The Second Fundamental Theorem of Welfare Economics and the Existence of Competitive Equilibrium over an Infinite Horizon with General Consumption Sets

The purpose of this paper is to prove the second fundamental theorem of welfare economics and the existence of competitive equilibrium in production economies over an infinite horizon with general consumption sets. In the literature of the studies for an economy of infinite dimmentional commodity space, the second fundamental theorem of welfare economics was proved only approximately with uniform properness that is an assumption on consumers' preferences. The existence of competitive equilibrium was also shown under the assumption. However, when we turn to the study of the long run path of the economy, especially of sustainable growth, the assumption that uniformly bounds the rate of substitution among goods is inconsistent with some important preferences of growth theory. We proved the both theorems without uniform properness. The irreducibility of an economy and aggregate adequacy assumption plays the key role. Our model follows Boyd-McKenzie(1993) and generalize their strong irreducibility asuumption on the economy to the usual irreducibility.

The role of hypoxia and complement receptor 2 or toll-like receptor 2 on B1 B cell effector function

Master of ScienceDivision of BiologySherry D. FlemingProfessional phagocytes play a critical role in maintaining homeostasis within a host through phagocytic, microbicidal, and inflammatory activity. Complement receptors (CR) and toll-like receptors (TLRs) aid in phagocytosis and stimulate these cells to enhance the immune response. Environmental factors such as hypoxia, prevalent at sites of tissue damage or infection, induce a similar effect. Systemic components such as opsonins may further enhance phagocyte activity. Similar to professional phagocytes, B1 B cells exhibit a broad range of immunological activity as well as expression of CRs and TLRs. Despite extensive studies with other phagocytes, the effects of CRs and TLRs expression, hypoxic stimulation, or opsonization on B1 B cell function remain unclear. We tested the hypothesis that TLR2 stimulation, hypoxia, CR2 expression, or opsonins would enhance B1 B cell phagocytic and inflammatory activity. Negatively selected peritoneal cavity B1 B cells from the (PerC) of wild type, Tlr2[superscript]-[superscript]/[superscript]-, and Cr2[superscript]-[superscript]/[superscript]- mice, or a B1 B-like cell line, Wehi 231, were subjected to normoxia or hypoxia with or without particles for phagocytosis, TLR2 agonists, or CR2 ligands. The PerC of Tlr2[superscript]-[superscript]/[superscript]- mice contained an altered B1 B cell subset distribution while Cr2[superscript]-[superscript]/[superscript]- mice exhibited a normal repertoire. We demonstrated that hypoxia significantly downregulated inflammatory cytokine production by B1 B cells, while upregulating phagocytic activity in a TLR2 or CR2 dependent manner. TLR2 or CR2 deficiency altered constitutive production of B1 B cell associated cytokines. The CR2 ligand C3d, an opsonin, significantly enhanced the phagocytic activity of B1 B cells but failed to stimulate cytokine production. However, Cr2[superscript]-[superscript]/[superscript]- B1 B cells phagocytosed C3d-coated particles suggesting multiple CR may play a role in B1 B cell phagocytosis. Overall, the data suggest TLRs, CRs, hypoxia, and opsonization all contribute to B1 B cell effector function similar to professional phagocytes