Reading Guide
Session 22: Emerging Electronic Markets
When we discussed search theory, we found that lower search costs could facilitate the
emergence of new markets. In some cases, those opportunities will be among people who
previously had little intera
Reading Guide and Assignment
Session 17: Experimentation, Replication and
Innovation
The mission of the MIT Sloan School is to develop principled, innovative leaders. How
can you use the most important business technology of our era to lead innovation?
Re
Partial Derivatives and the Ceteris
Paribus Assumption
The way in which economists use the ceteris
paribus assumption in their models to hold
constant a variety of outside influences so
the particular relationship being studied can
be explored in a simpli
MAXIMIZATION OF FUNCTIONS OF
SEVERAL VARIABLES
Using partial derivatives, we can now discuss how to find the
maximum value for a function of several variables. To understand
the mathematics used in solving this problem, an analogy to
the one-variable case
THE ENVELOPE THEOREM
One major application of the implicit function theorem is called the
envelope theorem; it concerns how the optimal value for a
particular function changes when a parameter of the function
changes. Because many of the economic problems
FUNCTIONS OF SEVERAL VARIABLES
Economic problems seldom involve functions of only
a single variable. Most goals of interest to economic
agents depend on several variables, and trade-offs
must be made among these variables.
For example, the utility an indi
CONSTRAINED MAXIMIZATION
So far we have focused our attention on finding the
maximum value of a function without restricting the
choices of the xs available. In most economic problems,
however, not all values for the xs are feasible. In many
situations, f
Second Order Conditions
Again, however, the conditions of Equations
)
2.19( f1 . f2 . . fn . 0:
are not sufficient to
ensure a maximum.
This can be illustrated by returning to an already
overworked analogy: All hilltops are
(more or less) flat, but not ev
Lagrangian multiplier method
One method for solving constrained maximization
problems is the Lagrangian multiplier method, which
involves a clever mathematical trick that also turns out to
have a useful economic interpretation. The rationale of this
metho
First Order Condition for a Maximum
This result is quite general. For a function of one
variable to attain its maximum value at some
point, the derivative at that point (if it exists) must be
0. Hence, if a manager could estimate
the function f .q. from s
Youngs theorem
These examples illustrate the mathematical result that, under quite
general conditions, the order in which partial differentiation is
conducted to evaluate second-order partial derivatives
does not matter. That is, fij . fji (2.16) for any
MAXIMIZATION OF A FUNCTION OF ONE
VARIABLE
Lets start our study of optimization with a simple example.
Suppose that a manager of a firm desires to maximize1 the profits
received from selling a particular good. Suppose also that the
profits . received depe
Reading Guide Session
15: Enterprise 2.0
The new Web 2.0 technologies are spawning new ways to work inside organizations:
Enterprise 2.0. For this class, we will look closely at one cluster of organizations in the
midst of this transformation, namely the
Reading Guide
Session 16:
Open Source and Innovation
Digital goods like software, information, music, video, e-books, etc. can be reproduced
almost costlessly. While this is provides obvious economic benefits, it also poses special
challenges for providin
Reading Guide
Session 18: Digital Advantage
The increased power of IT has led to complementary changes in business processes,
organizational capital and other types of intangible assets. To a growing extent,
understanding these changes is the key to gaini
Reading Guide
Session 19: Social Networks
Facebook now has the most page views of any site on the web, making it an apt symbol
of the ubiquity and relevance of social computing. The digitization of social networks is
not only creating new opportunities to
Reading Guide
Session 20: Information Analytics Gary Loveman
This session will look more closely at how better information analytics are changing
management, marketing and customer relationship management. Our guest speaker will
be Gary Loveman, CEO of Ha
Reading Guide
Session 23: The Future of the Information Economy
Its useful to understand what the future will be like. After all, well be spending the rest
of our lives there. Fortunately, some predictions are relatively easy to make. For
instance, we can
Implicit function theorem
It may not always be possible to solve implicit
functions of the form g.x, y. . 0 for unique
explicit functions of the form y . f .x.
Mathematicians have analyzed the conditions under
which a given implicit function can be solved