The optimal supply of liquidity and the regulations of money substitutes: a Baumol-Tobin approach

I use the Baumol-Tobin approach to examine the following propositions: (a) The optimal supply of liquidity requires a government loan program in addition to paying interest on reserves held by banks, (b) The adoption of the optimal policy will crowd out private credit arrangement and will thus shrink the financial sector and (c) regulations aimed at eliminating money substitutes may be redundant if the optimal policy is adopted but otherwise may improve welfare.