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Global Reach | Baker Library | Bloomberg Center | Harvard Business School

Skip to Main Content Exhibition Home Exhibition Business Education & The Case Method The General Shoe Company, 1921 Case Writing & Industry Expansion of the Case Method The Case View Details
  • January 1971 (Revised November 1975)
  • Background Note

Linear Programming: A Technique for Analyzing Resource Allocation Problems

By: Paul W. Marshall
Keywords: Problems and Challenges; Mathematical Methods; Management Analysis, Tools, and Techniques
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Marshall, Paul W. "Linear Programming: A Technique for Analyzing Resource Allocation Problems." Harvard Business School Background Note 171-322, January 1971. (Revised November 1975.)
  • 2020
  • Working Paper

Contract Duration and the Costs of Market Transactions

By: Alexander MacKay
The optimal duration of a supply contract balances the costs of reselecting a supplier against the costs of being matched to an inefficient supplier when the contract lasts too long. I develop a structural model of contract duration that captures this tradeoff and... View Details
Keywords: Vertical Relationships; Transaction Costs; Contract Duration; Identification; Supply Chain; Cost; Contracts; Auctions; Mathematical Methods
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MacKay, Alexander. "Contract Duration and the Costs of Market Transactions." Harvard Business School Working Paper, No. 18-058, December 2017. (Revised May 2020. Direct download.)
  • 1977
  • Chapter

A Diagnostic Model for Organizational Behavior

By: D. Nadler and M. Tushman
Keywords: Mathematical Methods; Organizational Design; Organizational Structure; Behavior
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Nadler, D., and M. Tushman. "A Diagnostic Model for Organizational Behavior." In Perspectives on Behavior in Organizations, edited by Richard J. Hackman, Edward E. Lawler, Lyman W. Porter, and Patricia S. Nave. New York: McGraw-Hill, 1977.
  • Article

Formal Measures in Informal Management: Can a Balanced Scorecard Change a Culture?

By: Robert Gibbons and Robert S. Kaplan
Agency theorists, historically, have analyzed what kinds of performance measures should be used in formal incentive contracts. For example, after Kaplan-Norton proposed a balanced scorecard of both financial and non-financial measures, some envisioned its role only in... View Details
Keywords: Relational Contracts; Performance Measurement; Informal Management; Balanced Scorecard; Economics; Mathematical Methods
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Gibbons, Robert, and Robert S. Kaplan. "Formal Measures in Informal Management: Can a Balanced Scorecard Change a Culture?" American Economic Review: Papers and Proceedings 105, no. 5 (May 2015).
  • 2007
  • Working Paper

Deferred Acceptance Algorithms: History, Theory, Practice, and Open Questions

By: Alvin E. Roth
The deferred acceptance algorithm proposed by Gale and Shapley (1962) has had a profound influence on market design, both directly, by being adapted into practical matching mechanisms, and, indirectly, by raising new theoretical questions. Deferred acceptance... View Details
Keywords: Education; Marketplace Matching; Market Design; Mathematical Methods; Theory; Practice
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Roth, Alvin E. "Deferred Acceptance Algorithms: History, Theory, Practice, and Open Questions." NBER Working Paper Series, No. 13225, July 2007.
  • November 2009
  • Journal Article

A Theory of Growth and Volatility at the Aggregate and Firm Level

By: Diego A. Comin and Sunil Mulani
This paper presents an endogenous growth model that explains the evolution of the first and second moments of productivity growth at the aggregate and firm level during the post-war period. Growth is driven by the development of both (i) idiosyncratic R&D innovations... View Details
Keywords: Volatility; Microeconomics; Innovation and Invention; Growth and Development Strategy; Resource Allocation; Performance Productivity; Mathematical Methods; Research and Development
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Comin, Diego A., and Sunil Mulani. "A Theory of Growth and Volatility at the Aggregate and Firm Level." Journal of Monetary Economics 56, no. 8 (November 2009): 1023–1042.
  • January 2006
  • Tutorial

Cost-Volume Profit Models

By: David F. Hawkins, V.G. Narayanan, Jacob Cohen and Michele Jurgens
Covers fixed, variable, and semivariable costs and their role in building and interpreting cost-volume-profit models. Introduces the cost-volume and contribution-volume-profit models and identifies some of their uses and limitations. Teaches how to use the... View Details
Keywords: Volume; Cost; Profit; Mathematical Methods
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"Cost-Volume Profit Models." Harvard Business School Tutorial 105-705, January 2006.
  • 2007
  • Working Paper

Mental Accounting and Small Windfalls: Evidence from an Online Grocer

By: Katherine L. Milkman, John Beshears, Todd Rogers and Max H. Bazerman
We study the effect of small windfalls on consumer spending decisions by examining the purchasing behavior of a sample of online grocery shoppers over the course of a year. We compare the purchases customers make when redeeming a $10-off coupon they received from their... View Details
Keywords: Spending; Consumer Behavior; Mathematical Methods; Food and Beverage Industry; Retail Industry
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Milkman, Katherine L., John Beshears, Todd Rogers, and Max H. Bazerman. "Mental Accounting and Small Windfalls: Evidence from an Online Grocer." Harvard Business School Working Paper, No. 08-024, September 2007. (Revised March 2008.)
  • July–August 2023
  • Article

Demand Learning and Pricing for Varying Assortments

By: Kris Ferreira and Emily Mower
Problem Definition: We consider the problem of demand learning and pricing for retailers who offer assortments of substitutable products that change frequently, e.g., due to limited inventory, perishable or time-sensitive products, or the retailer’s desire to... View Details
Keywords: Experiments; Pricing And Revenue Management; Retailing; Demand Estimation; Pricing Algorithm; Marketing; Price; Demand and Consumers; Mathematical Methods
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Ferreira, Kris, and Emily Mower. "Demand Learning and Pricing for Varying Assortments." Manufacturing & Service Operations Management 25, no. 4 (July–August 2023): 1227–1244. (Finalist, Practice-Based Research Competition, MSOM (2021) and Finalist, Revenue Management & Pricing Section Practice Award, INFORMS (2019).)
  • July 1990
  • Background Note

Perceptual Mapping: A Manager's Guide

By: Robert J. Dolan
Describes the perceptual mapping technique in a non-technical fashion. The procedure is useful for the depiction of the structure of the market. Discusses alternative methods, presents examples of each, and shows how the maps can be used in marketing decision making. View Details
Keywords: Mathematical Methods; Industry Structures; Marketing
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Dolan, Robert J. "Perceptual Mapping: A Manager's Guide." Harvard Business School Background Note 590-121, July 1990.
  • 1999
  • Other Unpublished Work

Estimating Industry Multiples

By: Malcolm Baker and R. S. Ruback
We analyze industry multiples for the S&P 500 in 1995. We use Gibbs sampling to estimate simultaneously the error specification and small sample minimum variance multiples for 22 industries. In addition, we consider the performance of four common multiples: the simple... View Details
Keywords: Management Analysis, Tools, and Techniques; Performance; Mathematical Methods
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Baker, Malcolm, and R. S. Ruback. "Estimating Industry Multiples." 1999.
  • 2023
  • Working Paper

How People Use Statistics

By: Pedro Bordalo, John J. Conlon, Nicola Gennaioli, Spencer Yongwook Kwon and Andrei Shleifer
We document two new facts about the distributions of answers in famous statistical problems: they are i) multi-modal and ii) unstable with respect to irrelevant changes in the problem. We offer a model in which, when solving a problem, people represent each hypothesis... View Details
Keywords: Decision Choices and Conditions; Microeconomics; Mathematical Methods; Behavioral Finance
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Bordalo, Pedro, John J. Conlon, Nicola Gennaioli, Spencer Yongwook Kwon, and Andrei Shleifer. "How People Use Statistics." NBER Working Paper Series, No. 31631, August 2023.
  • May 2020
  • Article

Identifying Sources of Inefficiency in Health Care

By: Amitabh Chandra and Douglas O. Staiger
In medicine, the reasons for variation in treatment rates across hospitals serving similar patients are not well understood. Some interpret this variation as unwarranted and push standardization of care as a way of reducing allocative inefficiency. However, an... View Details
Keywords: Health Care and Treatment; Performance Efficiency; Performance Productivity; Mathematical Methods
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Chandra, Amitabh, and Douglas O. Staiger. "Identifying Sources of Inefficiency in Health Care." Quarterly Journal of Economics 135, no. 2 (May 2020): 785–843.
  • 2019
  • Article

Ridesharing with Driver Location Preferences

By: Duncan Rheingans-Yoo, Scott Duke Kominers, Hongyao Ma and David C. Parkes
We study revenue-optimal pricing and driver compensation in ridesharing platforms when drivers have heterogeneous preferences over locations. If a platform ignores drivers' location preferences, it may make inefficient trip dispatches; moreover, drivers may strategize... View Details
Keywords: Ridesharing; Pricing; Compensation and Benefits; Geographic Location; Market Design; Mathematical Methods
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Rheingans-Yoo, Duncan, Scott Duke Kominers, Hongyao Ma, and David C. Parkes. "Ridesharing with Driver Location Preferences." Proceedings of the International Joint Conference on Artificial Intelligence (2019): 557–564.
  • 14 Jun 2017
  • Working Paper Summaries

Minimizing Justified Envy in School Choice: The Design of New Orleans' OneApp

Keywords: by Atila Abdulkadiroglu, Yeon-Koo Che, Parag A. Pathak, Alvin E. Roth, and Oliver Tercieux; Education
  • 1995
  • Chapter

Regression to the Mean, Expectation Inflation, and the Winner's Curse in Organizational Contexts

By: J. R. Harrison and M. H. Bazerman
Keywords: Mathematical Methods; Conflict and Resolution; Competition; Organizational Structure
Citation
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Harrison, J. R., and M. H. Bazerman. "Regression to the Mean, Expectation Inflation, and the Winner's Curse in Organizational Contexts." In The Social Context of Negotiation. edited by R. Kramer and D. M. Messick. Thousand Oaks, CA: Sage Publications, 1995.
  • January 2009 (Revised June 2010)
  • Teaching Note

Lyons Document Storage Corporation: Bond Math (Brief Case)

By: William J. Bruns Jr.
Teaching Note to 3215 View Details
Keywords: Financial Accounting; Quantitative Analysis; Securities; Debt Securities; Cash Flow; Mathematical Methods; Accounting
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Bruns, William J., Jr. "Lyons Document Storage Corporation: Bond Math (Brief Case)." Harvard Business School Teaching Note 093-216, January 2009. (Revised June 2010.)
  • 2008
  • Working Paper

CPC/CPA Hybrid Bidding in a Second Price Auction

By: Benjamin Edelman and Hoan Lee
We develop a model of online advertising in which each advertiser chooses from multiple advertising measurement metrics—paying either for each click on its ads (CPC), or for each purchase that follows an ad-click (CPA). Our analysis extends classic auction results by... View Details
Keywords: Online Advertising; Auctions; Bids and Bidding; Measurement and Metrics; Quality; Mathematical Methods; Web Sites
Citation
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Edelman, Benjamin, and Hoan Lee. "CPC/CPA Hybrid Bidding in a Second Price Auction." Harvard Business School Working Paper, No. 09-074, December 2008.
  • Working Paper

The Long-Run Dynamics of Electricity Demand: Evidence from Municipal Aggregation

By: Tatyana Deryugina, Alexander MacKay and Julian Reif
Economic theory suggests that demand is more elastic in the long run relative to the short run, but evidence on the empirical relevance of this phenomenon is scarce. We study the dynamics of residential electricity demand by exploiting price variation arising from a... View Details
Keywords: Energy; Demand and Consumers; Price; Policy; Mathematical Methods
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Deryugina, Tatyana, Alexander MacKay, and Julian Reif. "The Long-Run Dynamics of Electricity Demand: Evidence from Municipal Aggregation." NBER Working Paper Series, No. 23483, October 2017.
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