This study proposes a methodology for quantitatively estimating the appropriate scale of policy funds in the absence of a price mechanism, utilizing application and approval data as signals of demand and supply. A Bayesian structural model with a truncated normal distribution is constructed to express the structural credit access constraint faced by Small and Medium Enterprises (SMEs) with credit ratings of BBB- or below as an equilibrium relationship between demand and supply functions. Using policy fund data from the Korea SMEs and Startups Agency (KOSME) along with macroeconomic variables from 2000 to 2024, the analysis shows that policy fund demand is positively associated with GDP growth and decreases as the SME lending rate rises, while supply increases with fiscal expansion and improved economic outlook but contracts as government bond yields rise. The funding gap analysis indicates that latent demand exceeds actual approval by an average of 36 percent, with equilibrium supply capacity estimated at 24 percent, yielding an average annual demand gap of 1.07 trillion KRW and a supply gap of 0.66 trillion KRW over the observation period. During the economic crises of 2009 and 2020 - 2021, actual approvals exceeded predicted values, confirming the counter-cyclical function of policy funds. The estimated application coefficient of 0.550 suggests that approximately 55 percent of application amounts reflects equilibrium demand, with the remainder attributable to strategic overbidding behavior. By presenting an equilibrium model that captures the administrative allocation characteristics of policy funds in areas of commercial finance market failure, this study contributes to the evaluation of appropriate supply levels and the formulation of evidence-based policy.