# Computing + Mathematical Sciences Lecture

Tuesday
November 15, 2011
4:00 PM

**Equilibrium Pricing of Semantically Substitutable Digital Goods and Welfare Theorems for the Resulting Mixed Economy**

**Speaker:**Vijay Vazirani, College of Computing, Georgia Tech

**Location:**Annenberg 213

General Equilibrium Theory, the undisputed crown jewel of Mathematical Economics for over a century, gave a very satisfactory solution to the problem of arriving at a principled method of pricing goods and services. The solution was based on Adam Smith's principle of maintaining parity between supply and demand, Walras' notion of equilibrium, and the Arrow-Debreu Theorem, which proved the existence of equilibrium in a very general model of the economy.
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However, this solution, designed for conventional goods, is not applicable for digital goods -- once produced, a digital good can be reproduced at (essentially) zero cost, thus making its supply infinite. Considering the current size of the digital economy and its huge growth potential, it is imperative that we obtain an equally convincing theory for pricing of digital goods.
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For a broad class of digital goods, coming primarily from the entertainment industry, which we call semantically substitutable goods, we show how a suitable adaptation of the Arrow-Debreu model yields a simple equilibrium-based pricing structure. We also give examples of (multi-billion dollar) markets that use this pricing structure.
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The far reaching significance of a competitive equilibrium is made explicit in the Fundamental Theorems of Welfare Economics. We give an appropriate notion of efficiency under which both Welfare Theorems hold in our mixed economy consisting of conventional and digital goods. Finally, we outline a multitude of issues that still need to be addressed to obtain a theory for the digital economy that is on par with the original theory.
<br><br>Based on the following joint paper with Kamal Jain:<br> http://arxiv.org/abs/1007.4586

**Series**Computing + Mathematical Sciences Lecture Series

**Contact:** Sydney Garstang at x4555 sydney@caltech.edu