Efficiency and Total Value Maximization in Evaluating Institutions
"Tools" lecture. Concepts will be used a lot in the course.
Efficiency: An arrangement is efficient if and only if there exists
no alternative in the feasible set -- that is, which can be obtained with
given endowments and technology -- that is at least as good for everyone
and makes at least one individual better off.
We often talk about allocative or productive efficiency.
We can also apply the term to evaluate economic institutions.
An organizational or institutional structure is efficient if it
is not possible to make someone better off without making someone worse
off, allowing for compensation.
institutions in firm: hiring practices, hierarchies, compensation schemes,
production technology, business practices.
institutions in market: firms, collectives, governments...
Consider a simple firm in which there is an owner, who supplies capital
and receives profits, and several workers who have different jobs for which
they are compensated.
Start from a given situation.
Suppose you could rearrange things -- match individuals to different jobs
(perhaps because they like the new tasks better) in a way that increases
each individual's utility and raises the owner's profits.
Was the original situation -- organizational structure -- efficient? No.
Suppose instead that when you rearranged the workers, there was no way
of matching them all to jobs they preferred. Does this mean the original
organizational form was efficient?
No. It might be possible for the owners or other workers who were better
off from the new matching to compensate those who were made worse off in
a way that, in the end, left everyone better off than they were in the
original situation. If so, then the original arrangement was inefficient.
Efficiency as a Norm
Efficiency is a good candidate for evaluating/comparing organizations.
What are the problems associated with efficiency as a norm?
Inefficient arrangements "leave money on the table". One
would not want not to make someone better off without making anyone
else worse off.
[example of multiple efficient arrangements]
There may be many efficient arrangements. The efficiency rule does
not dictate how to choose among them.
But with these caveats we will proceed, and consider efficiency a goal.
Efficiency says nothing about distribution. One example of an efficient
economy is the following. Suppose one individual owns all endowments, including
other individuals' labor, and combines these endowments with technology
in a way that maximizes total wealth. And suppose all wealth accrues to
this single non satiated individual slave-holder. Alternative arrangements
may be preferable, so efficiency may be one of several inputs to how we
Incentives and Efficiency
Under certain conditions, efficiency tends to win out over inefficiency.
For this to be the case, individuals need to be able to bargain and enforce
their decisions at low cost.
Suppose an institution is inefficient.
Then someone always has an incentive to propose an efficient arrangement,
and there will always be a way to do so in a way that makes everyone at
least as well off as they were before.
This argument is often used to explain corporate takeovers.
In the simple firm example above, if it were known by someone -- either
inside or outside of the firm -- that there was a mismatching between workers
and jobs, they would buy the firm, then make the efficient changes (or
propose the efficient arrangement in a way which everyone would accept).
One example is in trade policy. Tariff reductions may increase efficiency.
But how to pay off those you make worse off is a problem. (A side issue
is "should you pay them off at all," but that is not the point
here.) And how do you know how much you have to pay off certain groups
when they have an incentive to overstate damages?
Disputes may arise when individuals propose different efficient arrangements.
Side payments may not be straightforward, particularly when individuals
have private information about their valuations regarding different arrangements.
Efficient institutional arrangements are stable in the sense
that no individual or coalition with the ability to change the arrangement
would actually do so. Ability means the authority to propose changes.
Total Value Maximization
It is very difficult to check whether an institution is efficient, because
it requires that you know the preferences of each individual, and see if
accounting for changes in each thing that they care about (not just wealth),
they are better off.
Theorem: If there are no wealth effects (with respect to individuals'
preferences), an arrangement is efficient only if it maximizes total value
with respect to these individuals.
This is useful because checking to see whether total value is maximized
is easier than evaluating how each individuals' utility changes.
But what does "no wealth effects" mean?
It means that consumers' preferences between any goods or bundles of goods
do not change with their wealth.
In effect, it means that we can separate wealth from all other goods in
the utility function: U(x, y1, ... yn)=f(x)+g(y1,...yn).
What must hold under the "no wealth effects" assumption? What
does this mean?
For example, some people would be unwilling to take certain jobs for any
amount of compensation. Suppose part of the wealth maximizing arrangement
were for me to work at USC tutoring offensive linemen. But there was no
amount of money available for me to accept such a heinous task. Then the
wealth maximizing arrangement will always leave me worse off than the present
non-wealth-maximizing arrangement, and hence cannot be ranked higher on
efficiency grounds. Here there are multiple efficient arrangements,
and at least one does not maximize wealth. (An a more prosaic level, morality
concerns may play a role. Orthodox Jews working on the Sabbath.)
change between two bundles of goods must be compensable
If individuals do not have the wealth to compensate others when they move
from a worse to the wealth maximizing arrangment, non-wealth-maximizing
arrangment may be efficient (cannot move to the wealth maximizing arrangement
without making someone worse off). It may be efficient to make Steve Lavin
financially responsible for reductions in alumni donations resulting from
poor basketball teams. But this would run into wealth constraints. Lavin
could not pay off in bad states of the world.
the amount of compensation to make the person indifferent between two
bundles of goods must not be dependent on their initial wealth. This is
illuminated in the ticket allocation example below.
individuals must have enough to compensate others for movements among
Ticket allocation example:
Consider Harold's preferences for seats at Dodgers'
Harold's preferences exhibit wealth effects. Why?
Harold prefers sitting in the box and spending
$10 to receiving the upper deck ticket for free.
Harold also prefers sitting in the upper deck
and receiving $10 to sitting in the box for free.
Suppose x represents Harold's initial wealth, B indicates
"box seat," and U indicates "upper deck." Then we can
represent Harold's preferences as:
If NWE holds, then subtracting $10 from Harold's
wealth in the second should not make him prefer the box to the upper deck.
But it does, since doing so yields U(U,x)>U(B,x-10), which contradicts
the first relationship.
U(B,x-10) > U(U,x)
U(U,x+10) > U(B,x)
Harold valuation sitting in the UD relative to the
box depends on his income. He prefers the upper deck when he has high income,
and the box when he has low income.(Interpretation might be: When you're
rich, you don't need status symbols to make you feel wealthy?)
Under no wealth effects....
The extra utility I get from having a box seat rather than the upper deck
does not depend on my wealth. Reasonable? Suppose I have a ticket for a
box and you have one for the upper deck. Then the amount you would have
to pay me to change seats would not differ between when I was a grad student
and once I became a professor.
But we still use this assumption. Why?
It is a good approximation under most of the conditions we study. Usually,
when comparing institutional arrangements in which there are small differences
in wealth, NWE is close to being true. (Small differences in wealth means
that the associated changes in preferences orderings associated with wealth
differences are probably very small.)