Profit Redistribution in a TANK Model with Price and Wage Rigidities: An Analytical Benchmark and an Own-Lag Comparison

This paper studies profit redistribution in a Two-Agent New Keynesian model with price and wage rigidities, type-specific wages, and type-specific labor supply. An aggregate-lag benchmark yields closed-form distributional allocations and impact and infinite-horizon cumulative monetary-policy multipliers. The local effect of the hand-to-mouth share on impact multipliers requires an additional root condition; its local effect on infinite-horizon cumulative multipliers requires determinacy. The own-lag comparison holds primitive cost coefficients fixed rather than equating economic rigidity across timings. Across a grid of policy feedback, household wage-subsidy financing, household shares, and duration targets, expansionary monetary shocks raise output and inflation and lower profits. The hand-to-mouth share increases 21-quarter cumulative responses under both timings and impact responses under own-lag adjustment, whereas the aggregate-lag impact ordering can reverse slightly. Timing changes inflation and profit persistence. The aggregate-lag benchmark compresses dispersion losses into a higher price-inflation weight; own-lag adjustment leaves inherited relative wages and dynamic dispersion terms.