Sustainability with endogenous discounting

We construct a dynamic competitive model with a stock of human‐made capital and several stocks of natural resources and ask under what conditions consumption will be constant if infinitesimal households with heterogeneous preferences and endowments discount their utility at an endogenous rate that depends on some macroeconomic variables. We show that for consumption to be constant, this function must be the marginal product of capital function. We demonstrate that Hartwick's rule holds in a modified form that takes account of natural growth of resource stocks.

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