This paper studies what structural factors determine the financial vulnerability from increased energy prices, other than income level. In particular, it investigated the energy cost of various heating system types in South Korea and examined its causal relationship with economic disparity. Through the empirical data from 1,200 surveys, we examined a tendency for low-income families to live in an old multiplex building or an old apartment with an individual heating system. In contrast, high-income families usually live in a comparatively newly built apartment complex with a district heating system. Also, with the empirical data, it was observed that the annual heating price (per square meter) of individual heating systems is 50% more expensive than the district heating system at the maximum. Here, we suspected that the economic disparity restricts not only the house options for a low-income family but also the options for the more efficient heating system that leaves them no choice but higher heating prices. Using an integrated methodology of Random forest and econometric method, we analyzed the causal connection between the low-income residents and the energy price for heating. Also, we studied its precise impact on economic disparity and vulnerability. Further, to suggest policy implications, we looked into the market and policy background on the house and heating system that caused such a structural gap.