Distributive justice and social conflict in an AK model

We introduce distributive justice into a simple model of growth and distribution. Two groups (‘classes’) of otherwise identical, capital-rich and capital-poor individuals (‘capitalists’) and (‘workers’) are in conflict over factor (labour-capital) shares. Capitalists’ (workers’) ideal labour share is low (high) – but always tempered by the recognition that everyone supplies one unit of labour inelastically and desires a wage; and that the labour share impacts growth negatively in our ‘AK’ production economy. Social conflict is defined as the difference between the ideal labour shares of the two classes. This conflict is resolved by the two positive and three normative criteria we consider. Thus, the macroeconomy (growth, factor shares, distribution), social conflict and the methods of its resolution are jointly determined in a complete socio-economic equilibrium. We believe both this approach and our rich set of results are novel.
We consider two positive (probabilistic voting and Nash bargaining, encapsulating electoral politics and socio-political bargaining) and two normative (justice) criteria (utilitarian and Rawlsian) of conflict resolution. Greater impatience, intensified status comparisons and negative consumption externalities, greater wealth inequality and a decline in productivity exacerbate social conflict. Status comparisons and wealth inequality tend to raise the labour share under all positive and normative criteria. Finally, we propose and analyse a criterion of ‘justice as minimal social friction’. Under the plausible assumption that the capitalists’ overall socio-political influence (numerical strength aside) is at least as high as that of workers, all positive methods imply a smaller labour share and more inequality than all our three criteria of distributive justice. We offer a numerical illustration of the key points.