Econ 201
1. Present value
a. Same as for 201
2. Static/Dynamic Efficiency
a. Exhaustible and non-exhaustible resources
i. E.g., oil (extractive resources)
ii. What is the optimal rate of extraction
b. Static Efficiency
i. One time-period world
1. Economic efficiency – minimize or no deadweight loss
c. Dynamic Efficiency
i. Simple case – two-period world
1. Comparing Benefits and Cost now and 1-year from now
ii. When there is no scarcity
1. Titenberg’s first example
a. 30 units avail
b. At P= MC, Qd is 15 each period
c. Today’s consumption does not reduce tomorrow’s
iii. With scarcity
1. Suppose total avail only 20
2. Demand in each period exceeds an even (10/10) split
3. How would we determine optimal split between current and future?
a. Maximize Net Present Value of the flow of benefits
i. Suppose current demand is given by
1. P (1)= 8 – 0.4 Q(1)
2. MC = constant $2 per unit
3. Net benefits then are
a. P(1)=(8-2) – 0.4 Q(1)
ii. For the next period we discount the $ value by (1+r)
1. NB(2) = 6/1.1 – 0.4Q(2)
iii. So flow of benefits
1. [6-.4Q(1)] +[ 5.45-0.4Q(2)]
2. Where Q(1) + Q(2) = 20
iv. Now solving for Q(1) and Q(2)
1. Trial and error
a. Different values of Q(1) and Q(2)
2. Or equate PV[MB(1)] to P V[ MB(2)]
a. See Tom’s graph
3. Solution is
a. Q(1) = 10.238
b. Q(2 ) = 9.762
c. Solving for P(1)
i. P(1) =1.905
d. What is P(1)?
i. Already accounted for MC
ii. Represents the scarcity cost,
price required to clear the
market and maximize NPV
v. So what price do we charge consumers to clear the
market (i.e., so Q(1) = 10.238)?
1. P(1) = 8-0.4x10.238 = 3.905
2. Or alternatively
a. P(1) = MC + Scarcity cost
b. = 2 + 1.905 = 3.905
3. Can perform similar calculation for P(2)
a. P(2) = 5.45 – 0.4x9.762
b. P(2) = 4.095
c. Scarcity Cost (2) = P(2) – MC
i. = 4.095 – 2 = 2.095
3. Sustainability Criteria
a. Economic/Dynamic Efficiency
i. Maximize Net Present Value of the (Net) Benefits from consuming the resource
b. The sustainability criteria
i. Future generations should be no worse off than current generation
c. Rawls’ Criteria (1971)
i. If individuals were decide on the rules (e.g., how the resource was allocated
over time), they would be indifferent between which time period they would
want to live in
ii. Hard to define a priori, but could be used to evaluate various proposed rules
d. Hartwick’s rule
i. Maintain a constant (equal) flow of benefits for all generations
1. Implies that you can not deplete the capital (K) stock
ii. More generally
1. Stock of depleted resource + Stock of capital created from the resource
does not decrease
iii.