Demand Functions in Decision Modeling: A Comprehensive Survey and Research Directions

Abstract

A variety of mathematical forms have been developed to characterize demand functions which depend on a firm's operational and marketing activities. Such demand functions are being increasingly used by researchers in economics and different functional areas of business. We provide a comprehensive survey of commonly used demand models which depend on (i) price, (ii) rebate, (iii) lead time, (iv) space, (v) quality, and (vi) advertising. Our survey includes single firm-demand models in each category, as well as game theoretic multifirm models involving strategic interaction among the firms. We observe that certain types of functional forms, such as linear, power/iso-elastic, multinomial logit, and multiplicative competitive interaction, have been widely used to construct various demand models in all six categories, but that a large majority of publications deal with categories (i) and (v) of demand models. For each of the six categories, we survey relevant functional forms in the representative papers, and discuss the main properties, the advantages, the disadvantages, and comment on possible future research directions. We also present discussions of the applications of these analytical demand models in empirical studies. The article ends with a summary of our major findings. Linear models (LM) LM I: Mills (1959), Petruzzi Dada (1999) d(p) = a − bp, where a, b > 0 LM II: Eliashberg and Steinberg (1987) d(p) = a(t) − bp(t), where a(t), b > 0, t ∈ [0, T ] LM III: Chou and Parlar (2006) d(p) = a(t) − b(t)p(t), where t ∈ [0, T ] LM IV(Reference-price model): Fibich et al. (2003) d(p, r) = a − δp − γ (p − r), where a, δ, γ > 0 Power models (PM) PM I(Isoelastic model): Karlin and Carr (1962), d(p) = ap −b , where a > 0, b > 1 Petruzzi and Dada (1999) PM II(Algebraic model): d(p) = (ap + b) −γ , where a, b > 0, γ > 1 Jeuland and Shugan (1988) PM III (Linear-power model): Song et al. (2008) d(p) = (a − bp) γ , where a, bγ > 0, γ ∈ (−∞, −1) ∪ (0, ∞) PM IV: Chen et al. (2006) d(p) = a − bp γ , where a, b > 0, γ ≥ 1 PM V: Ray et al. (2005) d(p) = (a − bp β ) γ , where a, b > 0, β ≥ 1, γ ≤ 1 PM VI: Agrawal and Ferguson (2007) d(p) = a/[a + bp γ ], where a, b, γ > 0 Hybrid Model (HM): Lau and Lau (2003)and 0 ≤ τ ≤ 1 Exponential models (EM) EM I: Hanssens and Parsons (1993), Jeuland and Shugan (1988), d(p) = a exp(−γp), where a > 0, γ > 0 Song et al. (2008) EM II: Chen et al. (2006), d(p) = exp(a − bp), where a > 0, b > 0 Song et al. (2008) EM III: Chen and Simchi-Levi (2004) d(p) = a − exp(γp), where a > 0, γ > 0 Logarithmic model (LgM): Chen et al. (2006), d(p) = ln[(a − bp) γ ], where a, b, γ > 0 Ray et al. (2005) Logit models (LtM) LtM I: Chen and Simchi-Levi (2012), d(p) = a exp(−bp)/[1 + exp(−bp)], where a, b > 0 LtM II: Phillips (2005) d(p) = 1/[1 + exp[a + bp]] Demand Functions in Decision Modeling

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