) 4) 5) MNB 0 = PV MNB 1 MNB = MB - MC MB = 8 – 0. 4 q MB – MC = (8 – 0. 4 q) – 2 = 6 – 0. 4 q MNB = 6 – 0. 4 q
1) 2) 3) 4) 5) 6) 7) 8) 9) MNB 0 = PV MNB 1 6 -. 4 q 0 = (6 -. 4 q 1)/1. 1 q 0 + q 1 = 20 6 -. 4 q 0 = (6 -. 4[20 -q 0])/1. 1(6 -. 4 q 0)= (6 -8+. 4 q 0) 6. 6 -. 44 q 0 = (-2 +. 4 q 0) 8. 6=. 84 q 0 = 10. 238 q 1 = 9. 762
This graph illustrates marginal net benefits: MB-MC=MNB $ MNB Quantity
Period t 0 $ MNB 0 Quantity MNB = MB – MC = 6 – 0. 4 q
Period t 1 $ 5. 45 PV MNB 1 Quantity Present value calculation: 6/1. 1 = 5. 45
$ 7 6 5. 45 5 MNB 0 4 MNB 1 3 2 1 t 0 0 5 10 15 15 10 5 Quantity q 0=10. 238 q 1=9. 762 0 t 1
n n MNB 0 = 6 – 0. 4(10. 238) = 1. 9048 MNB 1 = [6 – 0. 4(9. 762)]/1. 1 = 2. 9052/1. 1 = 1. 9048
$ 7 6 5. 45 5 MNB 0 4 MNB 1 3 MNB=1. 9048 2 1 t 0 0 5 10 15 15 10 5 q 0 Quantity q 1 0 t 1
To calculate total benefits, total costs, and net benefits: P 0 = 8 -. 4 q 0 P 0 = 8 -. 4(10. 238) P 0 = 3. 905 P 1 = 8 -. 4 q 1 P 1 = 8 -. 4(9. 762) P 1 = 4. 095
Period t 0 $ MB 3. 905 MC 10. 238 Quantity NB = ½(4. 095 x 10. 238) + (1. 905 x 10. 238) = 40. 46
Period t 1 $ MB 4. 095 MC 9. 762 Quantity NB = ½(3. 905 x 9. 762) + (2. 095 x 9. 762) = 39. 51
NB for t 0 = $40. 46 Present Value of NB for t 1 = 39. 51/(1+r) = 39. 51/1. 1 = $35. 92 Total net benefit for two periods = $40. 46+35. 92 = $76. 38
Comparing allocations: n Maximize NB to period 0 n n q 0 = q 1 n n TNB = $67. 73 TNB = $76. 36 Dynamically efficient allocation n TNB = $76. 38
Sustainability n Environmental sustainability n n Strong sustainability n n n Do not reduce total stock of natural capital Do not reduce productivity (value) of natural capital stock One type of natural capital may substitute for another Weak sustainability n n Do not reduce productivity of capital May substitute manufactured capital for natural capital
n With equal distribution NB 0 = $40 n NB 1 = $40 n n With efficient distribution NB 0 = $40. 46 n NB 1 = $39. 51 n n With sharing, keep NB 0 = $40, invest $. 46 @ 10%, send to t 1. 46(1. 1) =. 506 n NB 1 = $39. 51 +. 51 = $40. 02 n
Marginal User Cost n n n MNB 0 = 6 – 0. 4(10. 238) = 1. 905 MNB 1 = [6 – 0. 4(9. 762)]/1. 1 = 2. 0952/1. 1 = 1. 905 The value of the last unit extracted in t 0 n n Foregone benefit for t 1 Opportunity cost of choosing to extract the last unit used in t 0
User Cost and Natural Resource Rent n n P = MEC + MUC $3. 905 = $2. 00 + 1. 905 $ Period t 0 Rent MB Wages, etc. 3. 905 User Cost MC Quantity 10. 238
n n P = MEC + MUC $4. 095 = $2. 00 + 2. 095 MUC increases at the rate of discount 2. 095 = 1. 1(1. 905) $ Period t 1 Rent 4. 095 User Cost 9. 762 MB MC Quantity
Reading for Wed. Feb. 2: Hartwick and Olewiler, on ANGEL and Field, Ch. 6
- Slides: 42