A Multi Level Optimization Model Of Infrastructure Dependent Technology Adoption

Many technologies in energy, transportation, and telecommunications require large infrastructure systems to deliver benefits to adopters and society. Policymakers seeking to promote the diffusion of infrastructure-dependent technologies are often confronted with the ``chicken-and-egg" problem: consumers are reluctant to adopt the technology without adequate infrastructure available, and firms are reluctant to invest in infrastructure without a sufficient number of adopters. This chicken-and-egg problem can hinder the diffusion of new technologies and prolong the timeframe over which existing technological systems remain locked-in. In this paper, we formulate a stylized model of technology policy decision-making from the perspective of a policymaker who seeks to stimulate the market penetration of an infrastructure-dependent technology. Our model is a multi-level optimization problem in which a policymaker (first level) maximizes net social benefits by setting the levels of two incentives: a subsidy for a profit-maximizing firm (in equilibrium with two other firms, the second level) to invest in infrastructure that raises the benefit of adoption to consumers, and a direct subsidy for consumers to adopt the technology (third level). We analytically derive the firms' and consumers' optimal responses to the first-level policy decisions. Then, we analytically establish the optimal additional adoption -- beyond the laissez-faire level -- that the policymaker should stimulate by setting the subsidies. Finally, we present a case study on electric vehicle diffusion and obtain insights into how a policymaker should allocate resources to charging infrastructure and vehicle incentives. We also uncover a counterintuitive possibility where adoption can decrease with a technology's benefits.