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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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A Commodity Space

A Commodity Space

Chapter:
(p.125) Chapter 6 A Commodity Space
Source:
Recursive Models of Dynamic Linear Economies
Author(s):

Lars Peter Hansen

Thomas J. Sargent

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691042770.003.0006

This chapter describes a concept of value that will be used to formulate a model in which the decisions of agents are reconciled in a competitive equilibrium. It describes a commodity space in which quantities and prices both will reside. The stochastic Lagrange multipliers of Chapter 4 are closely related to equilibrium prices and live in the same mathematical space. The planning problem studied in Chapter 4 produces an outcome in which the process for consumption {ct} is an n-dimensional stochastic process that belongs to L20. The chapter presents a heuristic justification for the representation of the value of {ct}. It proceeds by reviewing several examples of commodity spaces and valuation functions.

Keywords:   valuation, competitive equilibrium, commodity space, stochastic Lagrange multipliers, consumption

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