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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