Optimal control of trade discount in a vertical distribution channel
|
|
- Susanna Lyons
- 6 years ago
- Views:
Transcription
1 Optimal control of trade discount in a vertical distribution channel Igor Bykadorov 1, Andrea Ellero 2, and Elena Moretti 2 1 Sobolev Institute of Mathematics Siberian Branch Russian Academy of Science Acad. Koptyug prospect 4, Novosibirsk , Russia bykad@math.nsc.ru 2 Dipartimento di Matematica Applicata Università Ca Foscari di Venezia Dorsoduro 3825/E, Venezia, Italy {ellero, emoretti}@unive.it Abstract. We consider a vertical control distribution channel in which a manufacturer sells a single kind of good to a retailer. We assume that wholesale price discount increases the retailer s sale motivation thus improving sales. We first analyze the manufacturer s profit maximization problem as an optimal control model in which the manufacturer s control is the discount on wholesale price (trade discount). We then embed the model in a Stackelberg game environment considering that manufacturer and retailer can both be leader of the channel, depending on the particular market structure. Keywords. Optimal control, sales motivation, vertical channel, trade discount. M.S.C. classification: 49N90. J.E.L. classification: C61, C73. 1 Introduction The aim of the paper is to investigate the relationships between the members of a distribution channel by means of optimal control models, the solution of which provide qualitative information on the channel members behaviors. We will consider a stylized vertical distribution channel: a manufacturer serves a single segment market through a single retailer. We investigate the incentive mechanism that can be used to drive channel members behaviors and consequently sales. Among the wide variety of marketing tools at disposal to manufacturers and retailers we will concentrate on simple contracts between suppliers and retailers based on trade discounts. A wholesale price discount is a promotional effort that has a double positive effect on sales: the first, on the market, is due to the fact This research has been supported by Università Ca Foscari di Venezia, CNR-NATO Senior Fellowships Programme 2003(no S), the Russian Federation for Basic Research (grant no ) and the Council for Grants (under RF President) and State Aid of Fundamental Science Schools (grant no. NSh ).
2 122 that a part of the wholesale price discount can be transferred to the final selling price (pass through). The second effect is on the retailer who becomes more motivated and then stimulated to work harder [6],[7]. We assume that an high price discount increases motivation and high motivation of retailer implies an higher effort in selling the product. The idea is that if the motivated retailer s performance is good in selling the product, the manufacturer s performance will be good as well. In Section 2 we propose an optimal control model in which the performance of the retailer is explicitly considered as a function of retailer s skill and motivation levels, taking also into account retailer s skill and other market parameters like consumer and retailer expectations. Optimal control models related to marketing problems have been widely studied in literature (see e.g. [4], [5]) also by the authors [1], [2]. A second way to analyze the relationship between manufacturer and retailer is the highlighting of their intrinsic conflict. In fact, their goals are different since each of the two firms aims at maximizing its own profit. In Section 3 we model the distribution channel as two different Stackelberg-games in which either the manufacturer or the retailer is the leader. In particular, in real distribution channels the retailer can become the leader when we consider large-scale retail stores. 2 The optimal control model We consider a manufacturer that sells a single kind of good during a time interval [, t 2 ]. The manufacturer acts as a monopolist in a vertical channel selling to the only downstream firm, the retailer, and, to improve sales, can produce a promotional effort by means of a wholesale price discount; moreover, the retailer transfers a part of the discount to the consumer. The aim of the manufacturer is to maximize the total profit in the given time period. The problem is formulated as an optimal control problem in which the state variables are the total sales and the retailer s motivation. The manufacturer s control is the discount on wholesale price. Define x(t) = total sales during time period [, t], p w (t) = wholesale price at time t, c 0 = unit production cost, α(t) = trade discount at time t, α(t) [α 1, α 2 ] [0, 1]. This way p w (t) = p(1 α(t)), where p is the wholesale price when no trade discount is applied. Remark that ẋ(t) represents the sales at time t and coincides with the consumer s demand at time t. This means that we assume that the firm sells exactly the produced quantity. The total profit of the manufacturer is (p w (t) c 0 )ẋ(t)dt,
3 123 i.e., assuming x( ) = 0, (p c 0 )x(t 2 ) p ẋ(t)α(t)dt. We assume that retailer s sales motivation at time t is increasing with respect to both consumer s demand and trade discount. More precisely the retailer s motivation is summarized by the state variable M(t) whose dynamics is given by where Ṁ(t) = γẋ(t) + ɛ(α(t) α), γ = sales productivity in terms of retailer s sales motivation, γ > 0, ɛ = price discount productivity in terms of retailer motivation, ɛ > 0, α = trade discount expected by the retailer, α (α 1, α 2 ). The parameter α takes into account the fact that the retailer has some expectations on the trade discount applied by the manufacturer, his motivation decreases if his expectations are disappointed, i.e. if α(t) < α, while he is happy if α(t) α. The dynamics of the total amount of sales at time t is defined by where ẋ(t) = θx(t) + δm(t) + ηβα(t), δ = retailer motivation productivity in terms of sales, δ > 0, η = price discount productivity in terms of sales, η > 0, β = part of wholesale price discount transferred to the consumer and θ > 0 is a saturation aversion parameter: in fact this way the sales rate decreases as the sales increase, modeling the market saturation effect. We assume β (0, 1), which means that we do not allow the retailer to retain the total discount and that in any case he will keep a part of it. This way the following optimal control problem can be formulated P : maximize subject to (p c 0 )x(t 2 ) p ẋ(t)α(t) dt, ẋ(t) = θx(t) + δm(t) + ηα(t), Ṁ(t) = γẋ(t) + ɛ(α(t) α), x( ) = 0, M( ) = M, α(t) [α 1, α 2 ] [0, 1], where M is the initial motivation of the retailer (we assume M > 0) and η = ηβ.
4 Solution of the optimal control problem Let us observe that problem P is linear with respect to the state variables and is quadratic with respect to control. We will assume that the product sold in the market is such that if α(t) is constant t [, t 2 ], i.e. the wholesale price is constant during the sale period, then the total sales function, x(t), is concave. This leads to the following conditions (see [3]): where a > 0, aδm + bα 2 + δɛα 0, (1) a = θ γδ, b = aη δɛ. (2) Obviously, profit must be nonnegative α(t) [α 1, α 2 ]. In particular, we require that the maximum allowed discount is such that the corresponding profit is equal to zero. At this aim we will set (see [3]) α 2 = p c 0 p. (3) Another requirement is that demand ẋ(t) must always be nonnegative. As it is shown in [3] it is sufficient that { b 0 aδm + aηα1 e a(t 2 ) + (bα 2 + δɛα)(1 e a(t 2 ) ) 0, b < 0 aδm + aηα 1 + δɛ(α α 1 )(1 e a(t 2 ) ) 0. (4) Therefore we will assume that the parameters of the model satisfy (4). Pontryagin Maximum Principle [8] allows to obtain the optimal control α (t) of problem P [3]: Proposition 21 1) Let b 0, i.e. δ θη ηγ+ɛ. Then τ [, t 2 ] such that { α α1, t [t (t) = 1, τ), D 1 e λt + D 2 e λt + α+α 2 2, t [τ, t 2 ], where D 1 and D 2 are constants and λ = increases on [τ, t 2 ]. 2) Let b < 0, i.e. δ θη (5) aδɛ η. Moreover function α (t) strictly ηγ+ɛ. Then τ 1 and τ 2 such that τ 1 τ 2 t 2 and α 1, t [, τ 1 ), α (t) = D 1 e λt + D 2 e λt + α+α 2 2, t [τ 1, τ 2 ], (6) α 1, t (τ 2, t 2 ], where D 1 and D 2 are constants. Moreover function α (t) is strictly concave on [τ 1, τ 2 ] and α (τ 1 ) α (τ 2 ) (7)
5 125 holds. Constants D 1, D 2 and the time of control s type changing (i.e τ if b 0 and τ 1, τ 2 if b < 0) can be found imposing continuity of the optimal control and the optimal trajectory (see [3]). Optimal sales level x (t) and optimal retailer motivation M (t) can then be calculated by substituting α (t) in the motion equations of Problem P. Observe that Proposition 2.1 states that the kind of optimal control depends on the value of δ. Parameter δ, retailer motivation productivity in terms of sales, describes retailer s selling skill, therefore the above proposition states that the kind of optimal control depends from the efficiency of the retailer. In particular with an inefficient retailer it is convenient to increase the discount during the selling period while with an efficient retailer it may be not convenient to increase the discount on wholesale price: in the latter case the manufacturer can improve profit reducing trade discount, the retailer is rather good and will sell a lot in any case. We provide now two examples which show the two possible optimal discount policies depending on the values of parameter δ as described in Proposition 21. In the first example we have increasing optimal trade discount during the sale period while in the second one the particular case in which the optimal discount is non-monotone is represented. Example 1. Let us consider problem P in the time period starting at = 0 and ending at t 2 = 2, with following values of the parameters: p = 2.9, c 0 = 0.8, β = , γ = 0.7 (1 β) = , ɛ = 0.6 (1 β) = , α = 0.25, α 1 = 0.2, α 2 = p c0 p , δ = 0.8, η = 0.8, θ = 10, M = 5. We have Case 1 of Proposition 21 and we obtain τ The optimal control of P is increasing in [, t 2 ] (see Figure 1). Example 2. Let us consider problem P with the same values of the parameters as in Example 1 except for: t 2 = 4, β = 0.15, γ = 0.7 (1 β) = 0.595, ɛ = 0.6 (1 β) = 0.51, θ = 1, M = 0.5. Now we have Case 2 of Proposition 21 and we can compute τ , τ The dynamics of optimal control is reported in Figure 2. 3 Stackelberg-game approach A different point of view on the channel marketing activity can be obtained considering the manufacturer and the retailer as the two players of a Stackelberg game, assuming that each of them, in turn, takes the role of the leader. In this framework we will consider two controls: trade discount α(t), which is the manufacturer s control, and pass-through β(t), which is the retailer s control.
6 126 Fig. 1. Example 1: optimal discount policy. Fig. 2. Example 2: optimal discount policy.
7 127 The total profit of the manufacturer is, as in the optimal control problem P, (p c 0 )x(t 2 ) p ẋ(t)α(t)dt, while the total profit of the retailer can be written as follows p ẋ(t)α(t)(1 β(t))dt. We will consider two cases, in the first one the manufacturer is the leader of the channel and trade promotion has to be fixed at constant value α(t) = α, in the second one the retailer is the leader and his control has to be fixed at a constant value β(t) = β. 3.1 The manufacturer is leader Consider the manufacturer as the channel leader: we assume in this case that the manufacturer can only choose a constant trade discount during the whole sales period. This way we formulate the following open-loop Stackelberg game: ML : maximize (p c 0 )x(t 2 ) pα ẋ(t) dt = x(t 2 )((p c 0 ) pα) where, for each fixed α, functions x(t), M(t) and β(t) are optimal solution of maximize subject to pα ẋ(t)(1 β(t)) dt, ẋ(t) = θx(t) + δm(t) + ηαβ(t), Ṁ(t) = γẋ(t) + ɛ(α α), x( ) = 0, M( ) = M, β(t) [0, 1]. 3.2 The retailer is leader Consider the retailer as the channel leader: we assume in this case that the retailer can only choose a constant pass-through during the whole sales period. This way a new Stackelberg game can be formulated as follows: RL : maximize (1 β)p ẋ(t)α(t) dt where, for each fixed β, functions x(t), M(t) and α(t) are optimal solution of maximize subject to (p c 0 )x(t 2 ) p ẋ(t)α(t) dt, ẋ(t) = θx(t) + δm(t) + ηβα(t), Ṁ(t) = γẋ(t) + ɛ(α(t) α), x( ) = 0, M( ) = M, α(t) [α 1, α 2 ].
8 128 Remark that the follower problem coincides with problem P of Section The particular case in which both controls are constant We consider now the particular case in which both controls must be constant during the whole period [, t 2 ]. In this case the solution of problems ML and RL becomes straightforward and allows to obtain some preliminary considerations on the models outcomes. In particular for what concerns problem M L, in which the manufacturer is the leader, the optimal trade discount and pass-through can be easily computed by integration of the motion equations and by substituting into the two functionals the expression of the optimal total sales trajectory x (t). If the optimal trade discount is an interior point of the interval [α 1, α 2 ] then the profit of the manufacturer is given by x (t 2 )((p c 0 ) pα ) where α = p c 0 2p K 2(H + L) (8) with H = η [ 1 e a(t2 t1)] > 0 a L = δɛ [ 1 a a 1 ] a e a(t2 t1) (t 2 ) > 0 K = δ [ M(e a(t 2 ) 1) + ɛα( 1 a a + 1 ] a e a(t 2 ) + (t 2 )). The optimal value of the total sales, x (t 2 ), depends explicitly from α. More precisely where the optimal pass-through β is x (t 2 ) = Hα β + Lα + K β = Hα Lα K 2Hα. (9) We can observe that in the above formulas the parameter η, which describes the reaction of the market to price discounts, affects only the value of H. The parameters α and M, instead, which describe threshold levels for motivation and trade discount expectations and are therefore characteristic attributes of the retailer, affect only K. This enables sensitivity analysis with respect to different properties of the market actors. For example it is easy to obtain from (8) that a trade discount higher than α 2 /2 = (p c 0 )/(2p) can only be obtained if K is
9 129 negative. This means for example that α, i.e. the expected trade discount, must be sufficiently high. Moreover the sign of K is crucial in determining the relation between α and β (see (9)). The optimal reaction of the retailer to increasing values of the optimal trade discount can increase or decrease depending on the sign of K. Similar computations allow to provide analogous results can be obtained also if we consider constant controls in problem RL where the retailer is leader. 4 Concluding remarks In this paper we explore the bilevel programming approach to the optimal control of trade discounts. In section 3 we have formalized the particular situation in which one of the controls is constant and in section 3.3 we present some results related to a preliminary study of the case in which both controls are constant. A deeper insight into the problem could be obtained by means of sensitivity analysis of the profit of retailer and manufacturer. Another subject of future research could be to allow piecewise constant controls both for the leader and/or for the follower. References 1. Bykadorov, I., Ellero, A. and Moretti, E.: Minimization of communication expenditure for seasonal products. RAIRO Operations Research 36 (2002) Bykadorov, I., Ellero, A. and Moretti, E.: A model for the marketing of a seasonal product with different goodwills for consumer and retailer. Journal of Statistics & Management Systems 6 (2003) Bykadorov, I., Ellero, A. and Moretti, E.: Optimal control of retailer s motivation by trade discounts. Report n.119/2004, Dipartimento di Matematica Applicata, Università di Venezia (2004). 4. Feichtinger, G., Hartl, R. F. and Sethi, S. P.: Dynamic optimal control models in advertising: recent developments. Management Science 40 (1994) Jørgensen, S., Zaccour, G.: Differential games in marketing. Kluwer Ac. Pub., London (2004). 6. Lawler E. E.: Motivation in work organizations. Brooks/Cole, Monterey - Cal (1973). 7. Mitchell T. R.: Motivation: new directions for theory, research and practice. Academy of management review 7 (1982) Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V. and Mishchenko, E.F.: The mathematical theory of optimal processes. Pergamon Press, London (1965).
10 130
Retail Competition and Cooperative Advertising
Retail Competition and Cooperative Advertising Xiuli He Anand Krishnamoorthy Ashutosh Prasad Suresh P. Sethi Belk College of Business, University of North Carolina, Charlotte, NC 813, xhe8@uncc.edu University
More informationThe Role of Price Floor in a Differentiated Product Retail Market 1
The Role of Price Floor in a Differentiated Product Retail Market 1 Barna Bakó 2 Corvinus University of Budapest Hungary 1 I would like to thank the anonymous referee for the valuable comments and suggestions,
More informationLinear models and advertising
Linear models and advertising Alessandra Buratto, Luca Grosset, and Bruno Viscolani Dipartimento di Matematica Pura ed Applicata Via Belzoni 7, I - 35131 Padova, Italy {buratto, grosset, viscolani}@math.unipd.it
More informationPrice competition in a differentiated products duopoly under network effects
Price competition in a differentiated products duopoly under network effects Krina Griva Nikolaos Vettas February 005 Abstract We examine price competition under product-specific network effects, in a
More informationPersuasive Advertising in Oligopoly: A Linear State Differential Game
Persuasive Advertising in Oligopoly: A Linear State Differential Game Roberto Cellini, # Luca Lambertini and Andrea Mantovani # Department of Economics, University of Catania cellini@unict.it Department
More informationA Note on Expanding Networks and Monopoly Pricing
A Note on Expanding Networks and Monopoly Pricing Jean J. Gabszewicz and Filomena Garcia CORE Discussion Paper 2005/95 Abstract We obtain explicitly the optimal path of prices for a monopolist operating
More information1.. There are two complementary goods that are consumed together (each individual good
University of California, Davis Department of Economics Time: 3 hours Reading time: 20 minutes PRELIMINARY EXAMINATION FOR THE Ph.D. DEGREE Industrial Organization June 22, 2004 Answer four of the six
More informationThe Dynamic Input-Output Model of the Russian Economy with a Human Capital Block
JEL C67, E24, J24, O15 A.O. Baranov 1,2, V.N. Pavlov 2,3, Yu. M. Slepenkova 1 1 Novosibirsk State University, 2 Pirogova St., Novosibirsk, 630090, Russian Federation 2 Institute of Economics and Industrial
More informationA nash equilibrium game and pareto efficient solution to a cooperative advertising
IOSR Journal of Mathematics (IOSR-JM) e-issn: 78-578, p-issn: 319-765X. Volume 11, Issue 1 Ver. V (Jan - Feb. 015), PP 100-104 www.iosrjournals.org A Nash Equilibrium Game and Pareto Efficient Solution
More informationPrice Coordination in Distribution Channels: A Dynamic Perspective
Price Coordination in Distribution Channels: A Dynamic Perspective Guiomar Martín-Herrán 1,, Sihem Taboubi 2 Abstract In this study, we investigate two important questions related to dynamic pricing in
More informationA Game Theoretic Framework for Competing/Cooperating Retailers under price and advertising dependent demand
MPRA Munich Personal RePEc Archive A Game Theoretic Framework for Competing/Cooperating Retailers under price and advertising dependent demand Dhouha Dridi and Slim Ben Youssef 29. March 2015 Online at
More informationOptimal Dynamic Pricing of Perishable Products Considering Quantity Discount Policy
Journal of Information & Computational Science 10:14 (013) 4495 4504 September 0, 013 Available at http://www.joics.com Optimal Dynamic Pricing of Perishable Products Considering Quantity Discount Policy
More informationSocial responsibility in a bilateral monopoly with R&D
MPRA Munich Personal RePEc Archive Social responsibility in a bilateral monopoly with R&D Arturo Garcia and Mariel Leal and Sang-Ho Lee Technologico de Monterrey, Mexico, Technologico de Monterrey, Mexico,
More informationInformal Input Suppliers
Sergio Daga Pedro Mendi February 3, 2016 Abstract While a large number of contributions have considered how market outcomes are affected by the presence of informal producers, there is scarce empirical
More informationLECTURE 13 THE NEOCLASSICAL OR WALRASIAN EQUILIBRIUM INTRODUCTION
LECTURE 13 THE NEOCLASSICAL OR WALRASIAN EQUILIBRIUM INTRODUCTION JACOB T. SCHWARTZ EDITED BY KENNETH R. DRIESSEL Abstract. Our model is like that of Arrow and Debreu, but with linear Leontief-like features,
More informationBuyer Heterogeneity and Dynamic Sorting in Markets for Durable Lemons
Buyer Heterogeneity and Dynamic Sorting in Markets for Durable Lemons Santanu Roy Southern Methodist University, Dallas, Texas. October 13, 2011 Abstract In a durable good market where sellers have private
More informationKey words: Franchise Fees, Competition, Double Marginalization, Collusion
The Role of Franchise Fees and Manufacturers Collusion DongJoon Lee (Nagoya University of Commerce and Business, Japan) Sanghoen Han (Nagoya University of Commerce and Business, Japan) Abstract: This paper
More informationWRITTEN PRELIMINARY Ph.D. EXAMINATION. Department of Applied Economics. Summer Natural Resource and Environmental Economics
WRITTEN PRELIMINARY Ph.D. EXAMINATION Department of Applied Economics Summer - 2006 Natural Resource and Environmental Economics Instructions: Identify yourself by your code letter, not your name, on each
More informationThe Incentive of a Multiproduct Monopolist to Provide All Goods. Nicholas Economides EC July 1995
The Incentive of a Multiproduct Monopolist to Provide All Goods by Nicholas Economides EC-95-09 July 1995 The Incentive of a Multiproduct Monopolist to Provide All Goods * by Nicholas Economides ** July
More informationAn Economic Order Quantity Model for Weibull Distribution Deterioration with Selling Price Sensitive Demand and Varying Hold Cost
Volume 118 No. 6 2018, 499-507 ISSN: 1311-8080 printed version); ISSN: 1314-3395 on-line version) url: http://www.ijpam.eu ijpam.eu An Economic Order Quantity Model for Weibull Distribution Deterioration
More informationOnline shopping and platform design with ex ante registration requirements
Online shopping and platform design with ex ante registration requirements O A Florian Morath Johannes Münster June 17, 2016 This supplementary appendix to the article Online shopping and platform design
More informationDEPARTMENT OF ECONOMICS
ISSN 0819-2642 ISBN 0 7340 2600 5 THE UNIVERSITY OF MELBOURNE DEPARTMENT OF ECONOMICS RESEARCH PAPER NUMBER 944 JULY 2005 SNOBS AND QUALITY GAPS by Suren Basov Department of Economics The University of
More informationThe Efficiency of Voluntary Pollution Abatement when Countries can Commit
The Efficiency of Voluntary Pollution Abatement when Countries can Commit by Robin Boadway, Queen s University, Canada Zhen Song, Central University of Finance and Economics, China Jean-François Tremblay,
More informationVolume 38, Issue 4. Market foreclosure, output and welfare under second-degree price discrimination
Volume 38, Issue 4 Market foreclosure, output and welfare under second-degree price discrimination Yong Chao University of Louisville Babu Nahata University of Louisville Abstract We compare second-degree
More informationRationing Poor Consumers to Reduce Prices
Rationing Poor Consumers to Reduce Prices Simona Grassi Ching-to Albert Ma Max Weber Fellow Department of Economics European University Institute Boston University Villa La Fonte, Via Delle Fontanelle,
More informationThe Impact of Market Structure on Innovation Incentives
The Impact of Market Structure on Innovation Incentives Dissertation zur Erlangung des Grades eines Doktors der Wirtschaftswissenschaften der Universität Bielefeld vorgelegt von Dipl.-Wirt. Math. Michael
More informationThe value of switching costs
The value of switching costs Gary Biglaiser University of North Carolina, Chapel Hill Jacques Crémer Toulouse School of Economics (GREMAQ, CNRS and IDEI) Gergely Dobos Gazdasági Versenyhivatal (GVH) June
More informationPOLICY FORECASTS USING MIXED RP/SP MODELS: SOME NEW EVIDENCE
Advanced OR and AI Methods in Transportation POLICY FORECASTS USING MIXED / MODELS: SOME NEW EVIDENCE Elisabetta CHERCHI 1, Italo MELONI 1, Juan de Dios ORTÚZAR Abstract. The application of discrete choice
More informationEvaluating the effect of environmental regulations on a closed-loop supply chain network: a variational inequality approach
Evaluating the effect of environmental regulations on a closed-loop supply chain networ: a variational inequality approach E. Allevi 1, A. Gnudi 2, I.V. Konnov 3, and G. Oggioni 4 Abstract Global climate
More informationPOLLUTION CONTROL UNDER UNCERTAINTY AND SUSTAINABILITY CONCERN
POLLUTION CONTROL UNDER UNCERTAINTY AND SUSTAINABILITY CONCERN Danilo Liuzzi, University of Milan, Italy Davide La Torre, University of Milan, Italy Simone Marsiglio, University of Wollongong, Australia
More informationChapter 28: Monopoly and Monopsony
Chapter 28: Monopoly and Monopsony 28.1: Introduction The previous chapter showed that if the government imposes a tax on some good that there is a loss of surplus. We show a similar result in this chapter
More informationThe Construction of the Green Supply System based on Game Theory
211 International Conference on Social Science and Humanity IPEDR vol.5 (211) (211) IACSIT Press, Singapore The Construction of the Green Supply System based on Game Theory Jia Liu, Nan Liu, Yao Li School
More informationWORKING PAPER SERIES Judo Economics in Markets with Asymmetric Firms Daniel Cracau Working Paper No. 2/2013
WORKING PAPER SERIES Impressum ( 5 TMG) Herausgeber: Otto-von-Guericke-Universität Magdeburg Fakultät für Wirtschaftswissenschaft Der Dekan Verantwortlich für diese Ausgabe: Otto-von-Guericke-Universität
More informationApplying Stackelberg Game to Find the Best Price and Delivery Time Policies in Competition between Two Supply Chains
Int. J. Manag. Bus. Res., 2 (4), 313-327, Autumn 2012 IAU Applying Stackelberg Game to Find the Best Price and Delivery Time Policies in Competition between Two Supply Chains 1 M. Fathian, *2 M. Narenji,
More informationPricing in Dynamic Advance Reservation Games
Pricing in Dynamic Advance Reservation Games Eran Simhon, Carrie Cramer, Zachary Lister and David Starobinski College of Engineering, Boston University, Boston, MA 02215 Abstract We analyze the dynamics
More informationPricing Game under Imbalanced Power Structure
Pricing Game under Imbalanced Power Structure Maryam Khajeh Afzali, Poh Kim Leng, Jeff Obbard Abstract The issue of channel power in supply chain has recently received considerable attention in literature.
More informationINTERACTION BETWEEN A MANUFACTURER AND A RISK-AVERSE RETAILER: A SUPPLY CHAIN PERSPECTIVE ON RISK-AVERSE NEWSVENDOR MODEL
The Journal of Japanese Operations Management and Strategy, Vol. 4, No. 2, pp. 31-45, 2014 INTERACTION BETWEEN A MANUFACTURER AND A RISK-AVERSE RETAILER: A SUPPLY CHAIN PERSPECTIVE ON RISK-AVERSE NEWSVENDOR
More informationNotes on Intertemporal Consumption Choice
Paul A Johnson Economics 304 Advanced Topics in Macroeconomics Notes on Intertemporal Consumption Choice A: The Two-Period Model Consider an individual who faces the problem of allocating their available
More informationA SURVEY OF STACKELBERG DIFFERENTIAL GAME MODELS IN SUPPLY AND MARKETING CHANNELS
J Syst Sci Syst Eng (Dec 7) 6(4): 385-43 DOI:.7/s58-7-558- ISSN: 4-3756 (Paper) 86-9576 (Online) CN-983/N A SUVEY OF STACKELBEG DIFFEENTIAL GAME MODELS IN SUPPLY AND MAKETING CHANNELS Xiuli HE Ashutosh
More informationCURRENT STATE OF WINDOWS/LINUX COMPETITION IN THE EAST-ASIAN SERVER OPERATING SYSTEMS MARKET
V.I. Soloviev, Ph.D. State University of Management, Moscow, Russia CURRENT STATE OF WINDOWS/LINUX COMPETITION IN THE EAST-ASIAN SERVER OPERATING SYSTEMS MARKET The paper is motivated by Microsoft Windows
More informationUniform and Targeted Advertising with Shoppers and. Asymmetric Loyal Market Shares
Uniform and Targeted dvertising with Shoppers and symmetric Loyal Market Shares Michael rnold, Chenguang Li and Lan Zhang October 9, 2012 Preliminary and Incomplete Keywords: informative advertising, targeted
More informationECONOMIC EFFECTS OF PURITY STANDARDS IN BIOTECH LABELING LAWS
ECONOMIC EFFECTS OF PURITY STANDARDS IN BIOTECH LABELING LAWS KONSTANTINOS GIANNAKAS AND NICHOLAS KALAITZANDONAKES Paper prepared for presentation at the American Agricultural Economics Association Annual
More informationA Walrasian Theory of Commodity Money: Paradoxical Results *
Walrasian Theory of Commodity Money: Paradoxical Results * Xavier Cuadras-Morató Department of Economics Universitat Pompeu Fabra Ramon Trias Fargas, 25-27 08005 BRCELON e-mail: xavier.cuadras@econ.upf.es
More informationLecture 10: Price discrimination Part II
Lecture 10: Price discrimination Part II EC 105. Industrial Organization. Matt Shum HSS, California Institute of Technology EC 105. Industrial Organization. (Matt Shum HSS, CaliforniaLecture Institute10:
More informationOn cleaner technologies in a transboundary pollution game
On cleaner technologies in a transboundary pollution game Hassan Benchekroun a Amrita Ray Chaudhuri b January 2009 a Department of Economics, McGill University, 855 Sherbrooke Ouest, Montreal, QC, Canada,
More informationA Game-Theoretic Approach to Pricing in a Two-Level Supply Chain Considering Advertising and Servicing
International Journal of Industrial Engineering & Production Research (017) June 017, Volume 8, Number pp. 01-15 DOI: 10.068/ijiepr.8..01 http://ijiepr.iust.ac.ir/ Supply Chain Considering Advertising
More informationAdvance Selling, Competition, and Brand Substitutability
Advance Selling, Competition, and Brand Substitutability Oksana Loginova October 27, 2016 Abstract This paper studies the impact of competition on the benefits of advance selling. I construct a two-period
More informationMass versus Direct Advertising and Product Quality
Journal of Economic Theory and Econometrics, Vol. 29, No. 3, Sep. 2018, 1 22 Mass versus Direct Advertising and Product Quality Lola Esteban José M. Hernández Abstract This paper analyzes how the use of
More informationExclusion by a manufacturer without a first-mover advantage
Exclusion by a manufacturer without a first-mover advantage Bo Shen Jan, 2014 Abstract The existing literature on naked exclusion argues that exclusive contracts can be used by an incumbent firm to anti-competitively
More informationChild Labour and Inequality
MPRA Munich Personal RePEc Archive Child Labour and Inequality Simone D Alessandro and Tamara Fioroni University of Pisa, University of Palermo 22 April 2011 Online at https://mpra.ub.uni-muenchen.de/30454/
More informationCompeting Suppliers under Price Sensitive Demand with a Common Retailer
Proceedings of the World Congress on Engineering 213 Vol I, WCE 213, July 3-5, 213, London, U.K. Competing Suppliers under Price Sensitive Demand with a Common Retailer Chirawan Opornsawad, Rawinkhan Srinon,
More informationResearch on inventory and transportation integrated optimization model of supply chain on online shopping based on the revenue sharing contract
Available online www.jocpr.com Journal of Chemical Pharmaceutical Research, 04, 6(6:-6 Research Article ISSN : 0975-784 CODEN(USA : JCPRC5 Research on inventory transportation integrated optimization model
More informationModeling of competition in revenue management Petr Fiala 1
Modeling of competition in revenue management Petr Fiala 1 Abstract. Revenue management (RM) is the art and science of predicting consumer behavior and optimizing price and product availability to maximize
More informationConsumer Conformity and Vanity in Vertically Differentiated Markets
Consumer Conformity and Vanity in Vertically Differentiated Markets Hend Ghazzai Assistant Professor College of Business and Economics Qatar University P.O. Box 2713 Doha, Qatar. Abstract Consumers' choice
More informationBargaining over managerial contracts: a note
MPRA Munich Personal RePEc Archive Bargaining over managerial contracts: a note Giorgos Stamatopoulos University of Crete 12 April 2018 Online at https://mpra.ub.uni-muenchen.de/86143/ MPRA Paper No. 86143,
More informationPrice Discrimination through Corporate Social Responsibility
Price Discrimination through Corporate Social Responsibility Suman Ghosh Kameshwari Shankar Abstract A common form of Corporate Social Responsibility (CSR) by firmsistoagreetodonatea fixed portion of private
More informationCARTEL STABILITY AND THE CURVATURE OF MARKET DEMAND. Luca Lambertini *
CARTEL STABILITY AND THE CURVATURE OF MARKET DEMAND Luca Lambertini * Dipartimento di Scienze Economiche # Università degli Studi di Bologna Strada Maggiore 45 4025 Bologna ITALY tel 39-5-6402600 fax 39-5-6402600
More informationA MODEL FOR DETERMINING AN OPTIMAL LABOR CONTRACT UNDER PROFIT SHARING SYSTEM
Proceeding of International Conference On Research, Implementation And Education Of Mathematics And Sciences 2014, Yogyakarta State University, 18-20 May A MODEL FOR DETERMINING AN OPTIMAL LABOR CONTRACT
More informationEC Lecture 11&12. Vertical Restraints and Vertical Mergers
EC 36 - Lecture 11&1 Vertical Restraints and Vertical Mergers What are vertical restraints? In most markets producers do not sell directly to consumers but to retailers who then sell to consumers. Some
More informationECO 310: Empirical Industrial Organization Lecture 6 - Demand for Differentiated Products (III) The Almost Ideal Demand System
ECO 310: Empirical Industrial Organization Lecture 6 - Demand for Differentiated Products (III) The Almost Ideal Demand System Dimitri Dimitropoulos Fall 2014 UToronto 1 / 29 References Deaton, A. and
More informationResearch Article Price and Service Competition of Dual-Channel Supply Chain with Consumer Returns
Discrete Dynamics in Nature and Society, Article ID 565603, 10 pages http://dx.doi.org/10.1155/2014/565603 Research Article Price and Service Competition of Dual-Channel Supply Chain with Consumer Returns
More informationIO Field Examination Department of Economics, Michigan State University May 17, 2004
IO Field Examination Department of Economics, Michigan State University May 17, 004 This examination is four hours long. The weight of each question in the overall grade is indicated. It is important to
More informationThe Management of Marketing Profit: An Investment Perspective
The Management of Marketing Profit: An Investment Perspective Draft of Chapter 1: A Philosophy of Competition and An Investment in Customer Value Ted Mitchell, May 1 2015 Learning Objectives for Chapter
More informationBonanno, G. (1987), Location Choice, Product Proliferation and Entry Deterrence, Review of
References Bonanno, G. (1987), Location Choice, Product Proliferation and Entry Deterrence, Review of Economic Studies, 54, pp.37-46. Besanko, D., S. Donnenfeld and L. White (1987), Monopoly and Quality
More informationHard to Get, Easy to Lose Endogenous Reputation and Underinvestment
Hard to Get, Easy to Lose Endogenous Reputation and Underinvestment Guillermo L. Ordoñez July, 2007 Abstract Reputation concerns may help to achieve efficiency in cases where imperfect information impedes
More informationEconomics of Information and Communication Technology
Economics of Information and Communication Technology Alessio Moro, University of Cagliari October 26, 2017 Sequential innovation ICT products are extremely complex. Technological progress allows to integrate
More informationAgglomeration in a vertically-linked oligopoly
Agglomeration in a vertically-linked oligopoly José Pedro Pontes This paper examines the location of three vertically-linked firms. In a spatial economy composed of two regions, a monopolist firm supplies
More informationCentre for Computational Finance and Economic Agents WP Working Paper Series. Biliana Alexandrova-Kabadjova, Edward Tsang and Andreas Krause
Centre for Computational Finance and Economic Agents WP016-08 Working Paper Series Biliana Alexandrova-Kabadjova, Edward Tsang and Andreas Krause Finding Profit-Maximizing Strategies for the Artificial
More informationCoordinating a Supply Chain With a Manufacturer-Owned Online Channel: A Dual Channel Model Under Price Competition
University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Supply Chain Management and Analytics Publications Business, College of 2013 Coordinating a Supply Chain With a Manufacturer-Owned
More informationEfficiency in a Search and Matching Economy with a Competitive Informal Sector
DISCUSSION PAPER SERIES IZA DP No. 6935 Efficiency in a Search and Matching Economy with a Competitive Informal Sector Olivier Charlot Franck Malherbet Mustafa Ulus October 2012 Forschungsinstitut zur
More informationGlobalization and Social Networks
Globalization and Social Networks Georg Durnecker University of Mannheim Fernando Vega-Redondo European University Institute September 14, 2012 Duernecker & Vega-R. (Mannheim & EUI) Globalization and Social
More informationCompetitive and Cooperative Degree in Supply Chain: Supplier Selection between Competitors and Third-Party Suppliers
Competitive and Cooperative Degree in upply Chain: upplier election between Competitors and Third-Party uppliers Bo Xie, Xianjia Wang, and Chuan Zhou 2 Wuhan University, Economics and Management chool,
More informationQuasi linear Utility and Two Market Monopoly
Quasi linear Utility and Two Market Monopoly By Stephen K. Layson Department of Economics 457 Bryan Building, UNCG Greensboro, NC 27412 5001 USA (336) 334 4868 Fax (336) 334 5580 layson@uncg.edu ABSTRACT
More informationLinear Incentive Contract with Different Types of Agents KANGSIK CHOI
THE INSTITUTE OF ECONOMIC RESEARCH Working Paper Series No. 85 Linear Incentive Contract with Different Types of Agents by KANGSIK CHOI March 17, 2004 KAGAWA UNIVERSITY Takamatsu, Kagawa 760-8523 JAPAN
More informationDurable Goods Monopoly with Endogenous Quality
Durable Goods Monopoly with Endogenous Quality Jong-Hee Hahn Keele University (Preliminary) March 30, 2004 Abstract This paper examines the dynamic pricing problem of a durable-good monopolist when product
More informationOnline shopping and platform design with ex ante registration requirements. Online Appendix
Online shopping and platform design with ex ante registration requirements Online Appendix June 7, 206 This supplementary appendix to the article Online shopping and platform design with ex ante registration
More informationIntergenerational altruism: A solution to the climate problem?
Intergenerational altruism: A solution to the climate problem? Frikk Nesje 1 Geir B. Asheim 2 May 18, 2017 Abstract The future effects of climate change may induce increased intergenerational altruism.
More informationEconomics of Daily-deal Business Models
Economics of Daily-deal Business Models Shivendu Shivendu Zhe Zhang sshivend@uci.edu zhez1@uci.edu University of California Irvine, Irvine, CA 92617 Abstract Daily-deal business model is a type of performance-based
More informationShapley Value and Monopoly Power In A Two- Sector Model
Economic Staff Paper Series Economics 7-1976 Shapley Value and Monopoly Power In A Two- Sector Model Roy Gardner Iowa State University Follow this and additional works at: http://lib.dr.iastate.edu/econ_las_staffpapers
More informationAbstract Keywords 1. Introduction
Abstract Number: 011-0133 The effect of the number of suppliers and allocation of revenuesharing on decentralized assembly systems Abstract: In this paper, we study a decentralized supply chain with assembled
More informationRe-visiting the Porter Hypothesis
Re-visiting the Porter Hypothesis Indrani Roy Chowdhury* and Sandwip K. Das** Abstract We provide a new formulation of the Porter hypothesis that we feel is in the spirit of the hypothesis. Under this
More informationOn the effects of firing costs on employment and welfare in a duopoly market with entry *
On the effects of firing costs on employment and welfare in a duopoly market with entry * Simone D Alessandro, Nicola Meccheri and Davide M. oluccia 1. Introduction The aim of this paper is to investigate
More informationOptimal selling strategy in dual-channel supply chains
ISSN 1816-6075 (Print), 1818-0523 (Online) Journal of System and Management Sciences Vol. 3 (2013) No. 2, pp. 10-19 Optimal selling strategy in dual-channel supply chains Yong He 1, Houfei Song 1, Peng
More informationOPTIMAL PRODUCT LINE DESIGN WHEN CONSUMERS EXHIBIT CHOICE SET DEPENDENT PREFERENCES
OPTIMAL PRODUCT LINE DESIGN WHEN CONSUMERS EXHIBIT CHOICE SET DEPENDENT PREFERENCES A.YEŞIM ORHUN Preliminary, Comments Welcome January 2006 Haas School of Business, University of California at Berkeley
More informationImperfect Competition Among Liquidity Providers
Imperfect Competition Among Liquidity Providers Angad Singh Caltech November 2018 Angad Singh (Caltech) November 2018 1 / 22 Table of Contents 1 Motivation & Related Work 2 The Model 3 Equilibrium Characterization
More informationWORKING PAPERS IN ECONOMICS AND ECONOMETRICS
THE AUSTRALIAN NATIONAL UNIVERSITY WORKING PAPERS IN ECONOMICS AND ECONOMETRICS Bundling and Foreclosure Tina Kao Australian National University Flavio Menezes University of Queensland September 29, 2006
More informationReal-Time Pricing and Imperfect Competition in Electricity Markets
Real-Time Pricing and Imperfect Competition in Electricity Markets Stephen Poletti and Julian Wright May, 2017 Abstract We analyze the effects of the adoption of real-time pricing RTP of electricity when
More informationOn the mode of Competition as a Collusive Perspective in Unionized Oligopoly
On the mode of Competition as a Collusive Perspective in Unionized Oligopoly Minas Vlassis * Maria Varvataki Department of Economics, University of Crete, Gallos University Campus, Rethymnon 74100, Greece
More informationA reverse discount model for dynamic demands. Abhishek Chakraborty. Indian Institute of Management Calcutta
A reverse discount model for dynamic demands Abhishek Chakraborty Indian Institute of Management Calcutta Diamond Harbour Road, Joka, Kolkata-700104, India Email: abhishekc08@iimcal.ac.in and Ashis Chatterjee
More informationNRG WORKING PAPER SERIES MAIL-IN-REBATES VS. COMBINED REBATE MECHANISM:- WHICH OF THEM IS MORE EFFECTIVE FOR SUPPLY CHAIN COORDINATION?
NRG WORKING PAPER SERIES MAIL-IN-REBATES VS. COMBINED REBATE MECHANISM:- WHICH OF THEM IS MORE EFFECTIVE FOR SUPPLY CHAIN COORDINATION? Nyenrode Research Group Vijayender Reddy Nalla Jack van der Veen
More informationInduced Innovation and Marginal Cost of New Technology
School of Economic Sciences Working Paper Series WP 2008-6 Induced Innovation and Marginal Cost of New Technology By Liu Y. and Shumway C.R. 2008 Induced Innovation and Marginal Cost of New Technology
More informationAn Integrative Framework of Cooperative Advertising: Should Manufacturers Continuously Support Retailer Advertising?
An Integrative Framework of Cooperative Advertising: Should Manufacturers Continuously Support Retailer Advertising? Guiomar Martín-Herrán 1,, Simon P. Sigué 2, Abstract A two-period game is developed
More informationBeliefs, Market Size and Consumer Search
Beliefs, Market Size and Consumer Search Maarten Janssen and Sandro Shelegia March 30, 2014 Abstract We analyze how the market power of firms in consumer search markets depends on how consumers form beliefs
More informationSupply Chain Contract Incorporating Fairness under Asymmetric Information
Open Journal of Social Sciences, 016, 4, 35-39 Published Online July 016 in Scies. http://www.scirp.org/journal/jss http://dx.doi.org/10.436/jss.016.47005 Supply Chain Contract Incorporating Fairness under
More informationWage bargaining under an employment target
University of Rome III From the SelectedWorks of Lilia Cavallari 2013 Wage bargaining under an employment target Lilia Cavallari Available at: https://works.bepress.com/lilia_cavallari/19/ Wage bargaining
More informationA Simple EOQ-like Solution to an Inventory System with Compound Poisson and Deterministic Demand
A Simple EOQ-like Solution to an Inventory System with Compound Poisson and Deterministic Demand Katy S. Azoury San Francisco State University, San Francisco, California, USA Julia Miyaoka* San Francisco
More informationNetwork Interconnection with Participation Constraints
Network Interconnection with Participation Constraints Stephen Poletti a,,julian Wright b a Department of Economics, University of Auckland, Private Bag 9019, Auckland, New Zealand b Department of Economics,
More informationarxiv: v1 [q-fin.gn] 20 Sep 2009
arxiv:0909.3655v1 [q-fin.gn] 20 Sep 2009 Utility Function and Optimum in the models with Habit Formation and Catching up with the Joneses Roman Naryshkin a, and Matt Davison a a Department of Applied Mathematics,
More informationThis paper is not to be removed from the Examination Halls
~~EC2066 ZA d0 This paper is not to be removed from the Examination Halls UNIVERSITY OF LONDON EC2066 ZA BSc degrees and Diplomas for Graduates in Economics, Management, Finance and the Social Sciences,
More informationEstimating imperfect competition impact on producer prices in Russia in
Estimating imperfect competition impact on producer prices in Russia in 2003-2010 Topic: Examinations of Input-Output Price Model Author: Artem Denisov Co-author: Vadim Gilmundinov Monetary instruments
More information