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To AI or not to AI, to Buy Local or not to Buy Local: A Mathematical Theory of Real Price

Author

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  • Huan Cai
  • Catherine Xu
  • Weiyu Xu

Abstract

In the past several decades, the world's economy has become increasingly globalized. On the other hand, there are also ideas advocating the practice of ``buy local'', by which people buy locally produced goods and services rather than those produced farther away. In this paper, we establish a mathematical theory of real price that determines the optimal global versus local spending of an agent which achieves the agent's optimal tradeoff between spending and obtained utility. Our theory of real price depends on the asymptotic analysis of a Markov chain transition probability matrix related to the network of producers and consumers. We show that the real price of a product or service can be determined from the involved Markov chain matrix, and can be dramatically different from the product's label price. In particular, we show that the label prices of products and services are often not ``real'' or directly ``useful'': given two products offering the same myopic utility, the one with lower label price may not necessarily offer better asymptotic utility. This theory shows that the globality or locality of the products and services does have different impacts on the spending-utility tradeoff of a customer. The established mathematical theory of real price can be used to determine whether to adopt or not to adopt certain artificial intelligence (AI) technologies from an economic perspective.

Suggested Citation

  • Huan Cai & Catherine Xu & Weiyu Xu, 2023. "To AI or not to AI, to Buy Local or not to Buy Local: A Mathematical Theory of Real Price," Papers 2305.05134, arXiv.org.
    • Handle: RePEc:arx:papers:2305.05134
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    References listed on IDEAS

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    1. Carson Young, 2022. "Should You Buy Local?," Journal of Business Ethics, Springer, vol. 176(2), pages 265-281, March.
    2. Joseph E. Stiglitz, 2017. "The overselling of globalization," Business Economics, Palgrave Macmillan;National Association for Business Economics, vol. 52(3), pages 129-137, July.
    3. Freund, Caroline L. & Weinhold, Diana, 2004. "The effect of the Internet on international trade," Journal of International Economics, Elsevier, vol. 62(1), pages 171-189, January.
    4. David Hummels, 2007. "Transportation Costs and International Trade in the Second Era of Globalization," Journal of Economic Perspectives, American Economic Association, vol. 21(3), pages 131-154, Summer.
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