Pricing External Equity for Dynamic Supplier Innovation: Shareholder Wealth and Supply-Chain Value Appropriation

Abstract

A supplier's decision to finance long-run innovation with external equity links a dynamic operating problem to the pricing of a new ownership claim. Innovation effort builds a depreciating technology-performance stock that changes Stackelberg prices, demand, and operating returns. Equity has two effects: cash expands feasible effort paths, while the claim reallocates supplier value between outside investors and original shareholders. The retailer creates a third allocation boundary by benefiting from the technology stock without paying innovation or upkeep costs. We solve the supplier's control problem with an HJB-Riccati approach and connect the budget multiplier to the issue amount under three claim-pricing rules. Competitive investor break-even pricing eliminates value transfer to new investors but does not coordinate channel investment. An exogenous fixed-pre-money benchmark transfers part of the innovation surplus and induces underfunding. Near the supplier's preferred funding level, a small financing contraction causes a second-order loss in supplier surplus but a first-order loss in retailer value; a unique threshold determines when the retailer gains more from the program than the supplier. Once the supplier's budget is slack, additional unrestricted equity does not change effort, technology, or prices, so coordination must alter the supplier's marginal return or cost of innovation. The results distinguish fair claim pricing from efficient channel investment and trace how external equity shapes technology formation, downstream value capture, and original-shareholder wealth.