Essays in the Theory of Risk-bearing

action activities amount argued argument assumed assumption behavior under uncertainty benefits and costs certainly choose commodity conditional distribution conditional probability distributions consequences consider cost of risk-bearing decisions decreasing defined demand discount discussion E₁ E₂ economic existence expected return expected utility expected value F₁ finite follows given Hence Hirshleifer hold hypothesis implies income increasing indifferent individual insurance policy law of large Lemma limited marginal utility Marschak maximize measure monotone decreasing moral hazard optimal allocation organization outcome output perfect competition physician possible potential surprise preferred price discrimination price system priori probabilities probability distribution probability measure problem production profits public investment random variable rate of return relative risk aversion risky asset Section secure asset sequence shift social statistical sufficiently large Suppose theorem tion utility function welfare welfare economics X₁ Y₁ yield zero