In this paper we investigate the formation of the white-light (WL) continuum during solar flares and its relationship to energy deposition by electron beams inferred from hard X-ray emission. We analyze nine flares spanning GOES classifications from C4.8 to M9.1, seven of which show clear cospatial RHESSI hard X-ray and TRACE WL footpoints. We characterize the TRACE WL/UV continuum energy under two simplifying assumptions: (1) a blackbody function, or (2) a Paschen-Balmer continuum model. These set limits on the energy in the continuum, which we compare with that provided by flare electrons under the usual collisional thick-target assumptions. We find that the power required by the white-light luminosity enhancement is comparable to the electron beam power required to produce the HXR emission only if the low-energy cutoff to the spectrum is less than 25 keV. The bulk of the energy required to power the white-light flare (WLF) therefore resides at these low energies. Since such low-energy electrons cannot penetrate deep into a collisional thick target, this implies that the continuum enhancement is due to processes occurring at moderate depths in the chromosphere.