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Dynamic advertising and pricing with constant demand elasticities

机译:具有恒定需求弹性的动态广告和定价

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In this paper we analyze a stochastic dynamic advertising and pricing model with isoelastic demand. The state space is discrete, time is continuous and the planing horizon is allowed to be finite or infinite. A dynamic version of the Dorfman-Steiner identity will be derived. Explicit expressions of the optimal advertising and pricing policies, of the value function and of the optimal advertising expenditures will be given. The general results will be used to analyze the case of impatient customers. Furthermore, particular time inhomogeneous models and homogeneous ones with and without discounting will be examined. We will study the social efficiency of a monopolist's optimal policies and the consequences of specific subsidies. From a buyer's perspective, our analysis reveals that waiting - when looking at (immediate) expected prices - is never profitable should two or more units be available. But we will also prove that the sequence of average sales prices is monotone decreasing. Moreover, the techniques applied to solve the discrete stochastic advertising and pricing problem will be used to solve a related deterministic control problem with continuous state space.
机译:在本文中,我们分析了具有等弹性需求的随机动态广告和定价模型。状态空间是离散的,时间是连续的,并且平面范围可以是有限的或无限的。将导出动态版本的Dorfman-Steiner身份。将给出最佳广告和定价政策,价值函数和最佳广告支出的明确表示。总体结果将用于分析不耐烦客户的情况。此外,将检查特定时间的非均质模型和带或不带折扣的均质模型。我们将研究垄断者最优政策的社会效率以及特定补贴的后果。从买方的角度来看,我们的分析表明,等待(当看(即时)预期价格时)如果有两个或更多的可用单元永远不会盈利。但是,我们还将证明平均销售价格的序列是单调递减的。此外,用于解决离散随机广告和定价问题的技术将用于解决具有连续状态空间的相关确定性控制问题。

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