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Recursive Models of Dynamic Linear Economies$
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Lars Peter Hansen and Thomas J. Sargent

Print publication date: 2013

Print ISBN-13: 9780691042770

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691042770.001.0001

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Competitive Economies

Competitive Economies

(p.131) Chapter 7 Competitive Economies
Recursive Models of Dynamic Linear Economies

Lars Peter Hansen

Thomas J. Sargent

Princeton University Press

This chapter describes a decentralized economy. It assigns ownership and decision making to three distinct economic entities, a household and two kinds of firms. It defines a competitive equilibrium. Two fundamental theorems of welfare economics connect a competitive equilibrium to a planning problem. A price system supports the competitive equilibrium and implies interest rates and prices for derivative assets. The chapter proceeds as follows. It begins by describing the choice problem facing each of the three classes of agents in terms of a Lagrangian. Next it obtains first-order conditions for these Lagrangians. Matching these first-order conditions to the Chapter 5 first-order conditions for the planning problem accomplishes two goals. First, the two fundamental theorems of welfare economics for the economy can be verified. Second, an efficient algorithm for computing the equilibrium price system in terms of the Chapter 5 matrices associated with the multipliers for the planning problem can be described.

Keywords:   decentralized economy, competitive equilibrium, welfare economics, Lagrangian, price system

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