Dynamic pricing with constant demand elasticity

The model of Gallego and van Ryzin (1994) is specialized to the case of constant elasticity of demand. A closed form is developed, which has an even simpler form than that arising with exponential demand, and possesses an excellent approximation. It is shown in this environment that monopoly is efficient, which means that all the behavior usually attributed to monopoly pricing is actually a consequence of efficient pricing and would arise even in a perfectly competitive environment. If the initial supply is not too large, it is shown that consumers have no incentive to delay their purchases in order to get a lower price at the average inventory prevailing at any time

Optimal monopoly investment and capacity utilization under random demand

Unique value-maximizing programs of irreversible capacity investment and capacity utilization are described and shown to exist under general conditions for monopolist exhibiting capital adjustment costs and serving random consumer demand for a nondurable good over an infinite horizon. Stationary properties of these programs are then fully characterized under the assumption of serially independent demand disturbances. Optimal monopoly behavior in this case includes acquisition of a constant and positive level of capacity, the maintenance of a positive expected value of excess capacity in each period, and an asymmetrical response of price to unanticipated fluctuations in consumer demand. Under a general form of Markovian demand, the effect of uncertainty on irreversible capacity investment is also described in terms of the discounted flow of expected revenue accruing to the marginal unit of existing capacity and the option value of deferring the acquisition of additional capital. The option value of deferring such acquisition, created by the irreversibility of capacity investment, is characterized directly in terms of the value function of the firm, and is then shown to be zero in a stationary equilibrium with serially independent demand disturbances. The response of investment to increase demand uncertainty depends, as a result, directly on the properties of the marginal revenue product of capital. A non-negative response of optimal capacity to increased uncertainty in market demand is demonstrated for a general class of aggregate consumer preferences.Industrial capacity

Modeling Electricity Markets as Two-Stage Capacity Constrained Price Competition Games under Uncertainty

The last decade has seen an increasing application of game theoretic tools in the analysis of electricity markets and the strategic behavior of market players. This paper focuses on the model examined by Fabra et al. (2008), where the market is described by a two-stage game with the firms choosing their capacity in the first stage and then competing in prices in the second stage. By allowing the firms to endogenously determine their capacity, through the capacity investment stage of the game, they can greatly affect competition in the subsequent pricing stage. Extending this model to the demand uncertainty case gives a very good candidate for modeling the strategic aspect of the investment decisions in an electricity market. After investigating the required assumptions for applying the model in electricity markets, we present some numerical examples of the model on the resulting equilibrium capacities, prices and profits of the firms. We then proceed with two results on the minimum value of price caps and the minimum required revenue from capacity mechanisms in order to induce adequate investments

Monopoly Pricing of Experience Goods

We develop a dynamic model of experience goods pricing with independent private valuations. We show that the optimal paths of sales and prices can be described in terms of a simple dichotomy. In a mass market, prices are declining over time. In a niche market, the optimal prices are initially low followed by higher prices that extract surplus from the buyers with a high willingness to pay. We consider extensions of the model to integrate elements of social rather than private learning and turnover among buyers.Monopoly, dynamic pricing, learning, experience goods, continuous time, Markov perfect equilibrium

Auctioning of EU ETS Phase II allowances: how and why?

The European Directive on the EU ETS allows governments to auction up to 10% of the allowances issued in phase II 2008-2012, without constraints being specified thereafter. This article reviews and extends the long-standing debate about auctioning, in which economists have generally supported and industries opposed a greater use of auctioning. The article clarifies the key issues by reviewing six `traditional' considerations, examines several credible options for auction design, and then proposes some new issues relevant to auctioning. It is concluded that greater auctioning in aggregate need not increase adverse competitiveness impacts, and could in some respects alleviate them, particularly by supporting border-tax adjustments. Auctioning within the 10% limit might also be used to dampen price volatility during 2008-2012 and, in subsequent periods, it offers the prospect of supporting a long-term price signal to aid investor confidence. The former is only possible, however, if Member States are willing to coordinate their decision-making (though not revenue-raising) powers in defining and implementing the intended pricing mechanisms

Investment and Pricing with Spectrum Uncertainty: A Cognitive Operator's Perspective

This paper studies the optimal investment and pricing decisions of a cognitive mobile virtual network operator (C-MVNO) under spectrum supply uncertainty. Compared with a traditional MVNO who often leases spectrum via long-term contracts, a C-MVNO can acquire spectrum dynamically in short-term by both sensing the empty "spectrum holes" of licensed bands and dynamically leasing from the spectrum owner. As a result, a C-MVNO can make flexible investment and pricing decisions to match the current demands of the secondary unlicensed users. Compared to dynamic spectrum leasing, spectrum sensing is typically cheaper, but the obtained useful spectrum amount is random due to primary licensed users' stochastic traffic. The C-MVNO needs to determine the optimal amounts of spectrum sensing and leasing by evaluating the trade off between cost and uncertainty. The C-MVNO also needs to determine the optimal price to sell the spectrum to the secondary unlicensed users, taking into account wireless heterogeneity of users such as different maximum transmission power levels and channel gains. We model and analyze the interactions between the C-MVNO and secondary unlicensed users as a Stackelberg game. We show several interesting properties of the network equilibrium, including threshold structures of the optimal investment and pricing decisions, the independence of the optimal price on users' wireless characteristics, and guaranteed fair and predictable QoS among users. We prove that these properties hold for general SNR regime and general continuous distributions of sensing uncertainty. We show that spectrum sensing can significantly improve the C-MVNO's expected profit and users' payoffs.Comment: A shorter version appears in IEEE INFOCOM 2010. This version has been submitted to IEEE Transactions on Mobile Computin

"On the Determinants of Exporters' Currency Pricing: History vs. Expectations"

The purpose of this paper is to investigate why the choice of invoice currency under exchange rate uncertainty depends not only on expectations but also on history. The analysis is motivated by the fact that the U.S. dollar has historically been the dominant vehicle currency in developing countries. The theoretical analysis is based on an open economy model of monopolistic competition. When the market is competitive enough, the exporting firms tend to set their prices not to deviate from those of the competitors. As a result, a coordination failure can lead the third currency to be a less efficient equilibrium invoice currency. The role of expectations is important in selecting the equilibrium in the static framework. However, in the dynamic model with staggered price-setting, the role of history becomes another key determinant of the equilibrium currency pricing. The role of history may dominate the role of expectations when the firms are myopic, particularly in the competitive local market. It also becomes dominant in the staggered price setting when a small fraction of the new price setters are backward-looking. The result suggests the importance of history in explaining why the firm tends to choose the US dollar as vehicle currency.