Shadow Pricing in Economics
AN EXAMPLE:THE DISCOUNT RATE
Virtually all important environmental or ecological
problems involve intertemporal choices and trade-
offs. To deal with intertemporal matters, it is neces-
sary to devise weighting schemes for comparing
benefits (or costs) today with corresponding ben-
efits in the future. The answers chosen are ex-
tremely critical in determining the direction of social
policy, particularly with respect to environmental
assets that are typically long lived. For example, if
we discount the future heavily enough, it is possible
to justify policies that generate a short-term benefit
at the expense of extensive long-term environmen-
tal damage. For this reason and others, discounting
has a bad reputation in some circles, so it is impor-
tant to understand the arguments for and against it.
IMPATIENCE AND PRODUCTIVITY
The main argument in favor of time discounting
derives from the use of market prices. The (risk-
free) interest rate is a price that enables one to
convert money today into more money tomorrow.
Namely, for every dollar invested in a ‘‘safe’’ saving
instrument today, the saver will get $1 1 r one
period later (where r is the one period interest rate);
therefore, the price of a dollar tomorrow(referred to
in the sequel as the ‘‘discount factor’’) is 1/(1 1 r) in
that if this amount is invested today the investment
will ‘‘purchase’’ $1 tomorrow. As long as all agents
have access to these opportunities, each will equate
relative preference (valuation) to the discount fac-
tor and by the argument given in the previous
section the discount factor is appropriate for weight-
ing in the social objective.
Consequently if interest rates are positive, this
accounting, indeed, will count future dollars less
than current ones. Generally, we do see positive
interest rates in the market, and there are compel-
ling reasons to believe thatwe should. First, physical
assets are productive—producers can take a dollar’s
worth of resources today and produce from them
more than a dollar’s worth of goods tomorrow.
Second, households are impatient—they will only
loan money to finance these investments if the rate
of return is positive. These reasons together guaran-
tee a positive equilibrium interest rate.
There are a number of arguments against the
position just stated, but in the interests of brevity we
will focus here on the one that seems most ger-
mane. The logic of market-based measures of value
requires that all relevant agents have free access to
the associated market. For one-period-ahead assets
this is okay, but for many periods ahead (where
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