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Matching and Saving in Continuous Time: Theory

  • Christian Bayer


    (Institute of Mathematics, Technische Universität Berlin, Germany)

  • Klaus Wälde

    (Chair in Macroeconomics, Johannes Gutenberg-Universität Mainz, Germany)

We analyse optimal saving of risk-averse households when labour income stochastically jumps between two states. The generalized Keynes-Ramsey rule includes a precautionary savings term. A phase diagram analysis il- lustrates consumption and wealth dynamics within and between states. There is an endogenous lower and upper limit for wealth. We derive the Fokker-Planck equations for the densities of individual wealth and em- ployment status. These equations also characterize the aggregate distrib- ution of wealth and allow us to describe general equilibrium. An optimal consumption path exists and distributions converge to a unique limiting distribution.

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Paper provided by Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz in its series Working Papers with number 1004.

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Length: 28 pages
Date of creation: 13 Jan 2010
Date of revision: 13 Jan 2010
Handle: RePEc:jgu:wpaper:1004
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