The question then arises: with identical products and quality, what sets one shop apart from the others? The answer lies in a theory known as Hotelling's law, devised by Harold Hotelling, which sheds light on why businesses selling the same items often choose to set up shop in close proximity.

Hotelling's law suggests that competing businesses located near each other may not always be in fierce competition. Instead, their proximity can prove mutually beneficial. This concept is particularly applicable to shops arranged in a continuous line, catering to customers scattered across the area.

Consider the familiar scenario of beachfront shops. Typically, purchasing something entails wasting time and incurring transportation costs. When all shops offer similar products, proximity becomes a significant factor influencing consumer choices.

Imagine a beach one kilometer wide. Mr. A opens a soft drink shop at the beginning of the beach, while Mr. B opens a similar shop at the opposite end. If both shops set the same selling price, a clear division point emerges at 500 meters, as people will naturally gravitate towards the shop closest to them.

However, if Mr. B decides to charge a higher price than Mr. A, the customer division point shifts towards the beginning of the beach. Consumers are willing to travel farther for a better deal, as per Hotelling's law formula: x* = (PB - PA + t)/2t. As the price difference (PB - PA) increases, customers move towards Mr. A's shop, providing him with a competitive edge.

In essence, Hotelling's law reveals that, when product quality is constant, price and travel expenses become pivotal factors in consumer decision-making. Furthermore, as stores move closer together, the travel distance for customers hardly differs. This ensures equal opportunities for each store, eliminating any advantage or disadvantage in their proximity.

Understanding Hotelling's law can provide valuable insights for businesses in competitive landscapes, offering a strategic perspective on how proximity and pricing can influence consumer behavior.