Bitte verwenden Sie diesen Link, um diese Publikation zu zitieren, oder auf sie als Internetquelle zu verweisen: https://hdl.handle.net/10419/70462 
Erscheinungsjahr: 
2010
Schriftenreihe/Nr.: 
CAE Working Paper No. 10-03
Verlag: 
Cornell University, Center for Analytical Economics (CAE), Ithaca, NY
Zusammenfassung: 
An intriguing problem in stochastic growth theory is as follows: even when the return on investment is arbitrarily high near zero and discounting is arbitrarily mild, long run capital and consumption may be arbitrarily close to zero with probability one. In a convex one-sector model of optimal stochastic growth with i.i.d. shocks, we relate this phenomenon to risk aversion near zero. For a Cobb-Douglas production function with multiplicative uniformly distributed shock, the phenomenon occurs with high discounting if, and only if, risk aversion diverges to infinity sufficiently fast as consumption goes to zero. We specify utility functions for which the phenomenon occurs even when discounting is arbitrarily mild. For the general version of the model, we outline sufficient conditions under which capital and consumption are bounded away from zero almost surely, as well as conditions under which growth occurs almost surely near zero; the latter ensures a uniform positive lower bound on long run consumption (independent of initial capital). These conditions require the expected marginal productivity at zero to be above the discount rate by a factor that depends on the degree of risk aversion near zero.
Schlagwörter: 
Stochastic Growth
Sustained Consumption
Extinction
Risk Aversion
JEL: 
D9
E2
O41
Dokumentart: 
Working Paper

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