Static Pricing Problems under Mixed Multinomial Logit Demand

Price differentiation is a common strategy for many transport operators. In this paper, we study a static multiproduct price optimization problem with demand given by a continuous mixed multinomial logit model. To solve this new problem, we design an efficient iterative optimization algorithm that asymptotically converges to the optimal solution. To this end, a linear optimization (LO) problem is formulated, based on the trust-region approach, to find a "good" feasible solution and approximate the problem from below. Another LO problem is designed using piecewise linear relaxations to approximate the optimization problem from above. Then, we develop a new branching method to tighten the optimality gap. Numerical experiments show the effectiveness of our method on a published, non-trivial, parking choice model

International price discrimination in the European car market: An econometric model of oligopoly behavior with product differentiation

Car Industry;Oligopoly;Product Differentiation;Econometric Models;Price Discrimination

Market Segmentation and the Sources of Rents from Innovation: Personal Computers in the Late 1980's

This paper evaluates the sources of transitory market power in the market for personal computers (PCs) during the late 1980's. Our analysis is motivated by the coexistence of low entry barriers into the PC industry and high rates of innovative investment by a small number of PC manufacturers. We attempt to understand these phenomena by measuring the role that different principles of product differentiation (PDs) played in segmenting this dynamic market. Our first PD measures the substitutability between Frontier (386-based) and Non- Frontier products, while the second PD measures the advantage of a brand-name reputation (e.g., by IBM). Building on advances in the measurement of product differentiation, we measure the separate roles that these PDs played in contributing to transitory market power. In so doing, this paper attempts to account for the market origins of innovative rents in the PC industry. Our principal finding is that, during the late 1980's, the PC market was highly segmented along both the Branded (B versus NB) and Frontier (F versusNF) dimensions. The effects of competitive events in any one cluster were confined mostly to that particular cluster, with little effect on other clusters. For example, less than 5% of the market share achieved by a hypothetical entrant would be market-stealing from other clusters. In addition, the product diffe- rentiation advantages of B and F were qualitatively different. The main advantage of F was limited to the isolation from NF competitors it provided; Brandedness both shifted out the product demand curve as well as segmenting B products from NB competition. These results help explain how transitory market power (arising from market segmentation) shaped the underlying incen- tives for innovation in the PC industry during the mid to late 1980s.

Multimodal and nested preference structures in choice-based conjoint analysis: a comparison of bayesian choice models with discrete and continuous representations of heterogeneity

Die Choice-Based Conjoint-Analyse (CBC) ist heutzutage die am weitesten verbreitete Variante der Conjoint-Analyse, einer Klasse von Verfahren zur Messung von Nachfragerpräferenzen. Der Hauptgrund für die zunehmende Dominanz des CBC-Ansatzes in jüngerer Zeit besteht darin, dass hier das tatsächliche Wahlverhalten von Nachfragern sehr realistisch nachgestellt werden kann, indem die Befragten wiederholt ihre bevorzugte Alternative aus einer Menge mehrerer Alternativen (Choice Sets) auswählen. Im Rahmen der CBC-Analyse ist das Multinomiale Logit- (MNL) Modell das am häufigsten verwendete diskrete Wahlmodell. Das MNL-Modell weist jedoch zwei wesentliche Einschränkungen auf: (a) Es impliziert proportionale Substitutionsmuster zwischen den Alternativen, was als Independence of Irrelevant Alternatives- (IIA) Eigenschaft bezeichnet wird, und (b) es berücksichtigt keine Nachfragerheterogenität, da per Definition Teilnutzenwerte für alle Konsumenten als homogen angenommen werden. Seit den 1990er-Jahren werden hierarchisch bayesianische (HB) Modelle für die Teilnutzenwertschätzung in der CBC-Analyse verwendet. Solche HB-Modelle ermöglichen zum einen eine Schätzung individueller Teilnutzenwerte, selbst bei einer beschränkten Datenlage, zum anderen können sie aufgrund der Modellierung von Heterogenität die IIA-Eigenschaft stark abmildern. Der Schwerpunkt der vorliegenden Thesis liegt auf der Verwendung von HB-Modellen mit unterschiedlichen Darstellungen von Nachfragerheterogenität (diskret vs. kontinuierlich) für CBC-Daten sowie außerdem auf einem speziellen HB-Modell, das die IIA-Eigenschaft durch Berücksichtigung von unterschiedlichen Ähnlichkeitsgraden zwischen Teilmengen von Alternativen (Nestern) zusätzlich abschwächt. Insbesondere wird die statistische Performance von einfachen MNL-, Latent Class- (LC) MNL-, HB-MNL-, Mixture-of-Normals- (MoN) MNL-, Dirichlet Process Mixture- (DPM) MNL- und HB-Nested Multinomialen Logit- (NMNL) Modellen (unter experimentell variierenden Bedingungen) hinsichtlich der Recovery von Präferenzstrukturen, der Anpassungsgüte und der Prognosevalidität analysiert. Dazu werden zwei umfangreiche Monte-Carlo-Studien durchgeführt, ferner werden die verschiedenen Modelltypen auf einen empirischen CBC-Datensatz angewandt. In der ersten Monte-Carlo-Studie liegt der Fokus auf dem Vergleich zwischen dem HB-MNL und dem HB-NMNL bei multimodalen und genesteten Präferenzstrukturen. Die Ergebnisse zeigen, dass es keine wesentlichen Unterschiede zwischen beiden Modelltypen hinsichtlich der Anpassungsgüte und insbesondere hinsichtlich der Prognosevalidität gibt. In Bezug auf die Recovery von Präferenzstrukturen schneidet das HB-MNL-Modell zunehmend schlechter ab, wenn die Korrelation in mindestens einem Nest höher ist, während sich das HB-NMNL-Modell erwartungsgemäß an den Grad der Ähnlichkeit zwischen Alternativen anpasst. Die zweite Monte-Carlo-Studie befasst sich mit multimodalen und segmentspezifischen Präferenzstrukturen. Um Unterschiede zwischen den Klassen von Modellen mit unterschiedlichen Darstellungen von Heterogenität herauszuarbeiten, werden hier gezielt die Grade der Heterogenität innerhalb von Segmenten und zwischen Segmenten manipuliert. Unter experimentell variierenden Bedingungen werden die state-of-the-art Ansätze zur Modellierung von Heterogenität (einfaches MNL, LC-MNL, HB-MNL) mit erweiterten Wahlmodellen, die sowohl Nachfragerheterogenität zwischen Segmenten als auch innerhalb von Segmenten abbilden können (MoN-MNL und DPM-MNL), verglichen. Das zentrale Ergebnis dieser Monte-Carlo-Studie ist, dass sich das HB-MNL-Modell, welches eine multivariate Normalverteilung zur Modellierung von Präferenzheterogenität unterstellt, als äußerst robust erweist. Darüber hinaus kristallisiert sich der LC-MNL-Segmentansatz als der beste Ansatz heraus, um die „wahre“ Anzahl von Segmenten zu identifizieren. Abschließend werden die zuvor vorgestellten Wahlmodelle auf einen realen CBC-Datensatz angewandt. Die Ergebnisse zeigen, dass Modelle mit einer kontinuierlichen Darstellung von Heterogenität (HB-MNL, HB-NMNL, MoN-MNL und DPM-MNL) eine bessere Anpassungsgüte und Prognosevalidität aufweisen als Modelle mit einer diskreten Darstellung von Heterogenität (einfaches MNL, LC-MNL). Weiterhin zeigt sich, dass das HB-MNL-Modell für Prognosezwecke sehr gut geeignet ist und im Vergleich zu den anderen (erweiterten) Modellen mindestens ebenso gute, wenn nicht sogar wesentlich bessere Vorhersagen liefert, was für Manager eine zentrale Erkenntnis darstellt.Choice-Based Conjoint (CBC) is nowadays the most widely used variant of conjoint analysis, a class of methods for measuring consumer preferences. The primary reason for the increasing dominance of the CBC approach over the last 35 years is that it closely mimics real choice behavior of consumers by asking respondents repeatedly to choose their preferred alternative from a set of several offered alternatives (choice sets), respectively. Within the framework of CBC analysis, the multinomial logit (MNL) model is the most frequently used discrete choice model. However, the MNL model suffers from two major limitations: (a) it implies proportional substitution rates across alternatives, referred to as the Independence of Irrelevant Alternatives (IIA) property and (b) it does not account for unobserved consumer heterogeneity, as part-worth utilities are assumed to be equal for all respondents by definition. Since the 1990s, Hierarchical Bayesian (HB) models have been used for part-worth utility estimation in CBC analysis. HB models are able to determine part-worth utilities at the individual respondent level even with little individual respondent information on the one hand and, as a result of addressing consumer heterogeneity, can strongly soften the IIA property on the other hand. The focus of the present thesis is on CBC analysis using HB models with different representations of heterogeneity (discrete vs. continuous) as well as using a HB model which mitigates the IIA property to a further extent by allowing for different degrees of similarity between subsets (nests) of alternatives. In particular, we systematically explore the comparative performance of simple MNL, latent class (LC) MNL, HB-MNL, mixture-of-normals (MoN) MNL, Dirichlet Process Mixture (DPM) MNL and HB nested multinomial logit (NMNL) models (under experimentally varying conditions) using statistical criteria for parameter recovery, goodness-of-fit, and predictive accuracy. We conduct two extensive Monte Carlo studies and apply the different types of models to an empirical CBC data set. In the first Monte Carlo study, the focus lies on the comparative performance of the HB-MNL versus the HB-NMNL for multimodal and nested preference structures. Our results show that there seems to be no major differences between both types of models with regard to goodness-of-fit measures and in particular their ability to predict respondents’ choice behavior. Regarding parameter recovery, the HB-MNL model performs increasingly worse when correlation in at least one nest is higher, while the HB-NMNL model adapts to the degree of similarity between alternatives, as expected. The second Monte Carlo study deals with multimodal and segment-specific preference structures. More precisely, to carve out differences between the classes of models with different representations of heterogeneity, we specifically vary the degrees of within-segment and between-segment heterogeneity. We compare state-of-the-art methods to represent heterogeneity (simple MNL, LC-MNL, HB-MNL) and more advanced choice models representing both between-segment and within-segment consumer heterogeneity (MoN-MNL and DPM-MNL) under varying experimental conditions. The core finding from our Monte Carlo study is that the HB-MNL model appears to be highly robust against violations in its assumption of a single multivariate normal distribution of consumer preferences. In addition, the LC-MNL segment solution proves to be the best approach to recover the “true” number of segments. Finally, we apply the previously presented choice models to a real-life CBC data set. The results indicate that models with a continuous representation of heterogeneity (HB-MNL, HB-NMNL, MoN-MNL and DPM-MNL) perform better than models with a discrete representation of heterogeneity (simple MNL, LC-MNL). Further, it turns out that the HB-MNL model works extremely well for predictive purposes and provides at least as good if not considerably better predictions compared to the other (advanced) models, which is an important aspect for managers

CURRENT ISSUES AFFECTING TRADE AND TRADE POLICY: AN ANNOTATED LITERATURE REVIEW

This review provides a base of literature describing current issues and research on the impacts of lobalization and the industrialization of agriculture and recent approaches to analyze and model agricultural trade and trade policies. Three key factors of the survey are differentiated goods, global economic integration and international supply chain linkages. The review covers 182 publications, which are presented alphabetically by author with a brief annotation describing how it relates to the above criteria. The articles are also indexed by keyword. A brief summary highlights the documented literature and includes a series of issues for future discussion and research.International Relations/Trade,

Economic behaviour and decision making: theories of two-sided markets, multiproduct pricing and weighting for cumulative prospect theory

This thesis studies the microeconomic theories of two-sided markets, multiproduct pricing, and decision making in risky choice situations. In the first part of the thesis, we focus on a special kind of two-sided markets, where participants can act on both the buying side and the selling side of the market, which we call "mixed two-sided markets". The literature on two-sided markets has assumed that buyers cannot sell and sellers cannot buy. In real life, however, many markets are mixed, with examples ranging from telecommunication to stock exchange. We provide a general model for mixed two-sided markets. We observe that in practice, platforms in such markets often use a "hybrid" bundling strategy: A common membership fee gives access to both buying and selling services, while the individual transaction fees are separated. The main impact of this strategy is what we call the "two-part-tariff effect": Imposing a small bundled membership fee on top of any transaction fees always leads to zero first-order losses in the demand of consumers who use both services, thus enabling the platform to extract more surplus from them. When this positive effect dominates the losses in demand from single-service users, hybrid bundling dominates unbundled sales. We present general conditions that guarantee such an outcome. In the second part of the thesis, we show that the two-part-tariff effect still applies when such tariffs are used in a more general context of multiproduct pricing. We consider a monopolist provider of n (> 1) products who uses two-part tariffs consisting of a membership fee that is common to all consumers, and separate prices for different product bundles. We show that the change in demand for any bundle of k Epsilon [1, n] products caused by imposing an extra membership fee on top of any separate pricing strategy is proportional to the membership fee to the power of k. Therefore a small extra membership fee has no first-order impact on the demand for any multiproduct bundles, which enables the firm to extract more consumer surplus. When this positive effect dominates the loss of single-product demand, two-part tariff dominates separate pricing. We present conditions that guarantee such an outcome, which generalize McAfee, McMillan and Whinston (1989)'s result from two products to multiple products. The two-part-tariff effect provides a new multiproduct perspective for the wide application of two-part tariffs, complementary to the classical "single-product" efficiency-related explanation. Our results suggest that two-part tariffs can achieve multidimensional price discrimination and should be subject to similar regulatory scrutiny as other discriminatory strategies, such as mixed bundling. The theories discussed in the first two parts address market situations where participants face deterministic decision problems. However, many if not most decision making processes involve uncertainty. The third part of the thesis focuses on people's economic behavior in risky choice situations. In this context, the cumulative prospect theory (CPT) by Tversky and Kahneman (1992) has been accepted as one of the best descriptive models that reconcile, within one unified model, the major phenomena that violate standard utility models. However, the inverse S-shaped weighting of cumulative probabilities posited in CPT causes difficulties in preference representation, which hinders its application in wider situations of risky choice. We propose a simplified weighting function for CPT, the (Beta, c) model, which plays a similar role in models with risky choice as that of the quasihyperbolic discounting function in models with intertemporal choice. The (Beta, c) model has a weighting function that is linear with slope smaller than 1 on the open interval (0, 1), jumps down to 0 at end point 0, and jumps up to 1 at end point 1. It achieves highly tractable utility representation for CPT whilst preserving the basic tenets of CPT. It by construction can explain all four major phenomena of risky choice violating the standard model that CPT was developed to reconcile, including reference dependence and certainty effect. It also allows Bayesian updating (with distortions at certainty) which CPT cannot accommodate. We systematically examine the (Beta, c) representation of discrete and continuous lotteries, and provide four applications which illustrate that the (Beta, c) model is a useful work horse to analyze implications of preferences exhibiting certainty effect and reference dependence in standard models. More detailed critical discussions are provided in each part of the thesis

The Relationship between Market structure and innovation in industry equilibrium: a case study of the global automobile industry

We specify and estimate a dynamic game to study the equilibrium relationship between market structure and innovation in the automobile industry. The quality of each firm’s product for the average consumer, the key state variable, is modeled as stochastically increasing in innovation,the dynamic control, which is proxied by patent applications. Equilibrium innovation is a function of market structure, the vector of quality levels of all active firms, and the cost of R&D. Our main findings are as follows:(a) optimal innovation has an inverted-U shape in own quality; (b) holding own quality constant, innovation is declining in average rival quality but increasing in quality dispersion; and (c) following entry, each incumbent’s innovation declines, but aggregate innovation increases in most market structures. These findings are broadly consistent with the Schumpeterian hypothesis that market power leads to more innovation.status: publishe

Hospital efficiency analysis through individual effects: A Bayesian approach

Monte Carlo Technique;Hospitals;Bayesian Statistics;Markov Chains;Panel Data

Dynamic Price Competition: Theory and Evidence from Airline Markets

We introduce a model of dynamic pricing in perishable goods markets with competition and provide conditions for equilibrium uniqueness. Pricing dynamics are rich because both own and competitor scarcity affect future profits. We identify new competitive forces that can lead to misallocation due to selling units too quickly: the Bertrand scarcity trap. We empirically estimate our model using daily prices and bookings for competing U.S. airlines. We compare competitive equilibrium outcomes to those where firms use pricing heuristics based on observed internal pricing rules at a large airline. We find that pricing heuristics increase revenues (4-5%) and consumer surplus (3%)