Lagrange Multiplier Problems in Economics

Baxley, John V.; Moorhouse, John C.

doi:10.2307/2322987

Cited by 19 publications

(24 citation statements)

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“…Here, by direct comparison to the method of Lagrange multipliers, our approach leads to general expressions for the Lagrange multipliers themselves. Given the often found connection between the Lagrange multipliers and physical quantities, these new expressions may yield some different and useful insights into various constrained problems of interest [16].…”

Section: Discussionmentioning

confidence: 99%

Avoiding the Use of Lagrange Multipliers: I—Evaluating the Constrained Extrema of Functions with Projection Matrices

Corti

Fariello

2021

Oper. Res. Forum

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Section: Discussionmentioning

confidence: 99%

Avoiding the Use of Lagrange Multipliers: I—Evaluating the Constrained Extrema of Functions with Projection Matrices

Corti

Fariello

2021

Oper. Res. Forum

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“…The savings side of U it can be described log-linearly where λ i (Equation 3) is introduced to convert the monetary savings into utility. In an economic sense, the Lagrangian multiplier λ i can be interpreted as the marginal effect of the monetary constraint on the overall utility of the customer or the rate of change in U it relative to the monetary constraint (Baxley and Moorhouse 1984). It helps us transform the constrained optimization problem into an unconstrained optimization problem by providing a link between the constraint (y it ) and the overall utility (U it ).…”

Section: Methodsmentioning

confidence: 99%

Measuring the Lifetime Value of a Customer in the Consumer Packaged Goods Industry

Sunder

Kumar

Zhao

2016

Journal of Marketing Research

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In this study, the authors propose a flexible framework to assess customer lifetime value (CLV) in the consumer packaged goods (CPG) context. They address the substantive and modeling challenges that arise in this setting, namely, (1) multiple discreteness, (2) brand switching, and (3) budget-constrained consumption. Using a Bayesian estimation, the authors are also able to infer the consumer's latent budgetary constraint using only transaction information, thus enabling managers to understand the customer's budgetary constraint without having to survey or depend on aggregate measures of budget constraints. Using the proposed framework, CPG manufacturers can assess CLV at the focal brand level as well as at the category level, a departure from CLV literature, which has mostly been firm centric. The authors implement the proposed model on panel data in the carbonated beverages category and showcase the benefits of the proposed model over simpler heuristics and conventional CLV approaches. Finally, they conduct two policy simulations describing the role of the budget constraint on CLV, as well as the asymmetric effects of pricing in this setting, and develop managerial insights in this context.

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“…Such a description must be the cornerstone of an optimal 13 Dutton (2010), p. 197 at 219; Kontorovich (2010), pp. 15 Baxley and Moorhouse (1984), pp. 14 Becker (1968), at 209.…”

Section: Methodology and Limitationsmentioning

confidence: 99%