Armament, capital accumulation, and economic growth (analysis based on a multi-product growth model)

Abstract

Purpose: The aim of the article is to analyze the optimal allocation of production factors between sectors producing consumer, investment and military goods and services within the framework of supply-side, neoclassical models of economic growth and to find the golden rules of capital accumulation and armaments.

Design/methodology/approach: The proposed model is a compilation of Uzawa's two-sector growth model, Nonneman-Vanhoudt's multi-capital model, and the military-inclusive approach proposed by Filipowicz, Krawiec, and Tokarski (2025). The model assumes that the economy produces a finite number of consumer, investment, and military goods and services. The production processes of these goods and services are described by extended Cobb-Douglas production functions. The asymptotic stability of the nontrivial steady state of the examined growth model can be demonstrated using the Lyapunov function or the Grobman-Hartman theorem. Optimal allocation is determined by conditional maximization of the social utility function, defined as the weighted geometric mean of long-run consumption and long-run military production per worker.

Findings: This article derives formulas for the golden rule shares of factor inputs allocated to each of the three sectors of the economy, expressed in terms of the elasticities of the sectoral production functions and the elasticity  of the social utility function. It is shown that an increase in the share of factors engaged in the investment sector leads to an increase in long-run production in all three sectors, while shifts of factors to the consumer or military sectors generate crowding-out effects similar to those found in the IS-LM Hicks model. In borderline cases, when  (absolute security priority) civilian sector production approaches zero; however, when  (absolute welfare priority) the military sector is completely extinguished.

Originality/value: The authors' own contribution is the generalization of Uzawa's two-sector model to the multi-product case, its integration with the multi-capital Nonneman-Vanhoudt approach, and the formal inclusion of the military sector (rarely analyzed in mainstream economic growth theory). The model allows for a precise quantification of the "butter or guns" dilemma and provides golden rules for accumulation and armament that can be applied to economies with diverse geopolitical preferences