# Dynamic Programming with Homogeneous Functions

@article{lvarez1998DynamicPW, title={Dynamic Programming with Homogeneous Functions}, author={Fernando {\'A}lvarez and Nancy L. Stokey}, journal={Journal of Economic Theory}, year={1998}, volume={82}, pages={167-189} }

Abstract We show that the basic existence, uniqueness, and convergence results of dynamic programming hold when the return function is homogeneous of degreeθ⩽1 and the constraints are homogeneous of degree one.Journal of Economic Literature ClassificationNumber: C61.

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## References

SHOWING 1-10 OF 15 REFERENCES

A Convex Model of Equilibrium Growth: Theory and Policy Implications

- EconomicsJournal of Political Economy
- 1990

Our aim in this paper is to exposit a convex model of equilibrium growth. The model has two features that distinguish it from most other work on the subject: first, that the model is convex on the…

Recursive methods in economic dynamics

- Economics
- 1989

I. THE RECURSIVE APPROACH 1. Introduction 2. An Overview 2.1 A Deterministic Model of Optimal Growth 2.2 A Stochastic Model of Optimal Growth 2.3 Competitive Equilibrium Growth 2.4 Conclusions and…

Long-Run Policy Analysis and Long-Run Growth

- EconomicsJournal of Political Economy
- 1991

The wide cross-country disparity in rates of economic growth is the most puzzling feature of the development process. This paper describes a class of models in which this heterogeneity in growth…

Fertility Choice In A Model Of Economic Growth

- Economics
- 1988

Altruistic parents make choices of family size along with decisions about consumption and intergenerational transfers. The authors apply this framework to a closed economy, where the determination of…

Technology adoption, learning-by-doing, and economic growth

- Economics
- 1994

Abstract We develop a model in which firms choose which technologies to adopt as well as the timing of such adoptions. In between adoptions, a firm accumulates expertise in its technology which…