agenda monday -presentation of impacts in agriculture -discounting wednesday -presentation on...
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Agenda
Monday- Presentation of impacts in agriculture- Discounting
Wednesday- Presentation on extremes (hurricanes)- Summary on impacts- Pass out exam- Hand in pset 4Friday- Review exam- Go over any questions on psets 3 and 4
Discounting in economics:The fundamental determinants
Economics 331b
2
Start with a consumption path
c1(t)
time
For this, assume that:1.c is per capita consumption2.Population is constant3.c is a comprehensive measure (includes all external and non-market effects.
Which is the preferable path, c1 or c2?
c1(t)
c2(t)
time
For this, assume that:1.c is per capita consumption2.Population is constant3.c is a comprehensive measure (includes all external and non-market effects.
Which is the preferable path?
c1(t)
c2(t)
time
Which is the preferable path?
c1(t)
c2(t)
time
Philosophical-ethical foundations of environmental economics
Religious and Kantian views: Largely absentUtilitarianism: Bentham, J.S. Mill (Utilitarianism), Peter Singer (on animals)In modern bioethics: Maximize QALYs Happiness research and hedonic psychology (among behavior psychologists
and some economists)Welfarism (of the social welfare function): Bergson, Samuelson, FoundationsParetianism: An incomplete ordering of social states based on welfarism used
throughout economicsCritiques of Utilitarianism, conequentialism, and welfarism:
Ordinalists: cannot measure utilityPositivism: ethics as esthetics J. Rawls, Theory of Justice: emphasis on equality and justiceAmartya Sen, (Sen and Williams, Beyond Utilitarianism), emphasis on capabilities and equity
Ethical fundamentalsAlternative universes: {c1(t), …, cn(t)}
Process values, rules, religions,… Consequentialism
Human values, non-human (intrinsic) Human values values, …
Dynamic one-sided game Welfarism and individualistic “social among generations welfare function”: W = V(U1, … Un)
Ethical fundamentalsStates of the world: {c1(t), …, cn(t)}
.
.
. Welfarism and individualistic
“social welfare function”
Complex welfare functions Pure 19 th century(non-separable, “add them up”altruistic, dynastic,…) Standard approach in modern economics: DU
1( )
N
n nn
W U c
1( )
Tt
t tt
W U c e
Ethical fundamentalsStates of the world: {c1(t), …, cn(t)}
.
.
. Standard DU approach DU:
Alternative preference functions
Rawlsian: maximin or leximin Environmental (E) orW=min[c1, … ,cn,… ] other constraints
(1) U=V(c); E > E* (2) U=V(c) + Z(E)
Standard economic approach: can trade off environmental and non-environmental values
U = U(c, E)
The optimal growth setup withexogenous technological change
We assume that there is labor augmenting technological change, ,
at rate . This increases the "effective labor force," where .
(2b) Production function : ( , ) ( , )
E
h L LE
Y F K EL F K L
/ ( / ,1) ( )
(4a) Growth in effective labor supply :
/ = exogenous
So the new steady state is :
(6a) ( *) ( ) *
With long
y Y L LF K L Lf k
L L n h
sf k n h k
run growth rate of real output:
(7) Yg n h
11
The solution
In optimal economic growth, we choose the path of K(t) to maximize the utility of future consumption (alternatively, the savings rate).
Here is the semi-technical version (this is in the spirit of the calculus of variations).
“Splish splash” optimal growth experiment: Suppose that we invest in period t with a return in period (t+θ). An investment is a withdrawal from consumption of Δ, with the return being an increase in consumption with real rate of return r. The fundamentals are the following (with no population growth):
(8)
(9)
0
tW U[c(t)]e dt
1-U [c(t)] =c(t) / (1- )
Splish-splash
c(t)∆(1+r)θ
-∆
t t+θ
| |
Consumption
13
So the solution for the change in total welfare is:(10) change in 0
1
The marginal utility for our assumed utility function is
1
Let h = growth rate of
t (t ) r
(r )
(r )
W e u'[c(t)] e u'[c(t )][ e ]
or
u'[c(t)] u'[c(t )]e
u'[c(t)] c(t)
e [c(t ) / c(t)]
c(t), so .
This yields
Take logs, so
which is the basic result of the Ramsey model. Equation (11) is
called the "Ramsey equation."
(11)
h
(r ) h
[c(t ) / c(t)] e
e e
r h
0
tW L(t)U[c(t)]e dt
r h n
To add population growth, we change the objective function to the following:
If population growth is constant at rate n, we see that the new Ramsey equation is:
(12)
More…
15
Key distinction, often confused
Utility discount rate (pure rate of social time preference), ρ:This refers to the comparison of well-being or utilities over time, space,
or generations.
Goods discount rate (tradeoff in markets), r:This refers to the return on private or social investments in goods,
services, etc.
More…The debate on discounting generally will use the framework of the Ramsey
model. Begin with the Ramsey equation from (12) above:
This shows the relationship between the equilibrium real interest rate and underlying parameters.
Observables:
r = real interest rate or real return on capital
g = rate of growth of real consumption per capita
Non-observables:
r h n
rate of social time preference (time or utility discount rate)
curvature of utility function (inequality aversion, risk aversion)
Two schools of discounting theoryWhat real interest rate on goods shall we actually use for discounting costs
and benefits of long-term investments (climate, radioactive wastes, dams, technology,…)?
Descriptive: Argues that we can observe the rate of return and should make
sure that our decisions are consistent with opportunity cost on other investments. This leads to a relatively high utility discount rate (Feldstein, Eckstein, Lind, Nordhaus):
Prescriptive: Argues that we can know the normative parameters on philosophical grounds and derive the interest rate from that (Cline, Stern):
055 2 02 015r h . . .
001 1 013 014r h . . .
Why this is so important in climate-change analysis: Damages are so late in the game.
Numerical example of effect over 200 years
0.0010
0.0100
0.1000
1.0000
10.0000
100.0000
1,000.0000
10,000.0000
100,000.0000
1,000,000.0000
0 0.02 0.04 0.06 0.08 0.1 0.12
Pres
ent v
alue
(bill
ions
of
2010
$)
Discount rate
Why this is so important in climate-change analysis: Damages are so late in the game.
Numerical example of effect over 200 years
0
100,000
200,000
300,000
400,000
500,000
600,000
700,000
0 0.02 0.04 0.06 0.08 0.1 0.12
Pres
ent v
alue
(bill
ions
of
2010
$)
Discount rate
Problems with each
Major criticism of descriptive is that a positive ρ is unethical and violates intergenerational fairness. (Good point)
Major criticism of prescriptive is that it leads to distorted investment decisions because actual return on investment is much higher than the prescriptive discount rate. (Good point)
Is there any way to reconcile all this?
Two polar cases
The standard descriptive model uses market rates of return (circa 5-6 percent per year for goods and services). Assume g = 2 % per year
In the Ramsey framework, this can be interpreted as a solution of the following equation:5.5 = ρ + α 2
We take the solution of ρ = 1.5 and α = 2.
The prescriptive approach (Cline, Stern) argues that it is ethically indefensible to have generational discounting. Stern also assumes that α = 1. With their assumed g = 1.4 % per year, this yields:r = 0.1 + 1 (1.4) = 1.5 % per year
Conclusions on discountingRemember the ethical foundations.A key question is whether you take the mixed-market solution (prices) as a
constraint on decisions; or whether you want to argue that the preferences as revealed (by market prices) in the market are wrong.
In the ethical/prescriptive view, the goods discount rate will be determined by both time discounting and view on income distribution over time.
These issues are particularly important for very long-run decisions (global warming, radioactive wastes, …).
The arguments also involve questions such as market imperfections, taxes, the equity premium – pretty horrible.