Kang, Weisman, and Zhang (2000) demonstrated that, under a tighter price cap, consumer welfare increases with the independence of demands. Conversely, the tighter price cap may negatively impact consumer welfare in situations involving interdependent demands. This paper identifies an overlooked property of Kang et al. (2000), namely, that the cross-price effects should be symmetrical without an income effect and demand functions of a Hicksian type. This paper reveals the invariant conclusion that consumers always benefit from a tighter price cap. Besides, it further derives the effects of the tighter price cap on consumer utility, and concludes that the net price elasticity of demand is the key to the effect of the average revenue constraint.