# 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.

- 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. - 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.

- 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.
"
**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.
"
**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.- 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.
"
**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.
"
- 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.

## More information

Research fields, statistics, top rankings, if available.### Statistics

#### Access and download statistics for all items

### Rankings

This author is among the top 5% authors according to these criteria:- Number of Distinct Works, Weighted by Simple Impact Factor
- Number of Distinct Works, Weighted by Recursive Impact Factor
- Number of Distinct Works, Weighted by Number of Authors and Simple Impact Factors
- Number of Distinct Works, Weighted by Number of Authors and Recursive Impact Factors
- Number of Citations
- Number of Citations, Weighted by Simple Impact Factor
- Number of Citations, Weighted by Recursive Impact Factor
- Number of Citations, Weighted by Number of Authors
- Number of Citations, Weighted by Number of Authors, Discounted by Citation Age
- Number of Citations, Weighted by Number of Authors and Simple Impact Factors
- Number of Citations, Weighted by Number of Authors and Recursive Impact Factors
- Number of Journal Pages, Weighted by Number of Authors and Simple Impact Factors
- Number of Journal Pages, Weighted by Number of Authors and Recursive Impact Factors
- Euclidian citation score
- Wu-Index
- Record of graduates

### 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

## Corrections

All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. For general information on how to correct material on RePEc, see these instructions.

To update listings or check citations waiting for approval, Herbert E. Scarf should log into the RePEc Author Service.

To make corrections to the bibliographic information of a particular item, find the technical contact on the abstract page of that item. There, details are also given on how to add or correct references and citations.

To link different versions of the same work, where versions have a different title, use this form. Note that if the versions have a very similar title and are in the author's profile, the links will usually be created automatically.

Please note that most corrections can take a couple of weeks to filter through the various RePEc services.