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1+ro alternative amount analysis assets assume assumption Axiom b₁ beginning of period bonds brand budget constraint budget line bundles cent certainty line characteristics choice commodity competitive equilibrium composite commodity constant consumer's preference consumption set corner solutions decrease defined demand curve demand theory diminishing marginal utility dx₁ earnings Econ Economic elasticity of substitution equal example expected utility expected utility hypothesis Figure given hold hypothesis implies income effect increase indifference class indifference curve individual marginal rate market demand functions P₁ Pareto criterion Pareto optimum partial derivatives portfolio positive preference ordering prospects purchases quantities quasi-substitution effect rate of interest rate of substitution ratio reader section 9.2 slope Slutzky equation state-preference straight line strictly convex substitution effect sumer Technical Appendix u₁ u₂ uncertainty utility function utility of money utility of wealth utility-of-wealth vector welfare economics x₁ and x2