Banks' deposit market power is customer-specific: depositors who hold stocks, bonds, or investment fund shares (market-priced savings, MPS) have stronger outside options and therefore more elastic deposit demand. Using Danish administrative data linking the universe of deposit accounts to each depositor's complete investment portfolio, we show that banks price this elasticity: MPS holders receive a 6.6 bps larger deposit-rate increase per 100 bps policy-rate increase than comparable non-holders at the same bank in the same year. The premium opens when depositors acquire MPS and fades when they sell these assets. Inheritances following unexpected parental deaths provide exogenous variation: heirs who inherit stocks or bonds see pass-through rise 3 to 6 pp relative to heirs inheriting cash or real estate. Higher pass-through only partially offsets MPS holders' greater elasticity: per 100 bps of tightening, they reduce deposits 2.4 pp more, and the resulting funding pressure leads high-MPS banks to cut lending.