Monopolists and Viscous Demand

We characterize the optimal dynamic price policy of a monopolist who faces "viscous" demand for its services. Demand is viscous if it adjusts relatively slowly to price changes. We show that with the optimal policy the monopolist stops short of achieving 100% market penetration, even when all of the consumers have the same long-run willingness to pay for the service. Furthermore, for certain parameter values in the model, the price policy requires rapid oscillations of the price path.Information Systems Working Papers Serie

Viscous Demand

In many markets, demand adjusts slowly to changes in prices, i.e., demand is "viscous." For such a market, the time path of a firm's prices acquires added significance, compared with the case of instantaneous demand response. In this paper I explore some problems in strategic dynamic pricing of a service, in the presence of viscous demand, for simple models of a monopoly and a duopoly.Information Systems Working Papers Serie

Lock in and Switch: Asymmetric Information and New Product Diffusion

Many new web-based services are introduced as free services. Depending on the seller’s business model, some remain free in the long run, while others switch to pay mode at some point in time. I characterize the relation between buyers and a new service seller when the former are uncertain about the latter’s business model. I derive a natural signalling equilibrium where the seller plays a “lock-in-and-switch” strategy, while buyers play a “wait-and-see” strategy. I show the equilibrium entails diffusion even though consumers are identical and equally aware of the new service’s existence

Dynamic Pricing of Network Goods with Boundedly Rational Consumers

We present a model of dynamic monopoly pricing for a good that displays network effects. In contrast with the standard notion of a rational-expectations equilibrium, we model consumers as boundedly rational, and unable either to pay immediate attention to each price change, or to make accurate forecasts of the adoption of the network good. Our analysis shows that the sellerâÂÂs optimal price trajectory has the following simple structure: the price is zero when the product user base is below a specific threshold, and is chosen to keep user base stationary once this threshold demand level has been attained. We show that our prescribed pricing policy is robust to a number of extensions, which include the productâÂÂs user base evolving over time, a fraction of consumers being sufficiently rational to make accurate adoption forecasts, and consumers basing their choices on a mixture of a myopic and a "stubborn" expectation of adoption. Our results differ significantly from those that would be predicted by a model based on rational-expectations equilibrium, and are more consistent with the pricing of network goods observed in practice.Information Systems Working Papers Serie

Dynamic Duopoly with Differentiated Goods and Sluggish Demand

This thesis investigates dynamic Bertrand competition between two firms in a market where the goods are differentiated and demand is sluggish. Unlike homogeneous goods, differentiated goods are not perfect substitutes for each other. Sluggish demand means that there is a delay in the adjustment of demand after price changes. Sluggish demand is a remarkably ignored topic in the economic literature. The competitive situation is modelled as a differential game. The dynamic model employs the demand system as in Singh and Vives 1984 and dynamics as in Wirl 2010. It is shown that the dynamic model has a unique symmetric open-loop Nash equilibrium. The long-term open-loop steady state is compared with the equilibrium point of the static model. The fundamental mathematical theory and solution methods of optimal control theory and differential games that are required in the analysis of the model are also presented in the thesis. As the main result of the analysis of the model, it is shown that when sluggishness of demand is relatively small (i.e. the adjustment of demand after price changes is sufficiently fast), sluggishness of demand increases the market power and profits of the firms in the open-loop steady state compared to the equilibrium point of the static model. After sluggishness of demand exceeds a certain point, the profits of the firms decline below the static equilibrium profits. Moreover, it is shown that product differentiation relaxes price competition also in the presence of sluggish demand, as it does in a static model.Tutkielmassa tarkastellaan kahden yrityksen välistä dynaamista Bertrand-kilpailua markkinoilla, joilla hyödykkeet ovat differoituja ja kysyntä on jäykkää. Toisin kuin homogeeniset hyödykkeet, differoidut hyödykkeet eivät ole täydellisiä korvikkeita toisilleen. Kysynnän jäykkyys tarkoittaa sitä, että kysyntä sopeutuu viiveellä hinnanmuutoksiin. Kysynnän jäykkyys on yllättävän vähälle huomiolle jäänyt aihe taloustieteellisessä kirjallisuudessa. Kilpailutilanne mallinnetaan differentiaalisena pelinä. Dynaamisen mallin kysyntäjärjestelmä on kuten Singh ja Vivesin (1984) ja dynamiikka kuten Wirlin (2010) artikkelissa. Dynaamisella mallilla osoitetaan olevan uniikki symmetrinen open-loop Nash -tasapainostrategia. Pitkän aikavälin open-loop -tasapainopistettä vertaillaan staattisen Bertrand-mallin tasapainopisteen kanssa. Tutkielmassa esitetään lisäksi mallin tarkasteluun vaadittavan optimaalisen kontrolliteorian ja differentiaalisten pelien keskeinen matemaattinen teoria ja ratkaisumenetelmät. Mallin analyysin päätuloksena osoitetaan, että kun kysynnän jäykkyys on verrattain pientä (ts. kysynnän sopeutuminen hinnanmuutoksiin on riittävän nopeaa), kysynnän jäykkyys lisää yritysten markkinavoimaa ja voittoja open-loop -tasapainopisteessä verrattuna staattiseen tasapainopisteeseen. Kun kysynnän jäykkyys ylittää tietyn pisteen, yritysten voitot laskevat staattisten tasapainovoittojen alle. Lisäksi osoitetaan, että tuotedifferointi pehmentää hintakilpailua myös kysynnän jäykkyyden olosuhteissa, aivan kuten staattisessa mallissa

Dynamic Pricing of Network Goods with Boundedly Rational Consumers

We present a model of dynamic monopoly pricing for a good that displays network effects. In contrast with the standard notion of a rational-expectations equilibrium, we model consumers as boundedly rational, and unable either to pay immediate attention to each price change, or to make accurate forecasts of the adoption of the network good. Our analysis shows that the seller's optimal price trajectory has the following structure: the price is low when the user base is below a target level, is high when the user base is above the target, and is set to keep user base stationary once the target level has been attained. We show that this pricing policy is robust to a number of extensions, which include the product's user base evolving over time, and consumers basing their choices on a mixture of a myopic and a "stubborn" expectation of adoption. Our results differ significantly from those that would be predicted by a model based on rational-expectations equilibrium, and are more consistent with the pricing of network goods observed in practice.New York University Stern School of Business; Pomona College, Claremont, C

Dynamic Pricing of Network Goods with Boundedly Rational Consumers

We present a model of dynamic monopoly pricing for a good that displays network effects. In contrast with the standard notion of a rational-expectations equilibrium, we model consumers as boundedly rational, and unable either to pay immediate attention to each price change, or to make accurate forecasts of the adoption of the network good. Our analysis shows that the sellerâÂÂs optimal price trajectory has the following simple structure: the price is zero when the product user base is below a specific threshold, and is chosen to keep user base stationary once this threshold demand level has been attained. We show that our prescribed pricing policy is robust to a number of extensions, which include the productâÂÂs user base evolving over time, a fraction of consumers being sufficiently rational to make accurate adoption forecasts, and consumers basing their choices on a mixture of a myopic and a "stubborn" expectation of adoption. Our results differ significantly from those that would be predicted by a model based on rational-expectations equilibrium, and are more consistent with the pricing of network goods observed in practice.Information Systems Working Papers Serie

Dynamic Pricing of Network Goods with Boundedly Rational Consumers

We present a model of dynamic monopoly pricing for a good that displays network effects. In contrast with the standard notion of a rational-expectations equilibrium, we model consumers as boundedly rational, and unable either to pay immediate attention to each price change, or to make accurate forecasts of the adoption of the network good. Our analysis shows that the seller's optimal price trajectory has the following structure: the price is low when the user base is below a target level, is high when the user base is above the target, and is set to keep user base stationary once the target level has been attained. We show that this pricing policy is robust to a number of extensions, which include the product's user base evolving over time, and consumers basing their choices on a mixture of a myopic and a "stubborn" expectation of adoption. Our results differ significantly from those that would be predicted by a model based on rational-expectations equilibrium, and are more consistent with the pricing of network goods observed in practice.New York University Stern School of Business; Pomona College, Claremont, C

Emerging Operational Contracts in Competitive Markets.

This dissertation consists of three essays, each dealing with an emerging type of operational contracts. The first essay considers a resource exchange model where the effects of collaboration and competition are intertwined. Exchanging resources often improves utilization and is intended to increase profitability of involved firms. However, it does not guarantee success in competitive settings. More efficient use of resources might actually leads to increased competition. We explore how resource exchange contracts impact the firms and consumers. The results indicate that the resource exchange tends to benefit both firms and the consumers in most situations, except for the extreme situations where simultaneously competition is strong and the purchasing cost is either very low or very high. The second essay focuses on vertical pricing control contracts that manufacturers use to coordinate online and offline retailers. Resale Price Maintenance (RPM) policy requires all retailers to sell at the price suggested by manufacturers. Minimum Advertised Price (MAP) policy is less strict, as it allows retailers to sell at lower prices than the manufacturer suggested, as long as these lower prices are not advertised. This essay studies which of these two policies is more beneficial to each member of the supply chain. We show that manufacturers prefer MAP policy when the customers' valuations vary significantly and the information search requires significant effort. The MAP policy is also favorable to retailers and consumers under similar market conditions. The third essay concerns the contractual issues when energy service companies (ESCOs) provide energy efficiency projects to residential clients. While performance based contracts have been proven successful in public, commercial, and industrial sectors, ESCOs face challenges in the residential sector. Residential clients often change consumption behavior after the project, which makes the real energy savings difficult to measure. Additionally, residential clients are much more risk averse and vulnerable to uncertain outcomes of projects. We show that piecewise linear contracts perform reasonably well. To further improve profitability, ESCOs can either reduce uncertainty of technology involved or develop the ability to verify post-project energy efficiency. We also make recommendations in monetary incentives and regulations from policy makers' perspective.PhDBusiness AdministrationUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133457/1/lgding_1.pd