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A Constructive Proof of the Existence of Collateral Equilibrium for a Two-Period Exchange Economy Based on a Smooth Interior-Point Path

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  • Wei Ma

Abstract

In the real economic world, we often suffer from the default risk—the present financial crisis could serve as an evidence. The long established idea for inhibiting the default behavior is to resort to collateral, and this idea has profound effect on the market equilibrium. To study this effect, we make an investigation of the economy wherein default risk is present, assets are collateralized and households are risk-averse. We shall prove that the economy is in possession of an equilibrium. This proof is distinct from the existing one, in two respects: First it shows that equilibrium exists for the Leontief utility function, and second it is constructive. By constructive we mean that, on the basis of this proof, we can (and we shall) develop an algorithm for computing that equilibrium. The algorithm developed is of a path-following type. It starts from an economy which consists of several sub-economies, each with a complete market and a Cobb–Douglas utility function; and it terminates at the equilibrium of the economy under consideration. The algorithm is shown by simulation to be effective. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Wei Ma, 2015. "A Constructive Proof of the Existence of Collateral Equilibrium for a Two-Period Exchange Economy Based on a Smooth Interior-Point Path," Computational Economics, Springer;Society for Computational Economics, vol. 45(1), pages 1-30, January.
    • Handle: RePEc:kap:compec:v:45:y:2015:i:1:p:1-30
    DOI: 10.1007/s10614-013-9404-9
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    1. Piero Gottardi & Felix Kubler, 2015. "Dynamic Competitive Economies with Complete Markets and Collateral Constraints," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(3), pages 1119-1153.
    2. Magill, Michael & Quinzii, Martine, 1994. "Infinite Horizon Incomplete Markets," Econometrica, Econometric Society, vol. 62(4), pages 853-880, July.
    3. Brown, Donald J & DeMarzo, Peter M & Eaves, B Curtis, 1996. "Computing Equilibria When Asset Markets Are Incomplete," Econometrica, Econometric Society, vol. 64(1), pages 1-27, January.
    4. Zame, William R, 1993. "Efficiency and the Role of Default When Security Markets Are Incomplete," American Economic Review, American Economic Association, vol. 83(5), pages 1142-1164, December.
    5. Douglas W. Diamond, 1984. "Financial Intermediation and Delegated Monitoring," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 51(3), pages 393-414.
    6. Smale, Steve, 1976. "A convergent process of price adjustment and global newton methods," Journal of Mathematical Economics, Elsevier, vol. 3(2), pages 107-120, July.
    7. Hart, Oliver D., 1975. "On the optimality of equilibrium when the market structure is incomplete," Journal of Economic Theory, Elsevier, vol. 11(3), pages 418-443, December.
    8. Duffie, Darrell & Shafer, Wayne, 1985. "Equilibrium in incomplete markets: I : A basic model of generic existence," Journal of Mathematical Economics, Elsevier, vol. 14(3), pages 285-300, June.
    9. Radner, Roy, 1972. "Existence of Equilibrium of Plans, Prices, and Price Expectations in a Sequence of Markets," Econometrica, Econometric Society, vol. 40(2), pages 289-303, March.
    10. Townsend, Robert M., 1979. "Optimal contracts and competitive markets with costly state verification," Journal of Economic Theory, Elsevier, vol. 21(2), pages 265-293, October.
    11. Douglas Gale & Martin Hellwig, 1985. "Incentive-Compatible Debt Contracts: The One-Period Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(4), pages 647-663.
    12. Pradeep Dubey & John Geanakoplos & Martin Shubik, 2005. "Default and Punishment in General Equilibrium," Econometrica, Econometric Society, vol. 73(1), pages 1-37, January.
    13. Aloisio Araujo & Mário Rui Páscoa & Juan Pablo Torres-Martínez, 2002. "Collateral Avoids Ponzi Schemes in Incomplete Markets," Econometrica, Econometric Society, vol. 70(4), pages 1613-1638, July.
    14. Araújo, Aloísio & Kubler, Felix & Schommer, Susan, 2012. "Regulating collateral-requirements when markets are incomplete," Journal of Economic Theory, Elsevier, vol. 147(2), pages 450-476.
    15. Herbert E. Scarf, 1967. "The Approximation of Fixed Points of a Continuous Mapping," Cowles Foundation Discussion Papers 216R, Cowles Foundation for Research in Economics, Yale University.
    16. Joseph E. Stiglitz, 1982. "The Inefficiency of the Stock Market Equilibrium," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(2), pages 241-261.
    17. Eaves, B. Curtis & Schmedders, Karl, 1999. "General equilibrium models and homotopy methods," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1249-1279, September.
    18. Sabarwal Tarun, 2003. "Competitive Equilibria With Incomplete Markets and Endogenous Bankruptcy," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-42, January.
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    1. Wei Ma, 2017. "A Rejoinder to Notes on a ‘Constructive Proof of the Existence of a Collateral Equilibrium’," Computational Economics, Springer;Society for Computational Economics, vol. 49(1), pages 175-176, January.
    2. Venkatachalam Ragupathy & K. Vela Velupillai, 2016. "Notes on a ‘Constructive Proof of the Existence of a Collateral Equilibrium’," Computational Economics, Springer;Society for Computational Economics, vol. 48(1), pages 179-181, June.

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