Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/70462 
Year of Publication: 
2010
Series/Report no.: 
CAE Working Paper No. 10-03
Publisher: 
Cornell University, Center for Analytical Economics (CAE), Ithaca, NY
Abstract: 
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.
Subjects: 
Stochastic Growth
Sustained Consumption
Extinction
Risk Aversion
JEL: 
D9
E2
O41
Document Type: 
Working Paper

Files in This Item:
File
Size
402.23 kB





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.