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JRCOLL  February 2011

JRCOLL February 2011

Subject:

Junior Colloquium--Mark your calendar

From:

Conrad Plaut <[log in to unmask]>

Reply-To:

Announcements for the Mathematics Department Junior Colloquium <[log in to unmask]>

Date:

Mon, 7 Feb 2011 10:23:26 -0500

Content-Type:

text/plain

Parts/Attachments:

Parts/Attachments

text/plain (59 lines)

All,

The Junior Colloquium kicks off this Thursday with a talk by Hai Ngyuen, a
UT Math Honors graduate who is briefly back at UT to earn an MS in math
while pursuing a PhD in Economics at Johns Hopkins (see below).

This year the JC will be held on select Thursdays in the Ayres 4th floor
colloquium room at 3:35 (except Judy Walker's talk, which will be earlier
due to Honors Day). Pizza will be served on the forth floor prior to each
talk.

February 10--Hai Ngyuen
February 24--Professor Andrew Miller (Belmont University)
March 3--Professor Suzanne Lenhart (UTK)
March 10--Professor Tim Schulze (UTK)
March 24--Professor Mike Langston (UTK-computer science)
April 14--Professor Judy Walker (U. Nebraska)

This Thursday, February 10:

SPEAKER: Mr. Hai Nguyen
TITLE: "Analysis of the Expected Industry Price"
ABSTRACT: We explore an intuitive microeconomic question of the behavior
of the expected industry price, and see how we can apply basic concepts of
Calculus to arrive at the answer. The question here is: given firms in a
certain industry that are constrained by some production capacity K, what
will happen to the overall price when we exogenously raise K?

To answer this question, we consider a simplified market in which demand
is represented by a simple linear function, and supply is made available
by only two identical firms. Furthermore, capacities of the firms are
bounded by K. We then introduce some game theoretic notions to derive
firms' strategies in setting prices, given K. With appropriate
assumptions, the prices that firms set will be identical, and given in the
form of a probability distribution over a set of prices. This probability
distribution, as expected, is a function of K. We use this information,
together with the expected market share of each firm, to arrive at a
formula for the overall expected industry price. From there, we examine
the derivative of a double integral to obtain our primary result.

Intuitively, when firms are able to produce more, the competition in the
market becomes more intense, and thus the expected overall price will
drop. We will see that, indeed, this is the result that we get from our
calculations.

Join us for pizza in Ayres 401 prior to the talk.



Conrad Plaut
Professor, Director of UT Math Honors
Math Department
Ayres Hall 224C
University of Tennessee
Knoxville, TN 37996-0612

Phone: 865-974-4319
http://web.utk.edu/~cplaut

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