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Dynamic EconomicsOptimization by the Lagrange Method$
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Gregory C. Chow

Print publication date: 1997

Print ISBN-13: 9780195101928

Published to Oxford Scholarship Online: October 2011

DOI: 10.1093/acprof:oso/9780195101928.001.0001

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Economic Growth

Economic Growth

(p.32) Chapter Three Economic Growth
Dynamic Economics


Oxford University Press

Through dynamic programming, the Bellman equation could be set up from a simple optimal growth model that is subject to a constraint function which involves variables that denote consumption, capital stock, and random shocks. From such, the value function may be identified and solved. Because the Lagrange multiplier method does not require the value function, this seems to be an easier alternative to using dynamic programming. In this chapter, we look into a multisector growth model which is subject to the constraints provided by Cobb-Douglas production functions. This chapter introduces a model which serves as a simplified version of the model used by Radner that involves the utility function and making use of the method of Lagrange multipliers. Also, because improved human capital usually entails country development, this chapter introduces a model that produces a state of no growth and a state of continued growth. Also, we look into other factors that bring about economic growth such as technological advances.

Keywords:   dynamic programming, growth model, Cobb-Douglas, utility function, Lagrange multipliers, economic growth, technological advances

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