9781118041581

Next, because the original move was beneficial, we try moving farther east,

say, to town D. Again, the move reduces the TTM. (Check this.) What about a

move east again to town E? This brings a further reduction. What about a move

to town F? Now we find that the TTM has increased. (By how much?) Moreover,

any further moves east would continue to increase the TTM. Thus, town E is the

best site.

It is worth noting the simple but subtle way in which we found the optimal

site. The simple maxim of marginal analysis is as follows:

Make a “small” move to a nearby alternative if and only if the move will improve

one’s objective (in this case, reduce TTM). Keep moving, always in the direction of

an improved objective, and stop when no further move will help.

The subtlety of the method lies in its focus on changes. One need never

actually calculate a TTM (or even know the distances between towns) to prove

that town E is the optimal location. (We can check that town E’s TTM is 635.)

One requires only some simple reasoning about the effects of changes.

Of course, on the tip of your tongue may be the declaration, “This problem

is too simple; that is the only reason why the method works.” This protest is both

right and wrong. It is true that this particular location problem is special and

therefore somewhat artificial. (Two-dimensional siting problems are both more

realistic and more difficult.) But the simplicity of the setting was not the key to

why marginal analysis worked. The method and its basic reasoning can be used

in almost any optimization problem, that is, in any setting where a decision

maker seeks to maximize (or minimize) a well-defined objective.

A SIMPLE MODEL OF THE FIRM

The decision setting we will investigate can be described as follows:

1. A firm produces a single good or service for a single market with the
   objective of maximizing profit.


2. Its task is to determine the quantity of the good to produce and sell
   and to set a sales price.


3. The firm can predict the revenue and cost consequences of its price
   and output decisions with certainty. (We will deal with uncertainty in
   Chapters 12 and 13.)

Together these three statements fulfill the first four fundamental decision-

making steps described in Chapter 1. Statement 1 specifies the setting and

objective, statement 2 the firm’s possible decision alternatives, and statement

3 (along with some specific quantitative information supplied shortly) the link

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