How To Spend It? Capital Accumulation in a Changing World

Pierre Gosselin, Aïleen Lotz, Marc Wambst

Abstract: In a society characterized by a multitude of heterogeneous agents and a large number of possibly immaterial, i.e. cultural, educational, etc. goods, each one having distinct social (relative price) and personal value (individual preference), we study the impact of these relative prices on capital accumulation between generations, depending on internal economic and social parameters, i.e. capital mobility, productivity, personal and social values discrepancies.
We consider an arbitrary number of agents, modelled by a one-period production function and a two-period intertemporal utility. Agents live, produce and consume over one period, but optimize over two periods, so providing a stock of goods for the next generation.
In period one, the inherited stock may be disposed of to enable an alternate production of goods, depending on the agent individual preferences and on the present social value of goods. This creates a dynamics in capital accumulation that depends on the evolution of social and individual values.
A threshold phenomenon appears in the evolution of the stock of capital built by an agent and his heirs. Below a certain level, the initial stock will quickly fall to zero. Above, accumulation appears. This threshold strongly depends on the volatility of personal and social values.
If the social values vary strongly through time, the threshold increases: stocks will depreciate faster than what it takes to rebuild them. Shocks on social values of goods can drive the stock above or below the threshold, inducing in turn a reversal in dynamics. If an agent is a forerunner, i.e. his personal values will be next period social values, a strong mobility in capital will decrease his threshold: there is a gain to innovate. When social values are an average of several groups’ values, one group will ultimately dominate. Its values become society values. Its stock appreciates at the expense of others’.
Keywords: Capital theory, Capital accumulation, Investment allocation, Two-sector models, Disaggregated capital, Take-off, Threshold effect, Intergenerational models, Cambridge capital controversy.
JEL Classification: E22, O10, O30, O40.