Structural failure of marginal scarcity pricing: a common architectural root of retailer insolvency, risk–volume separation instability, and VoLL-dependent investment signals

Liberalised electricity markets exhibit three recurring pathologies typically treated as separate policy problems: retailer insolvency under regulated price caps, instability from the separation of volume risk and price risk, and the sensitivity of investment incentives to the administratively determined value of lost load (VoLL). This paper argues that these pathologies share a common architectural root: the marginal-pricing paradigm assigns too many incompatible functions to a single scarcity price. The claim is formalised through three structural lemmas. Lemma 1 shows retailer insolvency is a mathematical consequence of combining capped retail revenue with uncapped wholesale cost exposure under any finite equity buffer, given a sufficiently prolonged shock relative to that buffer. Lemma 2 shows risk–volume separation instability is unavoidable whenever a retail intermediary cannot simultaneously control consumed volume and charged price under a retail price cap. Lemma 3 proves that expected scarcity rents and the free-entry capacity level are continuous, strictly monotone functions of an administratively chosen VoLL, for which no market-internal principle identifies a unique correct value; gross producer operating surplus at fixed capacity is likewise monotone in VoLL. The lemmas are calibrated to the GB market using published bill-decomposition, supplier-failure and wholesale pricing data, showing the conditions for structural insolvency were met during the 2021–2022 crisis and that VoLL sensitivity is empirically material. The paper characterises the design requirements a reformed architecture must satisfy, arguing that effective reform requires architectural separation of the functions marginal pricing conflates, rather than incremental overlays on the existing framework.