The Digital Euro and Deposit-Market Competition: Portfolio Choice, Bank Switching, and Funding Adjustment

A non-remunerated central bank digital currency can change deposit competition even when households retain their bank accounts. I study a capped public-money option in a differentiated-bank model in which households choose both a bank and the division of liquid wealth between deposits and digital currency. Residual deposit demand responds through portfolio adjustment and bank switching; the latter depends on the second moment of deposit balances. This decomposition gives a conditional, rather than uniformly positive, deposit-rate response. With homogeneous customers and binding caps, a higher cap reduces the value of switching banks and lowers the equilibrium rate. I prove this result globally, show that it survives random-utility bank choice, and establish conditions under which wealth heterogeneity reverses it. A separate lending and wholesale-funding extension introduces an opposing scarcity effect and solves the joint deposit-pricing and lending response. Deposit markdowns, monetary-policy pass-through and household surplus need not move together. Piecewise-polynomial calculations verify all unilateral rate deviations in the numerical examples. Recent European and Indian evidence motivates the mechanisms without being treated as a calibration. The digital euro's institutional setting is assessed through 18 September 2026, with legislative proposals, pilot activity and actual issuance kept distinct.