This paper examines how, in the presence of individual risk, economic efficiency can be achieved without an unrealistically large number of contingent claims. Market uncertainty is specified in such a way that general types of individual risk and collective risk are properly accounted for and so that, specifically, market clearing is always satisfied ex post as well as ex ante . We show that consistency of beliefs and optimality of allocation can be guaranteed with an appropriate array of pure Arrow securities to spread collective risk and mutual insurance policies to pool individual risk . When there is individual risk common to like groups of individuals, pooling risk by means of mutual insurance permits substantial economizing on market transactions, as compared to those required if dealing instead with the full complement of pure Arrow securities . We show that if there are N households (consisting of H types), each facing the possibility of being in S individual states together with T collective states, then ensuring Pareto optimality requires only H(S -1)T independent mutual insurance policies plus T pure Arrow securities . Our results also help to clarify the question of which missing markets may affect allocational efficiency .
This paper describes the characterization and chromosomal distribution of three different rice (Oryza sativa) repetitive DNA sequences. The three sequences were characterized by sequence analysis, which gave 355, 498 and 756 bp for the length of the repeat unit in Os48, OsG3-498 and OsG5-756, respectively. Copy number determination by quantitative DNA slot-blot hybridization analysis showed 4000, 1080 and 920 copies, respectively, per haploid rice genome for the three sequences. In situ DNA hybridization analysis revealed that 95% of the silver grains detected with the Os48 probe were localized to euchromatic ends of seven long arms and one short arm out of the 12 rice chromosomes. For the OsG3-498 repetitive sequence, the majority of silver grains (58%) were also clustered at the same chromosomal ends as that of Os48. The minority (28%) of silver grains were located at heterochromatic short arms and centromeric regions. For the OsG5-756 repetitive sequence, 81% of the silver grains labeled the heterochromatic short arms and regions flanking all of the 12 centromeres. Thus, each of these three repetitive sequences was distributed at specific defined chromosomal locations rather than randomly at many chromosomal locations. The approximate copy number of a given repetitive DNA sequence at any specific chromosomal location was calculated by combining the information from in situ DNA hybridization analysis and the total copy number as determined by DNA slot-blot hybridization.
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