# Herbert E. Scarf

## Personal Details

This person is deceased (Date: 15 Nov 2015)First Name: | Herbert |

Middle Name: | E. |

Last Name: | Scarf |

Suffix: | |

RePEc Short-ID: | psc54 |

http://cowles.econ.yale.edu/~scarf/index.htm | |

Terminal Degree: | 1954 (from RePEc Genealogy) |

## Research output

Jump to: Working papers Articles Chapters Books### Working papers

- M.J. Todd & A. Fostel & H.E. Scarf, 2004.
"
**Two New Proofs of Afriat's Theorem**," Econometric Society 2004 North American Summer Meetings 632, Econometric Society.- A. Fostel & H. Scarf & M. Todd, 2004.
"
**Two new proofs of Afriat’s theorem**," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(1), pages 211-219, July.

- Anna Fostel & Herbert E. Scarf & Michael J. Todd, 2003.
"
**Two New Proofs of Afriat's Theorem**," Cowles Foundation Discussion Papers 1415, Cowles Foundation for Research in Economics, Yale University. - Herbert E. Scarf & Ana Fostel & Michael J. Todd, 2004.
"
**Two New Proofs of Afriat's Theorem**," Yale School of Management Working Papers ysm377, Yale School of Management.

- A. Fostel & H. Scarf & M. Todd, 2004.
"
- Herbert E. Scarf & Kevin M. Woods, 2004.
"
**Neighborhood Complexes and Generating Functions for Affine Semigroups**," Cowles Foundation Discussion Papers 1458, Cowles Foundation for Research in Economics, Yale University. - Herbert E. Scarf & Wilson, Charles A. Wilson, 2003.
"
**Uniqueness of Equilibrium in the Multi-Country Ricardo Model**," Cowles Foundation Discussion Papers 1431, Cowles Foundation for Research in Economics, Yale University. - William C. Brainard & Herbert E. Scarf, 2000.
"
**How to Compute Equilibrium Prices in 1891**," Cowles Foundation Discussion Papers 1272, Cowles Foundation for Research in Economics, Yale University. - Herbert E. Scarf, 2000.
"
**Optimal Inventory Policies When Sales Are Discretionary**," Cowles Foundation Discussion Papers 1270, Cowles Foundation for Research in Economics, Yale University.- Scarf, Herbert E., 2005.
"
**Optimal inventory policies when sales are discretionary**," International Journal of Production Economics, Elsevier, vol. 93(1), pages 111-119, January.

- Scarf, Herbert E., 2005.
"
- Imre Barany & Herbert E. Scarf, 1996.
"
**Matrices with Identical Sets of Neighbors**," Cowles Foundation Discussion Papers 1127, Cowles Foundation for Research in Economics, Yale University.- Imre Bárány & Herbert Scarf, 1998.
"
**Matrices with Identical Sets of Neighbors**," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 863-873, November.

- Imre Bárány & Herbert Scarf, 1998.
"
- Imre Barany & Herbert E. Scarf & David F. Shallcross, 1994.
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**The Topological Structure of Maximal Lattice Free Convex Bodies: The General Case**," Cowles Foundation Discussion Papers 1087, Cowles Foundation for Research in Economics, Yale University. - Herbert E. Scarf, 1994.
"
**The Allocation of Resources in the Presence of Indivisibilities**," Cowles Foundation Discussion Papers 1068, Cowles Foundation for Research in Economics, Yale University.- Herbert Scarf, 1994.
"
**The Allocation of Resources in the Presence of Indivisibilities**," Journal of Economic Perspectives, American Economic Association, vol. 8(4), pages 111-128, Fall.

- Herbert Scarf, 1994.
"
- Imre Barany & Roger Howe & Herbert E. Scarf, 1992.
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**The Complex of Maximal Lattice Free Simplices**," Cowles Foundation Discussion Papers 1032, Cowles Foundation for Research in Economics, Yale University. - Herbert E. Scarf, 1992.
"
**Tjalling Charles Koopmans (August 28, 1910-February 26, 1985)**," Cowles Foundation Discussion Papers 1029, Cowles Foundation for Research in Economics, Yale University. - William Cook & Thomas Rutherford & Herbert E. Scarf & David F. Shallcross, 1991.
"
**An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming**," Cowles Foundation Discussion Papers 990, Cowles Foundation for Research in Economics, Yale University.- William Cook & Thomas Rutherford & Herbert E. Scarf & David Shallcross, 1993.
"
**An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming**," INFORMS Journal on Computing, INFORMS, vol. 5(2), pages 206-212, May.

- William Cook & Thomas Rutherford & Herbert E. Scarf & David Shallcross, 1993.
"
- Herbert E. Scarf, 1991.
"
**Economic Equilibrium and Soviet Economic Reform**," Cowles Foundation Discussion Papers 969, Cowles Foundation for Research in Economics, Yale University. - Herbert E. Scarf & Shallcross, David F., 1991.
"
**Shortest Integer Vectors**," Cowles Foundation Discussion Papers 965, Cowles Foundation for Research in Economics, Yale University.- Herbert E. Scarf & David F. Shallcross, 1993.
"
**Shortest Integer Vectors**," Mathematics of Operations Research, INFORMS, vol. 18(3), pages 516-522, August.

- Herbert E. Scarf & David F. Shallcross, 1993.
"
- Herbert E. Scarf & Shallcross, David F., 1990.
"
**The Frobenius Problem and Maximal Lattice Free Bodies**," Cowles Foundation Discussion Papers 945, Cowles Foundation for Research in Economics, Yale University.- Herbert E. Scarf & David F. Shallcross, 1993.
"
**The Frobenius Problem and Maximal Lattice Free Bodies**," Mathematics of Operations Research, INFORMS, vol. 18(3), pages 511-515, August.

- Herbert E. Scarf & David F. Shallcross, 1993.
"
- Herbert E. Scarf & Laszlo Lovasz, 1990.
"
**The Generalized Basis Reduction Algorithm**," Cowles Foundation Discussion Papers 946, Cowles Foundation for Research in Economics, Yale University.- László Lovász & Herbert E. Scarf, 1992.
"
**The Generalized Basis Reduction Algorithm**," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 751-764, August.

- László Lovász & Herbert E. Scarf, 1992.
"
- Herbert E. Scarf, 1989.
"
**Mathematical Programming and Economic Theory**," Cowles Foundation Discussion Papers 930, Cowles Foundation for Research in Economics, Yale University.- Herbert E. Scarf, 1990.
"
**Mathematical Programming and Economic Theory**," Operations Research, INFORMS, vol. 38(3), pages 377-385, June.

- Herbert E. Scarf, 1990.
"
- Herbert E. Scarf & R. Kannan & Laszlo Lovasz, 1988.
"
**The Shapes of Polyhedra**," Cowles Foundation Discussion Papers 883, Cowles Foundation for Research in Economics, Yale University.- Ravi Kannan & Lászlo Lovász & Herbert E. Scarf, 1990.
"
**The Shapes of Polyhedra**," Mathematics of Operations Research, INFORMS, vol. 15(2), pages 364-380, May.

- Ravi Kannan & Lászlo Lovász & Herbert E. Scarf, 1990.
"
- Herbert E. Scarf, 1984.
"
**Neighborhood Systems for Production Sets with Indivisibilities**," Cowles Foundation Discussion Papers 728, Cowles Foundation for Research in Economics, Yale University.- Scarf, Herbert E, 1986.
"
**Neighborhood Systems for Production Sets with Indivisibilities**," Econometrica, Econometric Society, vol. 54(3), pages 507-532, May.

- Scarf, Herbert E, 1986.
"
- Herbert E. Scarf, 1982.
"
**Integral Polyhedra in Three Spaces**," Cowles Foundation Discussion Papers 632, Cowles Foundation for Research in Economics, Yale University.- Herbert E. Scarf, 1985.
"
**Integral Polyhedra in Three Space**," Mathematics of Operations Research, INFORMS, vol. 10(3), pages 403-438, August.

- Herbert E. Scarf, 1985.
"
- Herbert E. Scarf, 1979.
"
**Production Sets with Indivisibilities: Generalities and the Case of Two Variables**," Cowles Foundation Discussion Papers 526, Cowles Foundation for Research in Economics, Yale University. - Herbert E. Scarf, 1977.
"
**An Observation on the Structure of Production Sets with Indivisibilities**," Cowles Foundation Discussion Papers 453, Cowles Foundation for Research in Economics, Yale University. - Herbert E. Scarf, 1977.
"
**The Computation of Equilibrium Prices: An Exposition**," Cowles Foundation Discussion Papers 473, Cowles Foundation for Research in Economics, Yale University.- Scarf, Herbert E., 1993.
"
**The computation of equilibrium prices: An exposition**," Handbook of Mathematical Economics,in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 21, pages 1007-1061 Elsevier.

- Scarf, Herbert E., 1993.
"
- B. Curtis Eaves & Herbert E. Scarf, 1975.
"
**The Solution of Systems of Piecewise Linear Equations**," Cowles Foundation Discussion Papers 390, Cowles Foundation for Research in Economics, Yale University.- B. Curtis Eaves & Herbert Scarf, 1976.
"
**The Solution of Systems of Piecewise Linear Equations**," Mathematics of Operations Research, INFORMS, vol. 1(1), pages 1-27, February.

- B. Curtis Eaves & Herbert Scarf, 1976.
"
- Herbert E. Scarf, 1970.
"
**On the Existence of a Cooperative Solution for a General Class of N-Person Games**," Cowles Foundation Discussion Papers 293, Cowles Foundation for Research in Economics, Yale University.- Scarf, Herbert E., 1971.
"
**On the existence of a coopertive solution for a general class of N-person games**," Journal of Economic Theory, Elsevier, vol. 3(2), pages 169-181, June.

- Scarf, Herbert E., 1971.
"
- Herbert E. Scarf, 1969.
"
**An Example of an Algorithm for Calculating General Equilibrium**," Cowles Foundation Discussion Papers 276, Cowles Foundation for Research in Economics, Yale University. - Terje Hensen & Herbert E. Scarf, 1969.
"
**On The Applications of a Recent Combinatorial Algorithm**," Cowles Foundation Discussion Papers 272, Cowles Foundation for Research in Economics, Yale University. - 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. - Herbert E. Scarf, 1967.
"
**On the Computation of Equilibrium Prices**," Cowles Foundation Discussion Papers 232, Cowles Foundation for Research in Economics, Yale University. - Herbert E. Scarf, 1966.
"
**An Algorithm for a Class of Nonconvex Programming Problems**," Cowles Foundation Discussion Papers 211, Cowles Foundation for Research in Economics, Yale University. - Herbert E. Scarf, 1965.
"
**The Core of an N Person Game**," Cowles Foundation Discussion Papers 182R, Cowles Foundation for Research in Economics, Yale University. - Herbert E. Scarf, 1959.
"
**Some Examples of Global Instability of the Competitive Equilibrium**," Cowles Foundation Discussion Papers 79, Cowles Foundation for Research in Economics, Yale University.

### Articles

- Scarf, Herbert, 2009.
"
**My introduction to top-trading cycles**," Games and Economic Behavior, Elsevier, vol. 66(2), pages 630-631, July. - Scarf, Herbert E., 2005.
"
**Optimal inventory policies when sales are discretionary**," International Journal of Production Economics, Elsevier, vol. 93(1), pages 111-119, January.- Herbert E. Scarf, 2000.
"
**Optimal Inventory Policies When Sales Are Discretionary**," Cowles Foundation Discussion Papers 1270, Cowles Foundation for Research in Economics, Yale University.

- Herbert E. Scarf, 2000.
"
- William C. Brainard & Herbert E. Scarf, 2005.
"
**Brainard and Scarf on Equilibrium Prices**," American Journal of Economics and Sociology, Wiley Blackwell, vol. 64(1), pages 57-83, January. - A. Fostel & H. Scarf & M. Todd, 2004.
"
**Two new proofs of Afriat’s theorem**," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 24(1), pages 211-219, July.- M.J. Todd & A. Fostel & H.E. Scarf, 2004.
"
**Two New Proofs of Afriat's Theorem**," Econometric Society 2004 North American Summer Meetings 632, Econometric Society. - Anna Fostel & Herbert E. Scarf & Michael J. Todd, 2003.
"
**Two New Proofs of Afriat's Theorem**," Cowles Foundation Discussion Papers 1415, Cowles Foundation for Research in Economics, Yale University. - Herbert E. Scarf & Ana Fostel & Michael J. Todd, 2004.
"
**Two New Proofs of Afriat's Theorem**," Yale School of Management Working Papers ysm377, Yale School of Management.

- M.J. Todd & A. Fostel & H.E. Scarf, 2004.
"
- Herbert Scarf, 2004.
"
**Comments on "Optimal Policies for a Multi-Echelon Inventory Problem"**," Management Science, INFORMS, vol. 50(12_supple), pages 1791-1793, December. - Herbert E. Scarf, 2002.
"
**Inventory Theory**," Operations Research, INFORMS, vol. 50(1), pages 186-191, February. - Imre Bárány & Herbert Scarf, 1998.
"
**Matrices with Identical Sets of Neighbors**," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 863-873, November.- Imre Barany & Herbert E. Scarf, 1996.
"
**Matrices with Identical Sets of Neighbors**," Cowles Foundation Discussion Papers 1127, Cowles Foundation for Research in Economics, Yale University.

- Imre Barany & Herbert E. Scarf, 1996.
"
- Herbert Scarf, 1994.
"
**The Allocation of Resources in the Presence of Indivisibilities**," Journal of Economic Perspectives, American Economic Association, vol. 8(4), pages 111-128, Fall.- Herbert E. Scarf, 1994.
"
**The Allocation of Resources in the Presence of Indivisibilities**," Cowles Foundation Discussion Papers 1068, Cowles Foundation for Research in Economics, Yale University.

- Herbert E. Scarf, 1994.
"
- William Cook & Thomas Rutherford & Herbert E. Scarf & David Shallcross, 1993.
"
**An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming**," INFORMS Journal on Computing, INFORMS, vol. 5(2), pages 206-212, May.- William Cook & Thomas Rutherford & Herbert E. Scarf & David F. Shallcross, 1991.
"
**An Implementation of the Generalized Basis Reduction Algorithm for Integer Programming**," Cowles Foundation Discussion Papers 990, Cowles Foundation for Research in Economics, Yale University.

- William Cook & Thomas Rutherford & Herbert E. Scarf & David F. Shallcross, 1991.
"
- Herbert E. Scarf & David F. Shallcross, 1993.
"
**Shortest Integer Vectors**," Mathematics of Operations Research, INFORMS, vol. 18(3), pages 516-522, August.- Herbert E. Scarf & Shallcross, David F., 1991.
"
**Shortest Integer Vectors**," Cowles Foundation Discussion Papers 965, Cowles Foundation for Research in Economics, Yale University.

- Herbert E. Scarf & Shallcross, David F., 1991.
"
- Herbert E. Scarf & David F. Shallcross, 1993.
"
**The Frobenius Problem and Maximal Lattice Free Bodies**," Mathematics of Operations Research, INFORMS, vol. 18(3), pages 511-515, August.- Herbert E. Scarf & Shallcross, David F., 1990.
"
**The Frobenius Problem and Maximal Lattice Free Bodies**," Cowles Foundation Discussion Papers 945, Cowles Foundation for Research in Economics, Yale University.

- Herbert E. Scarf & Shallcross, David F., 1990.
"
- László Lovász & Herbert E. Scarf, 1992.
"
**The Generalized Basis Reduction Algorithm**," Mathematics of Operations Research, INFORMS, vol. 17(3), pages 751-764, August.- Herbert E. Scarf & Laszlo Lovasz, 1990.
"
**The Generalized Basis Reduction Algorithm**," Cowles Foundation Discussion Papers 946, Cowles Foundation for Research in Economics, Yale University.

- Herbert E. Scarf & Laszlo Lovasz, 1990.
"
- Ravi Kannan & Lászlo Lovász & Herbert E. Scarf, 1990.
"
**The Shapes of Polyhedra**," Mathematics of Operations Research, INFORMS, vol. 15(2), pages 364-380, May.- Herbert E. Scarf & R. Kannan & Laszlo Lovasz, 1988.
"
**The Shapes of Polyhedra**," Cowles Foundation Discussion Papers 883, Cowles Foundation for Research in Economics, Yale University.

- Herbert E. Scarf & R. Kannan & Laszlo Lovasz, 1988.
"
- Herbert E. Scarf, 1990.
"
**Mathematical Programming and Economic Theory**," Operations Research, INFORMS, vol. 38(3), pages 377-385, June.- Herbert E. Scarf, 1989.
"
**Mathematical Programming and Economic Theory**," Cowles Foundation Discussion Papers 930, Cowles Foundation for Research in Economics, Yale University.

- Herbert E. Scarf, 1989.
"
- Scarf, Herbert E, 1986.
"
**Neighborhood Systems for Production Sets with Indivisibilities**," Econometrica, Econometric Society, vol. 54(3), pages 507-532, May.- Herbert E. Scarf, 1984.
"
**Neighborhood Systems for Production Sets with Indivisibilities**," Cowles Foundation Discussion Papers 728, Cowles Foundation for Research in Economics, Yale University.

- Herbert E. Scarf, 1984.
"
- Herbert E. Scarf, 1985.
"
**Integral Polyhedra in Three Space**," Mathematics of Operations Research, INFORMS, vol. 10(3), pages 403-438, August.- Herbert E. Scarf, 1982.
"
**Integral Polyhedra in Three Spaces**," Cowles Foundation Discussion Papers 632, Cowles Foundation for Research in Economics, Yale University.

- Herbert E. Scarf, 1982.
"
- Scarf, Herbert E, 1981.
"
**Production Sets with Indivisibilities-Part II: The Case of Two Activities**," Econometrica, Econometric Society, vol. 49(2), pages 395-423, March. - Scarf, Herbert E, 1981.
"
**Production Sets with Indivisibilities-Part I: Generalities**," Econometrica, Econometric Society, vol. 49(1), pages 1-32, January. - Scarf, Herbert, 1981.
"
**Comment on: "On the Stability of Competitive Equilibrium and the Patterns of Initial Holdings: An Example"**," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 22(2), pages 469-470, June. - B. Curtis Eaves & Herbert Scarf, 1976.
"
**The Solution of Systems of Piecewise Linear Equations**," Mathematics of Operations Research, INFORMS, vol. 1(1), pages 1-27, February.- B. Curtis Eaves & Herbert E. Scarf, 1975.
"
**The Solution of Systems of Piecewise Linear Equations**," Cowles Foundation Discussion Papers 390, Cowles Foundation for Research in Economics, Yale University.

- B. Curtis Eaves & Herbert E. Scarf, 1975.
"
- Shapley, Lloyd & Scarf, Herbert, 1974.
"
**On cores and indivisibility**," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March. - Scarf, Herbert E., 1971.
"
**On the existence of a coopertive solution for a general class of N-person games**," Journal of Economic Theory, Elsevier, vol. 3(2), pages 169-181, June.- Herbert E. Scarf, 1970.
"
**On the Existence of a Cooperative Solution for a General Class of N-Person Games**," Cowles Foundation Discussion Papers 293, Cowles Foundation for Research in Economics, Yale University.

- Herbert E. Scarf, 1970.
"
- Scarf, Herbert, 1969.
"
**An Example of an Algorithm for Calculating General Equilibrium Prices**," American Economic Review, American Economic Association, vol. 59(4), pages 669-677, Part I Se. - Andrew J. Clark & Herbert Scarf, 1960.
"
**Optimal Policies for a Multi-Echelon Inventory Problem**," Management Science, INFORMS, vol. 6(4), pages 475-490, July.- Andrew J. Clark & Herbert Scarf, 2004.
"
**Optimal Policies for a Multi-Echelon Inventory Problem**," Management Science, INFORMS, vol. 50(12_supple), pages 1782-1790, December.

- Andrew J. Clark & Herbert Scarf, 2004.
"

### Chapters

- Scarf, Herbert E., 1993.
"
**The computation of equilibrium prices: An exposition**," Handbook of Mathematical Economics,in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 21, pages 1007-1061 Elsevier.- Herbert E. Scarf, 1977.
"
**The Computation of Equilibrium Prices: An Exposition**," Cowles Foundation Discussion Papers 473, Cowles Foundation for Research in Economics, Yale University.

- Herbert E. Scarf, 1977.
"

### Books

- Scarf,Herbert E. & Shoven,John B., 2008.
"
**Applied General Equilibrium Analysis**," Cambridge Books, Cambridge University Press, number 9780521070935, October.

## More information

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This author is among the top 5% authors according to these criteria:- Number of Distinct Works, Weighted by Simple Impact Factor
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### Co-authorship network on CollEc

### Featured entries

This author is featured on the following reading lists, publication compilations or Wikipedia entries:- Herbert Scarf in Wikipedia (German)

### NEP Fields

NEP is an announcement service for new working papers, with a weekly report in each of many fields. This author has had 5 papers announced in NEP. These are the fields, ordered by number of announcements, along with their dates. If the author is listed in the directory of specialists for this field, a link is also provided.- No paper was announced in a field specific NEP report

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