We analyze optimal monetary policy in a model with two distinct financial frictions: monopolistically competitive banks that charge endogenous lending spreads, and collateral constraints. We show that welfare maximization is equivalent to stabilization of four goals: inflation, output gap, the “consumption gap” between borrowers and savers, and a “housing gap” that measures the distortion in the distribution of the collateralizable asset between both groups. Collateral constraints create a trade‐off between stabilization goals. Following both productivity and financial shocks, and relative to strict inflation targeting, the optimal policy implies sharper movements in the policy rate, aimed primarily at reducing fluctuations in asset prices and hence in borrowers' net worth. The policy trade‐offs become amplified as banking competition increases, due to the fall in lending spreads and the resulting increase in borrowers' leverage.
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