Limited time commitment: Does competition for providing scarce products always improve the supplies?

In addition to the fact that goods and services typically become scarce because resources are scarce, scarcity involves a psychological aspect. When a product is limited in availability, or perceived as being limited, it becomes more attractive. As a result, as long as the product is viewed as scarce, a surplus in supplies implies an increase in consumption. Motivated by fresh-water scarcity, we address the problem of dynamic interaction between two firms committing to provide water supply within a limited time horizon. We find that competition does not necessarily reduce product scarcity compared to the monopolistic industry. In particular, commitment-based market equilibrium is characterized by a critical duration of the supply contract. Duopolistic competition within this duration is reminiscent of the conventional quantity competition—the supply grows and the price drops compared to the monopolistic output. On the other hand, a longer contract leads to a different operational outcome—the monopoly becomes gradually more beneficial in terms of supplies and, as the time horizon grows, even overwhelmingly advantageous, thereby resulting in lower scarcity of the products.