Sustained Positive Consumption in a Model of Stochastic Growth: The Role of Risk Aversion
AbstractAn 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.
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Bibliographic InfoPaper provided by Cornell University, Center for Analytic Economics in its series Working Papers with number 10-03.
Date of creation: Jul 2010
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Other versions of this item:
- Mitra, Tapan & Roy, Santanu, 2012. "Sustained positive consumption in a model of stochastic growth: The role of risk aversion," Journal of Economic Theory, Elsevier, vol. 147(2), pages 850-880.
- D90 - Microeconomics - - Intertemporal Choice - - - General
- E20 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - General (includes Measurement and Data)
- O41 - Economic Development, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models
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