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

Guerrazzi, Marco (2025): 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.

Abstract

In this paper, I develop a two-sector growth model with endogenous labour supply in which labour is employed only in the production of investment goods. From a theoretical point of view, I show that no matter the shape of the technology to produce consumption goods, a convex technology in the sector of investment goods is necessary and sufficient for a meaningful stationary solution and the determinacy of equilibrium trajectories. In addition, from a numerical perspective, I show that a calibrated version of the model relaxes the complementarity between the propensity to consume and to save and it is also able to provide a rationale for the procyclical patterns of the relative price of capital goods and the real wage.

• Item Type: MPRA Paper
• Language: English
• Keywords: Capital accumulation; Investment; Consumption; Two-sector growth model, Relative price of capital goods, Real wage.
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C61 - Optimization Techniques ; Programming Models ; Dynamic Analysis; E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E21 - Consumption ; Saving ; Wealth; E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E22 - Investment ; Capital ; Intangible Capital ; Capacity; O - Economic Development, Innovation, Technological Change, and Growth > O1 - Economic Development > O11 - Macroeconomic Analyses of Economic Development

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