• nonrenewable vs. renewable
– maximize pv of net benefit
– renewable includes growth functions
• characterize efficient allocations
• compare to market allocations
• discuss policy to make market allocations more efficient

• efficiency pricing:
P t
= MEC t
+ MUC t
• where
– MEC: Marginal Extraction Cost
– MUC: Marginal User Cost

MUC and Q over time
• efficient MUC rises, reflecting increasing scarcity
• in response, Q extracted falls over time until reaching zero, when total MC = highest WTP
(“choke price”) or reach backstop MC
• efficiency requires smooth transition to exhaustion of resource

constant MEC with no substitute

vulnerability premium

water efficient allocations: surface vs. groundwater
• surface water
– how to allocate a renewable supply among competing uses
– intergenerational effects less important (future supplies depend on natural phenomenon, e.g. rain, rather than current allocation)
• groundwater
– withdrawing now affects future supply

efficient allocation: surface water
1. balance btw users
• marginal net benefit equal across users
2. handle variability
• above-average and below-average flows must be accommodated

efficient allocation: groundwater
• if withdrawal > recharge, eventual exhaust resource
• MEC rises over time as water table falls
• pumping would stop:
– no water left
– MC pumping > benefit of water or MC of backstop resource
(desalination)
• price rises over time until choke price or switch point

utilities pricing: inverted block & seasonal rates
(potentially efficient)

forests: biological harvest rule
• MAI = cumulative volume end of decade / cumulative yrs of growth
• harvest when MAI maximized

biological harvesting decision

• harvest at age that maximizes PV of net benefits
1. planting costs
• borne immediately
• no discounting
2. harvesting costs
• time of harvest
• discounted

sample problem
Age Volume (cubic ft)
11
21
31
700
1,000
3,000
41
51
6,000
8,000 when to harvest using biological rule?
using economic rule?
Price: $2
Planting cost: $1,000
Harvest cost: $0.50
Discount rate: 3%

• discounting shortens optimal harvest time
– less tolerant of slow timber growth
– comparing no harvest (increase in value of timber) to harvest (sell and invest)
• high discount rates also destroy incentive to replant

fisheries: biological vs. economic harvest
• biology: “maximum sustainable yield”
(MSY)
– yields maximum growth
– largest catch that can be perpetually sustained
• economics: maximize net benefit

too much effort! policy responses
• increase MC– require fishing farther from shore, use smaller nets, boats, or motors
– but artificially increasing cost inefficient
• total allowable catch – restrictions on effort or size of catch
– monitoring, enforcement difficult, also creates race to catch
• individual transferable quotas –quotas allocated, then trade
– no race, allows most efficient fishers to buy rights from inefficient fishers

sample problem
• Costs fisher $20 to fish salmon
• Salmon sells for $10
• Harvest rate given X fishers is
S = 30X-2X 2
• How many people will go fishing, how many salmon will be caught, and what are total profits under
– Open access
– Limited entry (how many fishers should be allowed to maximize profit?)