Part I. Principles
A.
B.
C.
D.
E.
F.
Markets
Market failure
Discounting & PV
Markets 2
Dynamic efficiency
Pollution solutions
E. Dynamic efficiency
(End of chapter 2
&
Appendix 2B)
Dynamic Efficiency
• A static analysis is only concerned with 1
time period.
• If the optimal allocation of resources in 1
period depends on the optimizing decisions
of the past or future periods, then a dynamic
analysis must be employed.
Dynamic Efficiency
• Static example – a farmer has 100 acres of
cropland and decides to plant one type of
crop this year and a different crop next year,
in response to changes in market forces.
• Dynamic example – a farmer has 100 acres
of forest. A choice to cut trees this year and
plant corn means that in the next time
period cannot decide to have trees again.
Dynamic Efficiency &
Exhaustible Resources
• Since decisions made today can influence
the quality and stock of resources far into
the future, dynamic considerations
important in the study of environmental and
resource economics.
• E.g., the decision of how much oil to take
out the ground today effects our ability to
take oil out of the ground in the future.
• This will be based on how much people will
be WTP for oil in the future.
Dynamic Efficiency &
Exhaustible Resources
• Efficiency requires that you continue to sell
oil today until MC = MB.
• The way in which the future is represented
in this decision is to incorporate an
opportunity cost (also called user cost or
scarcity rent) into the decision making
process.
• The discount/interest rate becomes
important also.
Intertemporal efficiency
• The individual oil owner has two choices
for producing income in the future:
– Sell oil today and invest money and earn
interest income.
– Hold on to oil, sell in the future.
• Intertemporal efficiency requires that the
producer make a choice that will maximize
the sum of the PV of the earnings
potentially received in each period.
Sell today? Or…
• If current price perceived as low relative to future
price – producers want to sell in future.
• Present production withheld – drives up today’s
price – and at same time – expected future price
falls as realize too much oil being held for future
use
• Combination of rising present price + falling
future price makes selling today more attractive.
Sell tomorrow?
• Now assume that oil producers believe that the
future price will be too low, and they will be better
off selling oil now.
• Sales of oil now mean less oil available in the
future (this will cause future oil prices to rise).
• Sales of oil now will also depress current price of
oil.
• Combination of higher future prices and lower
present prices will make holding oil for sale in the
future more attractive.
Sale today = sale tomorrow
• As long as 1 option (selling in the present
versus selling in the future) appears to be a
more attractive option than the other, prices
will adjust.
• The process of price adjustment will
continue until owners of oil are indifferent
between the options of selling in the present
and selling in the future.
Opportunity cost
• Since the present price is dependent on the
future price, and the future price is
dependent on the present price, there is an
opportunity cost for using a barrel of oil at
any particular point in time.
• This opportunity cost is associated with
NOT having the barrel of oil available in
another time period.
Price equation
• The price of oil, at any particular time can
be represented by the following equation:
Pt = MUCt + MECt
• Where
– MUC refers to Marginal User Cost, and
– MEC refers to Marginal Extraction Cost
MUC and MEC
• The most important thing to understand
about this equation is that it is possible to
predict the changes in the price of oil by
predicting changes in the MEC and the
MUC.
• Especially MUC (opportunity cost)
Gulf war & oil
• August 1990 – Iraqi forces invade Kuwait –
looked like they might control or destroy
Saudi oil fields
• Price of oil immediately rose 50%
• Why?
• MUC rose dramatically as the taking of
Kuwait and threats to SA increased the
opportunity cost of using oil at that point in
time
Gulf war & oil cont.
• When US and the coalition began air attacks
in 1991, became apparent Iraq could not
damage Saudi oil fields or affect Persian
Gulf exports in long run
• People’s perceptions of the opportunity cost
(MUC) of using a barrel of oil decreased,
and price of oil decreased
MUC and MEC
• The existence of MUC means that price will
always be different from MEC. Remember,
MUC is a form of scarcity rent.
• If no scarcity, MUC = 0
• If scarcity, MUC = PV of marginal net
benefit in each time period
• If MEC = 0
– Competitive firm MUC = price = MB
– Monopoly MUC = MR = MB
MUC
• In order for an owner of oil to be indifferent
as to the period in which he or she sells, the
PV of the MUC must be the same in all
periods. This means that MUC of an
exhaustible resource will increase with the
discount rate.
Example:
Dynamically efficient extraction of an
exhaustible resource
•
•
•
•
•
100 tons of coal
2 periods
MEC = 0
Demand each period P = 500 – 0.5q
How will 100 tons be allocated over 2
periods?
2 ways to analyze
1. Maximize PS: Owners of coal max PV
income each period
2. Maximize Social Welfare (“benevolent
social planner”): CS + PS
Producer maximizes PV
income each period
• Revenue period 1 = (500 – 0.5 q1 ) q1
• Revenue period 2 = (500 – 0.5 q 2 ) q 2
• Since q1 + q 2 = 100

Revenue period 2 = [500 – 0.5(100 – q1)](100 – q1)
• If discount rate is 5%, PV revenue period 2 is…
Calculate PV
FV
PV 
t
(1  r)
PV period 2 
[500  0.5(100  q1)](100  q1)
1.05
 [476.2  0.4762(100  q1)](100  q1)
How much oil should be used each
period to max PS?
PV = (500-0.5 q1) q1 +
[476.2  0.4762(100  q1)](100  q1)
To maximize PV, set dPV/d q1 = 0, solve for
OR, use Microsoft Excel Solver!
Solution:
q1= 60.97, q 2= 39.02
p1= 469.5 p2= 480.5
q1
2 important points
1. Although MEC = 0, price in both periods
is positive. The price is composed
exclusively of user cost (the opportunity
cost of NOT having the coal available in
another period)
2. Price higher in 2nd period – reflects
positive rate of time preference
Previous analysis maxes PS only
• What about social welfare maximization?
• Social welfare max = CS + PS maximized
• Social welfare max is where demand curves
intersect, we consider both surpluses
• Can also be solved using MS Excel Solver
Graphical analysis of SW max
500
Demand 1
476.2
Demand 2
←q2
73
26
q1→
Interpretation
• Demand 1 is demand curve period 1
• Demand 2 is PV of demand period 2
• PV social welfare maximized where 2
curves intersect ( q1 = 73.17 and q 2 = 26.83)
• To left of intersection, can ↑ PV by
allocating more coal to period 1 since
price WTP period 1 > PV price in period 2
• To right, ↑ PV by allocating more coal to
period 2
Other Examples of
Dynamic Problems
• Stock pollutants that accumulate in the
environment.
– Today’s decision to generate a stock pollutant
(radioactive waste, lead) has an effect on
environmental quality far into the future.
• Changes in land use patterns can change
environmental resources that can never be
restored.
– Over-grazing of grasslands, clear-cutting of
tropical forests