Problem set # 2. Risk, expected utility, and loss aversion Due date: March 7I. Assume a household whose utility is neo-classical, U(x). Therealized income is random, high or low:probability 0.5[x₁ = Y(1+),x₁ = {x₂ = Y(1-8), probability 0.5'where & > 0 is the realized shock.Find the cost of volatility, measured by insurance that the household iswilling to pay, r, such that U(Y(1-7)) = E(U(x)),where E(U(x)) is the expected utility in the absence of insurance.Hint: this question can be solved graphically by looking at a chart of U'(x), themarginal utility as a function of income x, see the chart below. To simplify notation,assume normalized utility such that U(1) = U'(1) = 1.U'(x)1-1 1+X II Redo question I for the case of a loss-averse household -- when thebad shock happens, the utility weight associated with the loss is magnifiedby the rate of disappointment, B. Thus, the 'expected utility' of a loss-averse household is V=0.5U[Y(1+ɛ)] +0.5(1+B)U[Y (1–ɛ)].Hint: the hint of question 1 applies also to question 2; one can solve theabove graphically, or assume that U(x) = ln (x).III. Assume that B= 2, &=0.05, Y = 1. Calculate the cost ofvolatility for risk-averse and loss-averse consumer described in the firsttwo questions.

Given information Realized High income with 0.5 probability=Y(1+e)--- e>0 realized shock Realized…

Problem set # 2. Risk, expected utility, and loss aversion Due date: March 7 I. Assume a household whose utility is neo-classical, U(x). The realized income is random, high or low: x = Y(1+E), probability 0.5 x₂ , where & > 0 is the realized shock. x₂ = Y(1-8), probability 0.5' Find the cost of volatility, measured by insurance that the household is willing to pay, T, such that U(Y(1-7)) = E(U(x)), where E(U(x)) is the expected utility in the absence of insurance. Hint: this question can be solved graphically by looking at a chart of U'(x), the

Problem set # 2. Risk, expected utility, and loss aversion Due date: March 7 I. Assume a household whose utility is neo-classical, U(x). The realized income is random, high or low: x = Y(1+E), probability 0.5 x₂ , where & > 0 is the realized shock. x₂ = Y(1-8), probability 0.5' Find the cost of volatility, measured by insurance that the household is willing to pay, T, such that U(Y(1-7)) = E(U(x)), where E(U(x)) is the expected utility in the absence of insurance. Hint: this question can be solved graphically by looking at a chart of U'(x), the

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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