• Haggling/Negotiation
  The oldest form of price setting and still going strong, even on the internet.
  
  
• Posted Price
  The seller annouces a price and waits for buyers willing to transact at that price. This is really a particular haggling strategy where the seller makes a take it or leave it offer.
  
  
• Auctions
  The seller has buyers compete amongst themselves to determine the price at which a transaction will be executed. Like a posted price this should be viewed as particular haggling strategy.
  
  
• Market Mechansims
  Multiple buyers and sellers agree to particpate in an organized forum where the price is set to clear the market.

In this course I will discuss the pros and cons of the first three methods for price setting (the last is left to another course). An example of the kind of question I will ask (and answer) is this: Which of the three price setting methods generates the highest revenue/profit?

The second topic will be how to customize the price of the same product or service to different segements (otherwise known as price discrimination, but that sounds so perjorative). Here there are two issues of importance. The first is that such customization can lead to grey markets where customers who buy at the low price resell to customers facing the higher price. The second issue is that an offering to one segment may cannibalize sales to another segment.

The third topic will be the use of optimization models to set prices when the volume of demand is uncertain (revenue/yield management) as well pricing multiple substitute/complementary products.

The fourth topic will be pricing in competitive environments. Here I will discuss various strategies to soften price competition through differentiation, versioning, bundling and information.

Although not a lawyer I will play one in the classroom and summarize some of the legal aspects of pricing. I will spare you the trip to prison for white collar criminals to point out that justice is blind, the law is an ass ( animal not the appendage) and jail is terrible.

Last, no discussion about pricing should begin without an understanding of how the buyer values the product or service for sale. I will summarize some of the main techniques (regression, conjoint analysis, EVC) for gathering information about buyer valuations. I will also discuss some of the behavioral aspects of pricing.

The grade for the course will be based on class participation (cold calling) (10%), homeworks (40%) and a take home final (50%). The class is a mixture of lecture, case discussion, modeling/analysis (of the kind you have seen in DECS 434 and managerial econ) and some blah-blah (in which the softer side of management is dicussed leading to no firm conclusion but a warm fuzzy glow and the satisfaction that all sides of the issue have been brought to light; group hugs optional).

• Required for the course will be a note packet which will contain cases as well as a copy of the lecture notes. Optional, but not required for the course is the book `The Strategy and Tactics of Pricing' by Nagle and Holden. Be warned, there are many versions of the book out there. All the same , but they vary in price!
  
  
• The course time-table for Winter 2007 (due dates, assignments etc) can be downloaded by clickingFT syllabus or PT syllabus.
  
  
• You can find a collection of articles on pricing here.

• TIMES: The time of this class for the Fall has yet to be decided.
  
  

Student registering for the class should e-mail their available times to me by September 18th so that I can set the time. Plan on two meetings a week of about 2 hours each (with a break in between).

All of economic theorizing reduces, in the end to the solution of one of three problems.

Given a function f and a set S:

1)find an x such that f(x) is in S. This is the feasibility question.

2)Find an x in S that optimizes f(x). This is the problem of optimality.

3) Find an x in S such that f(x) = x; this is the fixed point problem.

These three problems are, in general, quite difficult. However, if one is prepared to make assumptions about the nature of the underlying function (say it is linear, convex or continuous) and the nature of the set S (convex, compact etc.) it is possible to provide answers and very nice ones at that. This course is about the answers as well as the relationships between them.

Some of what I cover (without the embellishments, amplifications or intuitions) can be found in the Mathematical Appendix of ` Microeconomic Theory' by Mas-Collel, Whinston and Green.

The bulk of the course emphasizes the applications of these techniques. Some are standard, like fixed points to existence of equilibria. Most are not, like linear programming to auctions, options pricing and social choice; Tarski's theorem to stable matchings.

This is a Ph.D. level course. The text for the course is Advanced Mathematical Economics, by yours truly.

The book is published by Routledge .

If you present me with a receipt for the purchase of the book, I will refund that portion of the portion price that corresponds to my royalty.

• Social Choice
  Here I will emphasize the use of linear programming techniques to obtain possibility and impossibility results.
  
  
• Stable Marriages and Stable Roommates
  Again the emphasis will be on linear programming methods to derive results.
  
  
• The Stable Set
  This was von-Neumann and Morgenstern's answer to the question of what is the outcome of a game. Since it does not exist in general, no one pays attention to it. Nevertheless the idea crops up every now and then.
  
  
• Axiomatic Approaches
  Lets be 'normative' for a change and suggest solutions. I'll illustrate with: bargaining (Nash, Kalai-Smorodinsky), measuring income inequality (Lorenz curve, Gini) , bankruptcy (talmudic version) , apportionment.
  
  
• Matroids and Discrete Convexity
  By and large economists stay away from indivisibilities because one cannot take derivatives. Here I will describe some tools that work in the discrete world and have some applications to exchange economies with indivisibilities ( so I lied about GE).
  
  
• Differential Games
  We will meet twice a week for 1.5 hours, time to be determined. Grade will be assessed by intermittent homeworks and a take home final or a paper.

Introduction to Management Science

This is a (10 week) MBA level course that covers Linear Programming, Decision Analysis and Simulation at the Fisher College of Business, Ohio State University. Yes, its a CORE course. In fact the MBA core was revised in '96 and this material REMAINS in the core. Given the current anti-analytical climate in B-schoools, this is unusual. It is.
If you want to find out about the philosophy of the course click here.
In the new core, Fisher students take 10 weeks of statistics, 5 weeks of decision analysis, 5 weeks of linear programming and 5 weeks of game theory/industrial organization. Fisher students, as a consequence, can not only charm their way out of a paper bag but think their way out as well!

Managerial Econimics
A ten week core Fisher MBA class. The first 5 weeks is devoted to basic micro and the remainder to game theory and industrial organization.

Theory of Asset Pricing
Wiener Process, Ito's Lemma, Black-Scholes, Arbitrage Arguments, Risk Neutral Pricing, de Finetti's Theorem. Ph.D. level course.

Design and Analysis of Heuristics
Worst case and Probabilistic Analysis of Approximation Algorithms. Empirical Analysis of the performance of Heuristics for Integer Programming. Ph.D. level course.

Network Optimization
Network Algorithms, Network Recognition and Applications)- Ph.D. level course.

Theory of Games
Cooperative Games, Fair Allocation, Games of Incomplete Information, Bargaining and Social Choice - Ph. D. level course.

Polyhedral Combinatorics
Facets, Valid Inequalities and applications to compuational Integer Programming- Ph. D. level course taught jointly with Marc Posner.

Advanced Integer Programming
Lattices, Superadditivity, Projections, Blocking and Totally Dual Integral Systems) - Ph. D. level course taught jointly with Marc E. Posner.

Probabilistic Analysis of Combinatorial Algorithms
Random Graphs, Bin Packing, Scheduling- Ph. D. level course taught jointly with Boris Pittel.

Behavioral Decision Making
Biases, Heuristics, Risk, Utility Theory - Ph.D/M.B.A. level course.

Executive Education
·  Introduction to Management Science, Sloan Fellows Programme, MIT (Summer 93 and 96)

·  Inventory Management (for the Automative Warehouse Distributor Programme, The National Wholesaler and Distributor Programme and the Institute for Scrap Recycler's programme) Ohio State University.

·  The Kellogg Executive Managers Programme course in Managerial Economics.

·  Competive Pricing module of a short course on Pricing offered by the Kellogg Executive programme.