static efficiency, dynamic efficiency and sustainability wednesday, january 25
TRANSCRIPT
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Static Efficiency, Dynamic Static Efficiency, Dynamic Efficiency and Efficiency and SustainabilitySustainability
Wednesday, January 25Wednesday, January 25
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Represent the demand for a resource as: P = 8 – 0.4 q
Demand = marginal willingness to pay = Marginal Benefit (MB)
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P = 8 - 0.4qP = 8 - 0.4qqq PP
00 88
55 66
1010 44
1515 22
2020 00
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Represent the demand for a resource as: P = 8 – 0.4 q
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Demand
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Demand
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(5,6)
(15,2)
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Assume a constant marginal cost of extraction = $2.00(Marginal cost = supply)
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MC
Efficient allocation occurs where MB = MC, q = 15 units
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Static EfficiencyStatic Efficiency
MB = MCMB = MC Criteria for allocation in a given time Criteria for allocation in a given time
period, with no consideration of period, with no consideration of future time periodsfuture time periods
Efficiency: no one can be made Efficiency: no one can be made better off without making someone better off without making someone else worse offelse worse off
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$
Q
MC
MB
MB>MC
MC>MB
MB=MC
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What are the net benefits of the efficient allocation?
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MB
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MC
Efficient allocation occurs where MB = MC, q = 15 units
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TB (area under MB curve)=½(6x15) + (2x15)=45+30=75
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MC
MB
Quantity
$
TC (area under MC curve) = (2x15) = 30
NB = TB – TC = ½(6x15) = 45
NB
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MNB
Total NB (area under MNB curve) = ½(6x15) = 45
This graph illustrates marginal net benefits:
MB-MC = (8-0.4q)-2 = 6-0.4q = MNB
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Dynamic EfficiencyDynamic Efficiency
When the concern is efficient When the concern is efficient allocation of a nonrenewable allocation of a nonrenewable resource over multiple time periodsresource over multiple time periods
MNBMNB00 = PV MNB = PV MNB11 = PV MNB = PV MNB22 = … = PV = … = PV MNBMNBtt
t represents time periodt represents time period
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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 Only two time periods in this exampleexample
For present value calculations, r=.10For present value calculations, r=.10
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Period t0
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NB = Area = ½(6x15) = 45
MC
$
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MC
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Period t1
MB
NB = Area = ½(2x5) + (4x5) = 25
MC
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NB for t0 = $45
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
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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)
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NB = Area = ½(4x10) + (2x10) = 40
MC
$
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NB = Area = ½(4x10) + (2x10) = 40
MC
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NB for t0 = $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
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Recall, for dynamic efficiency (to maximize PV of total net benefits), MNB0 = PV MNB1
Find the dynamically efficient quantities for q0 and q1.
Find the efficient allocation of the resource over the two periods (dynamic efficiency).
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1)1) MNBMNB00 = PV MNB = PV MNB11
2) MNB = MB - MC 3) MB = 8 – 0.4q4) MB – MC = (8 – 0.4q) – 2 = 6 – 0.4q5) MNB = 6 – 0.4q
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1)1) MNBMNB00 = PV MNB = PV MNB11
2) 6 - .4q0 = (6 - .4q1)/1.1
3) q0 + q1 = 20
4) 6 - .4q0 = (6 - .4[20-q0])/1.1
5) 1.1(6 - .4q0)= (6-8+.4q0)
6) 6.6-.44q0 = (-2 +.4q0)
7) 8.6=.84q0
8) q0 = 10.238
9) q1 = 9.762
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MNB
This graph illustrates marginal net benefits: MB-MC=MNB
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MNB0
Period t0
MNB = MB – MC = 6 – 0.4q
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Period t1
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PV MNB1
5.45
Present value calculation: 6/1.1 = 5.45
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MNB0
51015
MNB1
5.45
q0=10.238
q1=9.762
t0
t1
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MNBMNB00 = 6 – 0.4(10.238) = 1.9048 = 6 – 0.4(10.238) = 1.9048
MNBMNB11 = [6 – 0.4(9.762)]/1.1 = [6 – 0.4(9.762)]/1.1
= 2.9052/1.1 = 1.9048= 2.9052/1.1 = 1.9048
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MNB0
51015
MNB1
5.45
q0
q1
t0
t1
MNB=1.9048
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To calculate total benefits, total costs, and net benefits:
P0 = 8 - .4q0
P0 = 8 - .4(10.238)
P0 = 3.905P1 = 8 - .4q1
P1 = 8 - .4(9.762)
P1 = 4.095
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10.238
NB = ½(4.095x10.238) + (1.905x10.238) = 40.46
3.905
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MC
9.762
NB = ½(3.905x9.762) + (2.095x9.762) = 39.51
4.095
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NB for t0 = $40.46
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
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Comparing allocations:Comparing allocations:
Maximize NB to period 0Maximize NB to period 0 TNB = $67.73TNB = $67.73
qq00 = q = q11
TNB = $76.36TNB = $76.36 Dynamically efficient allocationDynamically efficient allocation
TNB = $76.38TNB = $76.38
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SustainabilitySustainability Environmental sustainabilityEnvironmental sustainability
Do not reduce total stock of natural capitalDo not reduce total stock of natural capital Strong sustainabilityStrong sustainability
Do not reduce productivity (value) of Do not reduce productivity (value) of natural capital stocknatural capital stock
One type of natural capital may substitute One type of natural capital may substitute for anotherfor another
Weak sustainabilityWeak sustainability Do not reduce productivity of capitalDo not reduce productivity of capital May substitute manufactured capital for May substitute manufactured capital for
natural capitalnatural capital
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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
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Marginal User CostMarginal User Cost MNBMNB00 = 6 – 0.4(10.238) = 1.905 = 6 – 0.4(10.238) = 1.905
MNBMNB11 = [6 – 0.4(9.762)]/1.1 = [6 – 0.4(9.762)]/1.1 = 2.0952/1.1 = 1.905= 2.0952/1.1 = 1.905
The value of the last unit extracted in tThe value of the last unit extracted in t00 Foregone benefit for tForegone benefit for t11
Opportunity cost of choosing to extract the last Opportunity cost of choosing to extract the last unit used in tunit used in t00
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P = MEC + MUCP = MEC + MUC $3.905 = $2.00 + 1.905$3.905 = $2.00 + 1.905
User Cost and Natural Resource User Cost and Natural Resource Rent Rent
Quantity
Period t0
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MC
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10.238
3.905
Rent
Wages, etc.
User Cost
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P = MEC + MUCP = MEC + MUC $4.095 = $2.00 + 2.095$4.095 = $2.00 + 2.095 MUC increases at the rate of discountMUC increases at the rate of discount 2.095 = 1.1(1.905)2.095 = 1.1(1.905)
Period t1
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MBMC
9.762
4.095
Rent
User Cost
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Reading for Wed. Feb. 2:
Hartwick and Olewiler, on ANGEL
and
Field, Ch. 6