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How To Spend It? Capital Accumulation in a Changing World

Gosselin, Pierre and Lotz, Aïleen and Wambst, Marc (2016): How To Spend It? Capital Accumulation in a Changing World.

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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 a distinct social (relative price) and personal value (individual preference), we study the impact of these relative values’ evolution on capital accumulation, depending on economic and social parameters, such as capital mobility, productivity, and personal and social values discrepancies. We consider an arbitrary number of agents, each endowed with 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 partly disposed of to produce alternate goods, depending on the agent individual preferences and on the present goods’ social value, thus creating a dynamics in capital accumulation. A phenomenon of threshold appears in the dynamics of the agent capital stock. Below this threshold, the initial stock will quickly fade away; above, capital accumulation is possible. The threshold strongly depends on both personal and social values volatilities. When social values vary strongly, the threshold increases, and stocks depreciate faster than they are replaced. Shocks on the goods’ social values may drive stocks above or below the threshold, in turn inducing a reversal in dynamics. For a precursor, i.e. an agent whose personal values will be next period social values, a strong mobility in capital will decrease the threshold: there is a gain to innovate. When social values are an average of several sectors' values, one sector will ultimately dominate. Its values will become social values, and its stock will appreciate at the expense of other sectors.

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