Extended Version: Market-Driven Equilibria for Distributed Solar Panel Investment

Abstract: This study investigates market-driven long-term investment decisions in distributed solar panels by individual investors. We consider a setting where investment decisions are driven by expected revenue from participating in short-term electricity markets over the panel's lifespan. These revenues depend on short-term markets equilibria, i.e., prices and allocations, which are influenced by aggregate invested panel capacity participating in the markets. We model the interactions among investors by a non-atomic game and develop a framework that links short-term markets equilibria to the resulting long-term investment equilibrium. Then, within this framework, we analyze three market mechanisms: (a) a single-product real-time energy market, (b) a product-differentiated real-time energy market that treats solar energy and grid energy as different products, and (c) a contract-based panel market that trades claims or rights to the production of certain panel capacity ex-ante, rather than the realized solar production ex-post. For each, we derive expressions for short-term equilibria and the associated expected revenues, and analytically characterize the corresponding long-term Nash equilibrium aggregate capacity. We compare the solutions of these characterizing equations under different conditions and theoretically establish that the product-differentiated market always supports socially optimal investment, while the single-product market consistently results in under-investment. We also establish that the contract-based market leads to over-investment when the extra valuations of users for solar energy are small. Finally, we validate our theoretical findings through numerical experiments.