Dynamic advertising and pricing with constant demand elasticities

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.     

Attitude toward imprecise information

This paper presents an axiomatic model of decision making under uncertainty which incorporates objective but imprecise information. Information is assumed to take the form of a probability–possibility set, that is, a set P of probability measures on the state space. The decision maker is told that the true probability law lies in P and is assumed to rank pairs of the form (P,f) where f is an act mapping states into outcomes. The key representation result delivers maxmin expected utility (MEU) where the min operator ranges over a set of probability priors—just as in the MEU representation result of Gilboa and Schmeidler [Maxmin expected utility with a non-unique prior, J. Math. Econ. 18 (1989) 141–153]. However, unlike the MEU representation, the representation here also delivers a mapping, , which links the probability–possibility set, describing the available information, to the set of revealed priors. The mapping is shown to represent the decision maker's attitude to imprecise information: under our axioms, the set of representation priors is constituted as a selection from the probability–possibility set. This allows both expected utility when the selected set is a singleton and extreme pessimism when the selected set is the same as the probability–possibility set, i.e., is the identity mapping. We define a notion of comparative imprecision aversion and show it is characterized by inclusion of the sets of revealed probability distributions, irrespective of the utility functions that capture risk attitude. We also identify an explicit attitude toward imprecision that underlies usual hedging axioms. Finally, we characterize, under extra axioms, a more specific functional form, in which the set of selected probability distributions is obtained by (i) solving for the “mean value” of the probability–possibility set, and (ii) shrinking the probability–possibility set toward the mean value to a degree determined by preferences.     

Advertising, Its Determinants, and Market Structure

This study derives a formal model of firm advertising behavior and applies it to the industry level to figure out the relationship between advertising and market structure. The firm advertising model shows that both consumer preference andfirm-specific advertising competence jointly determineprofit-maximizing advertising intensity. At the industry level, advertising intensity is represented multiplicatively by consumer preference and a measure of market structure, which reflects the joint distribution of the levels of advertising competence and market shares among firms. The new market structure measure suggests that those single-dimensional measures of market structure such as seller concentration and the Herfindahl index are inadequate in explaining interindustry differences in advertising intensity, and that the long-debated advertising-concentration relationship differs depending primarily on the appropriability of advertising. An empirical analysis of 426 five-digit Korean manufacturing industries shows that an inverted U-shaped relationship between the Herfindahl index and industry advertising intensity is observed for consumer goods industries but a lazy J-shaped relationship for producer goods industries.     

The evolution of futures in school education

School education seems to be mostly stuck in an outdated industrial era worldview, unable to sufficiently address the significance and increasing rapidity of changes to humanity that are upon us. An integrated forward-looking view should, now more than ever, be of central importance in how we educate. Yet there is little sign that—unlike corporations—school systems are recognising the true value of futures studies. A brief history of futures in school education shows the significant role played by the World Futures Studies Federation in its evolution to date. The article also introduces integral analysis as a way of opening up new possibilities to help school education develop due foresight and to more fully realise its potential as a prime facilitator in individual and cultural evolution.     

Minimum cost spanning tree problems with indifferent agents

We consider an extension of minimum cost spanning tree (mcst) problems in which some agents do not need to be connected to the source, but might reduce the cost of others to do so. Even if the cost usually cannot be computed in polynomial time, we extend the characterization of the Kar solution (Kar, 2002) for classic mcst problems. It is obtained by adapting the Equal treatment property: if the cost of the edge between two agents changes, their cost shares are affected in the same manner if they have the same demand. If not, their changes are proportional to each other. We obtain a family of weighted Shapley values. Three interesting solutions in that family are characterized using stability, fairness and manipulation-proofness properties.     

Advertising and Steiner’s Dual Stage Model: Our Assessment

Between 1967 and 1979, we produced a number of studies that explored different facets of the economics of advertising. This work culminated in our 1974 book entitled Advertising and Market Power. Our leading hypothesis was that heavy advertising expenditures often but not always had anti‐competitive effects. And our primary empirical evidence in support of this hypothesis was that industries with heavy advertising expenditures also reported higher profit rates, which we interpreted as indicating that higher prices followed when manufacturers can effectively spend large amounts on advertising. Since that time, Robert Steiner has developed a model of firm behaviour for consumer goods industries. He finds that distribution margins are generally higher where manufacturer prices are lower. Furthermore, heavy manufacturer advertising is likely to depress distribution margins for heavily advertised products. While our earlier work implicitly assumed that distribution margins are generally the same regardless of the volume of advertising, Steiner’s results raise doubt on this assumption. Steiner’s model must therefore be acknowledged when interpreting our earlier findings.     

Optimal generic advertising in an imperfectly competitive food industry with variable proportions⋆

This paper determines the impact of food industry market power on farmers' incentives to promote in a situation where funds for promotion are raised through a per‐unit assessment on farm output and food industry technology is characterized by variable proportions. Specifically, building on earlier studies by Azzam [Am. J. Agric. Econ. 80 (1998) 76] and Holloway [Am. J. Agric. Econ. 73 (1991) 979], Muth's [Oxford Econ. Papers 16 (1965) 221] model is extended to consider the farm‐level impacts of generic advertising when downstream firms possess oligopoly and/or oligopsony power and advertising expenditure is endogenous at the market level. Applying the model to the US beef industry, we find that for plausible parameter values market power reduces farmers' incentives to promote. However, the disincentive is moderated by factor substitution, and effectively vanishes as the factor substitution elasticity approaches the retail demand elasticity. This suggests that the Dorfman–Steiner theorem, suitably modified to account for factor substitution, suffices to indicate optimal advertising intensity in the US beef sector.     

WDM全光网中的多播路由算法研究

研究了WDM全光网中多播路由的问题,并给出一种满足时延约束的多播路由与波长分配算法,此算法是在Chlam tac[2]等人提出的波长图的基础上,将路由与波长分配统一进行,构造了时延受限低代价多播树,克服了将寻径和波长分配分步进行的弊端,具有较低的时间复杂度,避免了同类算法的较高复杂性。