Closed-Form of Two-Agent New Keynesian Model with Price and Wage Rigidities

This paper analytically demonstrates that, in a Two-Agent New Keynesian model with Rotemberg-type price and wage rigidities, monetary transmission can be amplified when two mechanisms are sufficiently strong: the heterogeneity-induced IS-slope effect and the price-stickiness channel. We also show when amplification weakens or disappears, most notably under pure wage stickiness, where the price channel shuts down and the heterogeneity-driven term vanishes. The framework features household heterogeneity between savers and hand-to-mouth households and is derived from microeconomic foundations while avoiding restrictive assumptions on relative wages or labor supply across types that are common in prior analytical work. The closed-form solution makes transparent how price stickiness, wage stickiness, and the share of hand-to-mouth households jointly shape amplification. We further derive a modified aggregate welfare loss function that quantifies how heterogeneity, operating through distributional effects from firm profits, changes the relative importance of stabilizing inflation. Overall, the tractable yet micro-founded analytical framework clarifies the interaction between household heterogeneity and nominal rigidities and identifies sufficient conditions under which monetary policy gains or loses traction.