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

TL;DR

This paper derives a closed-form analytical solution for a Two-Agent New Keynesian model with price and wage rigidities, highlighting how household heterogeneity influences monetary transmission and policy effectiveness.

Contribution

It provides a novel micro-founded framework that explicitly incorporates household heterogeneity and derives conditions affecting monetary policy transmission.

Findings

Monetary transmission can be amplified by heterogeneity-induced effects and price stickiness.

Wage stickiness alone can weaken or eliminate amplification effects.

The framework clarifies how household heterogeneity and rigidities jointly influence stabilization.

Abstract

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.