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Sustainability with endogenous discounting

We construct a dynamic competitive model with a stock of man-made capital and several stocks of natural resources and ask under what conditions consumption will be constant if in…nitesimal households with heterogeneous preferences and endowments discount their utility ‡ows at an endogenous rate that depends 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 (that along the constant consumption path, resource rents must be invested in man-made capital) holds in a modi…ed form that takes account of natural growth of resource stocks.

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