Dear bsphater,
1.
First, let me explain the Production Possibility Frontier (PPF) in general
terms. The PPF for a given problem is a curve showing the balance between
two quantifiable production goals. Each point on the curve shows one pair
of production values when we are operating at maximum capacity. Points
beyond the curve cannot be attained, since we cannot operate beyond
maximum capacity by definition. Points inside the curve signify that we
are operating at less than maximum capacity, hence inefficiently.
The literature includes PPF curves that illustrate the trade-off between
producing food and cloth, or between food and machinery.
University of Maryland University College: Production Possibilities and
Opportunity Cost
http://nova.umuc.edu/~black/ec2.html
Drexel University: A Model Illustrating Scarcity, part II
http://william-king.www.drexel.edu/top/prin/txt/Neoch/Eco111p.html
An example of current events where we can use PPF to model the trade-off
between two conflicting production goals is the relief effort in New
Orleans in the aftermath of Hurricane Katrina.
For instance, consider the problem of allocating police resources to
(a) patrol downtown streets to guard against looting, or (b) search
a neighborhood to evacuate residents. The finite resource here is the
number of man-hours available for deployment by the police department. We
can quantify the use of this resource by considering the number of police
man-hours it takes to patrol one acre of commercial zoning for one day,
or the number of man-hours required to evacuate one acre of residential
zoning for one day.
Thus, we can calculate the maximum commercial area we could protect
if every policeman were deployed on patrol, or the maximum residential
area we could evacuate if every policeman were deployed on evacuation
duty. These are the extreme points of the PPF curve, lying respectively on
one axis marked "Commercial Protection" and another marked "Residential
Evacuation". Other points on the curve express the trade-off between
deploying the limited resource of police man-hours to each goal.
The PPF curve for this resource allocation problem would look something
like the following.
PNG image: Allocation of Police Resources in New Orleans
http://plg.uwaterloo.ca/~mlaszlo/answers/katrina.png
2.
A Pareto improvement is a change in resource allocation that benefits at
least one participant without harming any participant in the system. Such
an improvement is known colloquially as a "win-win", as opposed to a
"win-lose". Pareto optimality is a state in which no further Pareto
improvements are possible.
Wikipedia: Pareto efficiency
http://en.wikipedia.org/wiki/Pareto_efficiency
Many systems are inherently Pareto optimal, which is not necessarily a
good thing. It means that no Pareto improvements are possible. In other
words, every choice of resource allocation is to the detriment of some
participants while benefiting others. Pareto improvements are clearly
very valuable and should therefore be sought in every resource-allocation
problem.
GameTheory.net: Pareto optimal
http://www.gametheory.net/dictionary/ParetoOptimal.html
An example of Pareto improvement in my personal experience involved the
purchase of soft drinks for a refrigerator in the lounge of my dorm. We
had gone to a warehouse club to take advantage of the cost savings from
buying soft drinks in large cases. The problem was that we were buying
a small number of cases to share among all the members of our group,
who had varying beverage preferences. We ended up quarreling at the
checkout line, where we had one case of cola, one of diet cola, and one
of ginger ale. Some members insisted that root beer was more desirable
than ginger ale.
But if we were to buy a case of root beer, it meant we would have
no money left over for ginger ale. Fortunately, a bystander observed
that there were variety cases available at the same price as regular
cases. By purchasing a variety case that contained multiple six-packs
of root beer and ginger ale, we were able to satisfy several different
beverage preferences without increasing our purchase quantity. This
resource allocation was therefore a Pareto improvement.
Even if no variety packs had been available, I think we could have
achieved a Pareto improvement by substituting a uniform case of spicy
ginger beer for the ginger ale. I believe the ginger-ale drinkers would
not have objected to this more robust version of their beverage, while
the root-beer drinkers would surely have preferred it to ginger ale. If
my intuition is correct, this allocation of resources would also have
qualified as a Pareto improvement.
Another Pareto improvement occurred when we were driving around after a
party to drop off several of our off-campus friends. We initially decided
to drop everyone off in a certain order, but after consulting a map, we
found that we could drop off a different person first, at a substantial
time savings to him, without delaying anyone else in the group. This
was certainly a Pareto improvement in the allocation of our driving
resources. We could probably have found further Pareto improvements if
we had bothered to look hard enough, but, frankly, our foremost goal was
not really to minimize the time our passengers spent in the car. These
were our friends, after all.
I also recall that we made a Pareto improvement at a pizza delivery
joint while ordering dinner. We found that if we substituted a large
all-dressed pizza for two small pepperoni pizzas and an order of chicken
wings, we could feed four people instead of three while spending no more
money than before. This was a Pareto improvement in the allocation of
our dining budget.
Domino's: See The Menu
http://www.dominos.com/Public-EN/Site+Content/Primary/See+the+Menu/
It has been a pleasure to address this question on your behalf.
Regards,
leapinglizard |
