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.

翻译：过去几十年，全球经济日益全球化。另一方面，也有倡导“购买本地产品”的理念，即人们购买本地生产的商品和服务，而非远距离生产的产品。本文建立了一个实际价格的数学理论，该理论确定了主体在支出与获得效用之间最优权衡时的全球与本地消费比例。我们的实际价格理论依赖于与生产者和消费者网络相关的马尔可夫链转移概率矩阵的新近分析。我们证明，产品或服务的实际价格可由涉及的马尔可夫链矩阵确定，且可能与其标价显著不同。具体而言，我们表明产品和服务的标价往往并非“实际”或直接“有用”：对于提供相同短期效用的两种产品，标价较低者未必能提供更好的渐近效用。该理论表明，产品和服务的全球化或本地化对消费者支出—效用权衡确实存在不同影响。所建立的实际价格数学理论可用于从经济学角度判断是否采用某些人工智能技术。