Dynamic Economic Decision Making

This chapter presents dynamic optimization for economic decision making in the context of both dynamic cost minimization and dynamic profit maximization given different primal representations of the dynamic technology. The Bellman equation of dynamic programming serves as the analytical foundation for the duality between the production technology and the economic value function. The dynamic duality relationships in the form of intertemporal versions of Hotelling’s and Shephard’s lemmas are presented. The chapter concludes with the data envelopment perspective of the dynamic decision-making framework. Allowing the data to reveal the nature of the production technology, both the input and output quantities can be used to reveal the inner bound of the technology. Alternatively, the technological information can be recovered by exploiting the dynamic cost minimization behavior using input prices and input and output quantities, to reveal the outer bound of the input requirement set.

Focal Point Theory Models for Dissecting Dynamic Duality Problems of Microbial Infections

Extending along the dynamic continuum from conflict to cooperation, microbial infections always involve symbiosis (Sym) and pathogenesis (Pat). There exists a dynamic Sym-Pat duality (DSPD) in microbial infection that is the most fundamental problem in infectomics. DSPD is encoded by the genomes of both the microbes and their hosts. Three focal point (FP) theory-based game models (pure cooperative, dilemma, and pure conflict) are proposed for resolving those problems. Our health is associated with the dynamic interactions of three microbial communities (nonpathogenic microbiota (NP) (Cooperation), conditional pathogens (CP) (Dilemma), and unconditional pathogens (UP) (Conflict)) with the hosts at different health statuses. Sym and Pat can be quantitated by measuring symbiotic index (SI), which is quantitative fitness for the symbiotic partnership, and pathogenic index (PI), which is quantitative damage to the symbiotic partnership, respectively. Symbiotic point (SP), which bears analogy to FP, is a function of SI and PI. SP-converting and specific pathogen-targeting strategies can be used for the rational control of microbial infections.

Intergenerational equity and dynamic duality principles

The concept of intergenerational equity concerning intertemporal paths of consumption and capital accumulation is introduced and the analysis of the dynamic processes of capital accumulation and changes in environmental quality that are intergenerationally equitable is developed. The analysis is based upon the dynamic duality principles, as originally developed by Koopmans and Uzawa, and later extended to the case involving environmental quality.A time-path of consumption and capital accumulation is defined intergenerationally equitable when it is dynamically efficient and, at the same time, the imputed price of each kind of capital, either private capital, or social overhead capital, is identical over time. The existence of an intergenerationally equitable time-path of consumption and capital accumulation is guaranteed when the processes of various kind of capital are subject to the Penrose effect, exhibiting the law of diminishing marginal rates of investment capital accumulation.