C O M M 3 0 6 innovation, entertainment, & the arts For your final exam, please write a four-page, double-spaced essay as described below. As with your group projects, we encourage you to “think like a consultant”; put another way, think of this as the kind of material you could show to a prospective employer to illustrate how you can think analytically and strategically. Submit your essay via Turnitin by 4:00 PM (PST) on Monday, December 15th. NOTE: NO LATE ASSIGNMENTS WILL BE ACCEPTED. Citations (in any of the recognized academic styles) must be provided for any sources used. Your essay should consist of three linked components, outlined below. (Note that we are NOT asking you to turn in three separate short answers, but rather to write one essay that includes these three elements in a coherent progression.) 1. IMAGINE: What will the future look like? First, pick a media artifact; it can be one we’ve discussed in class on one of your own choosing. For example, you could talk about a song like Blowin’ in the Wind, a movie like Iron Man 3 or Mean Streets, a website like Facebook, a video game like Grand Theft Auto V or World of Warcraft, a newspaper like the New York Times, or any other piece of media that you find compelling (including books, magazines, and so on). What might this artifact be like if it were being released 15 years from now, in 2029? Note that you can either imagine a rebooted or revamped version of the original work, or you can simply imagine an alternate history where your artifact never existed in its original form and is instead being created for the first time in 2029. Describe this new version of your artifact in detail. You might focus on the media text itself, the process of creation, the process of distribution, the act or acts of consumption, audience engagement and response, or any combination of these elements. In addition, you can be relatively realistic or relatively optimistic in your predictions, but it may be helpful to provide supporting commentary or sources that justify why you think this is a viable future scenario; in other words, don’t just assert that we’ll all be watching TV on Google Glass without explaining why that’s likely to happen, either based on your own arguments about how audiences or media work, or relying on some other reasonable, evidence- based analysis. 2. ANALYZE: What can we learn from your imagined future about where we’re headed, and how should we feel about that trajectory? Think about how your new, speculative version of this artifact is different from the original; then, make an argument for what we can learn (about, say, business, art, or society) from these differences. What do these differences tell us about how things have changed, are changing, or should change? Does it instead prove how some things are unlikely to change? Finally, explain whether you think these developments (or lack thereof) are beneficia ...

1. C O M M 3 0 6
innovation, entertainment, & the arts
For your final exam, please write a four-page, double-spaced
essay
as described below. As with your group projects, we encourage
you
to “think like a consultant”; put another way, think of this as
the kind
of material you could show to a prospective employer to
illustrate
how you can think analytically and strategically.
Submit your essay via Turnitin by 4:00 PM (PST) on Monday,
December 15th. NOTE: NO LATE ASSIGNMENTS WILL BE
ACCEPTED.
Citations (in any of the recognized academic styles) must be
provided for any sources used.
Your essay should consist of three linked components, outlined
below. (Note that we are NOT asking you to turn in three
separate
short answers, but rather to write one essay that includes these
three
elements in a coherent progression.)
1. IMAGINE: What will the future look like?
First, pick a media artifact; it can be one we’ve discussed in

2. class on one
of your own choosing. For example, you could talk about a song
like
Blowin’ in the Wind, a movie like Iron Man 3 or Mean Streets,
a website like
Facebook, a video game like Grand Theft Auto V or World of
Warcraft, a
newspaper like the New York Times, or any other piece of
media that you
find compelling (including books, magazines, and so on). What
might this
artifact be like if it were being released 15 years from now, in
2029? Note
that you can either imagine a rebooted or revamped version of
the
original work, or you can simply imagine an alternate history
where your
artifact never existed in its original form and is instead being
created for
the first time in 2029. Describe this new version of your artifact
in detail. You
might focus on the media text itself, the process of creation, the
process
of distribution, the act or acts of consumption, audience
engagement
and response, or any combination of these elements. In addition,
you can
be relatively realistic or relatively optimistic in your
predictions, but it may
be helpful to provide supporting commentary or sources that
justify why
you think this is a viable future scenario; in other words, don’t
just assert

3. that we’ll all be watching TV on Google Glass without
explaining why
that’s likely to happen, either based on your own arguments
about how
audiences or media work, or relying on some other reasonable,
evidence-
based analysis.
2. ANALYZE: What can we learn from your imagined future
about where
we’re headed, and how should we feel about that trajectory?
Think about how your new, speculative version of this artifact
is different
from the original; then, make an argument for what we can learn
(about,
say, business, art, or society) from these differences. What do
these
differences tell us about how things have changed, are
changing, or
should change? Does it instead prove how some things are
unlikely to
change? Finally, explain whether you think these developments
(or lack
thereof) are beneficial or detrimental; this will help set up your
argument in
the final section of the assignment.
3. PLAN: What do we need to do to arrive at the future you
want to live in?
Given the scene you’ve painted of the future, and your analysis

4. of
whether this future is utopian or dystopian, articulate a specific
plan of
action: What innovations or policies are necessary to facilitate
or prevent
our achieving the future world you’ve depicted? Think about the
particular actors (e.g., one or more companies, governmental
bodies,
users, etc.), resources (e.g., finances, technologies, etc.), and/or
courses
of action (e.g., campaigns, legislation, business model
revisions, etc.) that
will be necessary for your desired outcome.
Think of yourself as a navigator of the future; speaking
metaphorically, then, this
assignment is just asking you to draw us a map, warn us of the
monsters that lie
ahead, and chart us a course forward.
Grading Guidelines
A response in the "A" range will likely have the following
characteristics:
• A clear, compelling, viable description of the future, a clear
and
compelling thesis comparing the past or present to this future,
and clear,
compelling, viable suggestions for achieving the most desirable

5. version of
the future
• A reasonable balance between all three components, such that
all
elements of the prompt are directly and fully addressed
• Evidence of unique insight (i.e., going beyond what was
shared in lectures
or readings)
• Adequate support for any assertions made (in the form of
analysis,
examples, or outside evidence)
• Elegant writing style free from grammatical or typographical
errors
• Sensible, compelling organization
• Polished formatting and a page length that meets the
requirements of the
assignment
A response in the "B" range will likely have the following
characteristics:
• A somewhat unconvincing depiction of the future, a somewhat
unclear or
superficial argument comparing the past or present with this
future,
and/or suggestions for the future that seem somewhat unclear,
lacking
insight, unreasonable, or unlikely to produce the desired goals
• All three components present, though perhaps in a somewhat

6. imbalanced fashion
• Application of relevant insights and examples from class
materials, without
necessarily demonstrating unique insight
• Weak support for assertions made
• Writing that is free from major grammatical or typographical
errors,
though still needs some polish
• A page length that meets the requirements of the assignment
A response in the "C" range will likely have the following
characteristics:
• An essay that fundamentally ignores a major portion of the
prompt (e.g.,
no clear description of an identifiable artifact, no clear
argument
comparing the past or present to the future, or no identifiable
plan of
action)
• Major oversight or mishandling of class concepts
• Consistently unsupported assertions or illogical arguments
• Major or consistent grammatical or typographical errors
A response in the “D” range will likely have the following
characteristics:

7. • No clear relationship to the prompt
• Failure to meet the page length required
A response in the “F” range will likely have the following
characteristics:
• No assignment turned in by the deadline indicated
• Elements of plagiarism, either via improper citation or no
citation of
outside materials, unapproved collaboration between students,
turning in
the same paper for more than one class, or any other violation
of
academic integrity as articulated by university policy (note that
violations
of academic integrity may also result in more extreme
disciplinary action)
1
Study Guide
1. Consider the production function y f (L, K ) LK 2 . Deno
te the factor prices of L and K
by w and r respectively and assume that these are given to the fi

8. rm. Also assume that the firm
is unable to influence the market price p of its output.
(a) Prove that the firm experiences increasing returns to scale.
[4]
(b) Consider the problem of profit maximization. Assuming for t
he moment that this is
unconstrained, the decision problem of the firm can be denoted
by
Max (L, K ) pf (L, K ) wL rK .
L,K
Prove that there is no finite level of input use for which the firm
maximizes profit.1 [8]
Interestingly, there is a finite combination (L*, K*) for which a
firm experiencing increasing
returns to scale minimizes the cost of production subject to an o
utput constraint. To see this,
consider the constrained cost minimization problem
Min. C wL rK subject to LK 2 y .
L,K
(c) Write down the Lagrangean for this problem. [2]
(d) Write down the first order necessary conditions (FOC) for a
minimum. [3]
(e) Simply state the mathematical condition that needs to hold f
or you to be able to solve the
FOCs explicitly for values of L and K. 2 [3]
(f) Assuming that the condition in part (e) holds, derive the valu
es L and K. [5]
(g) Verify that the values of L and K you obtained in part (f) are

9. , in fact, optimal by showing that
the second order sufficient condition for constrained minimizati
on (SOC) holds.3 [5]
(h) Write down the indirect objective function or value function
for the problem. [2]
(i) Prove that the indirect objective function is homogeneous of
degree one in both w and r . [3]
1 The easiest way to do this is to derive the values of L* and K*
implied by the first order conditions for
unconstrained maximization and then show that the second orde
r conditions are not satisfied with these (or for that
matter, any other) values.
2 You know that we are talking about the Implicit Function The
orem.
3 Recall that this will, in fact, ensure that the requirements for t
he Implicit Function Theorem will be satisfied.
(
where
f
L
,
f
K
0

10. ,
f
LL
,
f
KK
0
,
and
f
LL
f
KK
f
LK

11. 0
.
As
before,
the
price
p
of
output
and
the
)2
(j) Verify that partially differentiating the indirect objective fun
ction with respect to w should
give you the input demand function for labor L* L *(w, r, y)
you found in part (f). [2]
(k) Simply write down the name of the theorem which is being a
pplied implicitly in part (j). [1]
(l) Write down the expression for the Lagrange multiplier * f

12. or the problem.[2]
2. Consider a firm which operates with the general concave prod
uction function y f (L, K) ,
2
factor prices w of L and r of K are given to the firm. The objecti
ve of the firm is to maximize
profit subject to an output constraint f (L, K) y .
(a) Write down the Lagrangean for the problem. [2]
(b) Write down the first order necessary conditions (FOC) for a
maximum. [3]
(c) Verify that the second order sufficient condition (SOC) for
maximum is satisfied in the sense
that the Bordered Hessian determinant has the appropriate sign.
[6]
(d) If the second order condition in part (c) holds, you should b
e able to solve the first order
conditions derived in part (b) for the optimal values of L, K, an
d . Our goal is to see how the
conditional demand for labor L* responds to changes in w. To t
his end substitute the optimal
values L*, K* and * back into the FOC, partially differentiate
the three equations with respect
to w, and write down the resultant equations in matrix form.
[6]
(e) Solve for the partial derivative * using Cramer’s Rul
e and show that it is negative. [6]
3. Let us return to the cost minimization problem subject to an o

13. utput constraint. This time
assume the general Cobb-
Douglas production function y K , where 0 1
and
1
(a) Derive the levels of L* and K* that solve the decision proble
m of the firm and write down the
expression for the ratio L * K * . [6]
(b) Differentiate L * K * with respect to (w / r) and write down
the value of the derivative. [2]
(c) Find the magnitude of the term
d ( L * K *)
d (w r)
.
w / r
L * / K *
. [2]
(d) The term you found in part (c) is called the elasticity of s
ubstitution between L and K.
Write down a brief interpretation of the term. That is, what exac
tly is it measuring? [2]