Work

A two-sector model of optimal growth in which labour is employed only in the industry of investment goods: a complete characterization of equilibrium paths

Year: 2026

Type: article

Abstract: In this paper, I develop a two-sector growth model with endogenous labour supply in which the non-reproducible factor is employed uniquely in the production of investment goods. Relying on Cobb-Douglas technologies, logarithmic utility of consumption and separate CRRA disutility for labour provision, I show that a centralized solution characterized by a meaningful steady state and the determinacy of equilibrium trajectories requires constant returns to scale only in the production of new equipment. Moreover, I show that a calibrated version of the model tailored on the US economy leads to a marginal rate of transformation between consumption and investment goods lower than one in absolute value, and it is also able to provide a rationale for the procyclical patterns of the relative price of capital goods and the real wage.

Source: Decisions in Economics and Finance

DOI: 10.1007/s10203-026-00586-5

Author: Marco Guerrazzi

Institution: University of Genoa

Language: English

Topic: Economic theories and models

Subfield: Economics and Econometrics

Field: Economics, Econometrics and Finance

Domain: Social Sciences

SDG: Decent work and economic growth

Open Access status: hybrid

Estimated APC paid: $3,290