Static Efficiency, Dynamic Efficiency and Sustainability Wednesday, January 25

Represent the demand for a resource as: P = 8 – 0.4 q Demand = marginal willingness to pay = Marginal Benefit (MB) Demand Quantity Demand $

P = q qP

Represent the demand for a resource as: P = 8 – 0.4 q Demand Quantity Demand $ (5,6) (15,2)

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

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

$ Q MC MB MB>MC MC>MB MB=MC

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

TB (area under MB curve)=½(6x15) + (2x15)=45+30=75 MC MB Quantity $ TC (area under MC curve) = (2x15) = 30 NB = TB – TC = ½(6x15) = 45 NB

Quantity $ 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

Dynamic Efficiency When the concern is efficient allocation of a nonrenewable resource over multiple time periods When the concern is efficient allocation of a nonrenewable resource over multiple time periods MNB 0 = PV MNB 1 = PV MNB 2 = … = PV MNB t MNB 0 = PV MNB 1 = PV MNB 2 = … = PV MNB t t represents time period 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 Only two time periods in this example For present value calculations, r=.10 For present value calculations, r=.10

Quantity Period t 0 MB MC $

Quantity Period t 0 MB NB = Area = ½(6x15) = 45 MC $

$ Quantity Period t 1 MB MC

$ Quantity Period t 1 MB NB = Area = ½(2x5) + (4x5) = 25 MC

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 )

Quantity Period t 0 MB MC $

Quantity Period t 0 MB NB = Area = ½(4x10) + (2x10) = 40 MC $

Quantity Period t 1 MB NB = Area = ½(4x10) + (2x10) = 40 MC $

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

Recall, for dynamic efficiency (to maximize PV of total net benefits), MNB 0 = PV MNB 1 Find the dynamically efficient quantities for q 0 and q 1. Find the efficient allocation of the resource over the two periods (dynamic efficiency).

1) MNB 0 = PV MNB 1 2) 2) MNB = MB - MC 3) 3) MB = 8 – 0.4q 4) 4) MB – MC = (8 – 0.4q) – 2 = 6 – 0.4q 5) 5) MNB = 6 – 0.4q

1) MNB 0 = PV MNB 1 2) 2) 6 -.4q 0 = (6 -.4q 1 )/1.1 3) 3) q 0 + q 1 = 20 4) 4) 6 -.4q 0 = (6 -.4[20-q 0 ])/1.1 5) 5) 1.1(6 -.4q 0 )= (6-8+.4q 0 ) 6) 6) q 0 = (-2 +.4q 0 ) 7) 7) 8.6=.84q 0 8) 8) q 0 = ) 9) q 1 = 9.762

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

Quantity $ MNB 0 Period t 0 MNB = MB – MC = 6 – 0.4q

Period t 1 Quantity $ PV MNB Present value calculation: 6/1.1 = 5.45

Quantity $ MNB MNB q 0 = q 1 =9.762 t0t0 t1t1

MNB 0 = 6 – 0.4(10.238) = MNB 0 = 6 – 0.4(10.238) = MNB 1 = [6 – 0.4(9.762)]/1.1 MNB 1 = [6 – 0.4(9.762)]/1.1 = /1.1 = = /1.1 =

Quantity $ MNB MNB q0q0 q1q1 t0t0 t1t1 MNB=1.9048

To calculate total benefits, total costs, and net benefits: P 0 = 8 -.4q 0 P 0 = 8 -.4(10.238) P 0 = P 1 = 8 -.4q 1 P 1 = 8 -.4(9.762) P 1 = 4.095

Quantity Period t 0 MB MC $ NB = ½(4.095x10.238) + (1.905x10.238) =

$ Quantity Period t 1 MB MC NB = ½(3.905x9.762) + (2.095x9.762) =

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 = $ = $76.38

Comparing allocations: Maximize NB to period 0 Maximize NB to period 0 TNB = $67.73 TNB = $67.73 q 0 = q 1 q 0 = q 1 TNB = $76.36 TNB = $76.36 Dynamically efficient allocation Dynamically efficient allocation TNB = $76.38 TNB = $76.38

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

With equal distribution NB 0 = $40 NB 1 = $40 With efficient distribution NB 0 = $40.46 NB 1 = $39.51 With sharing, keep NB 0 = $40, invest 10%, send to t 1.46(1.1) =.506 NB 1 = $ = $40.02

Marginal User Cost MNB 0 = 6 – 0.4(10.238) = MNB 0 = 6 – 0.4(10.238) = MNB 1 = [6 – 0.4(9.762)]/1.1 MNB 1 = [6 – 0.4(9.762)]/1.1 = /1.1 = = /1.1 = The value of the last unit extracted in t 0 The value of the last unit extracted in t 0 Foregone benefit for t 1 Foregone benefit for t 1 Opportunity cost of choosing to extract the last unit used in t 0 Opportunity cost of choosing to extract the last unit used in t 0

P = MEC + MUC P = MEC + MUC $3.905 = $ $3.905 = $ User Cost and Natural Resource Rent Quantity Period t 0 MB MC $ Rent Wages, etc. User Cost

P = MEC + MUC P = MEC + MUC $4.095 = $ $4.095 = $ MUC increases at the rate of discount MUC increases at the rate of discount = 1.1(1.905) = 1.1(1.905) Period t 1 $ Quantity MB MC Rent User Cost

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