Only answer a, b, and c 3. For all of the following questions, consider a situation with two states ofthe world in which state 1 has probability = 1/3 and state 2 thereforehas probability 1 = 2/3. An individual is endowed with wealthof W = $40,000 in state 2, but faces a possible loss of L = $30,000in state 1, bringing wealth down to $10,000. Insurance is available: itcosts 50 cents up front for each $1 dollar of insurance paid out in state1.(a) Is the insurance actuarially fair or actuarially unfair?(b) Give the formula for consumption in each state if insurance payingout $Y in state 1 is purchased. (c) Draw the corresponding budget set with axes corresponding toconsumption in state 1 and in state 2. In addition, make sure tolabel the point where the individual purchase no insurance, andthe point where the individual purchases full insurance.(d) Assuming that the expected utility function u: [0, 40000] → R isstrictly concave, give the formula for the corresponding expectedutility, denoted V(Y), and write the first order condition to de-termine Y, the optimal level of insurance to purchase.(e) Solve the model to determine Ŷ for the special case of log utility,u(c) = Inc.Using this, find the optimal amount of consumption in states 1and 2 (₁ and ₂).(f) Draw the indifference curves to illustrate this solution, makingsure to mark in the slope on the 45-degree line of any indifferencecurves drawn.

(a) In the given scenario, there is a possibility of a loss in state 1 (the probability of state 1…

3. For all of the following questions, consider a situation with two states of the world in which state 1 has probability = 1/3 and state 2 therefore has probability 1 = 2/3. An individual is endowed with wealth of W = $40,000 in state 2, but faces a possible loss of L = $30,000 in state 1, bringing wealth down to $10,000. Insurance is available: it costs 50 cents up front for each $1 dollar of insurance paid out in state 1. (a) Is the insurance actuarially fair or actuarially unfair? (b) Give the formula for consumption in each state if insurance paying out $Y in state 1 is purchased.

3. For all of the following questions, consider a situation with two states of the world in which state 1 has probability = 1/3 and state 2 therefore has probability 1 = 2/3. An individual is endowed with wealth of W = $40,000 in state 2, but faces a possible loss of L = $30,000 in state 1, bringing wealth down to $10,000. Insurance is available: it costs 50 cents up front for each $1 dollar of insurance paid out in state 1. (a) Is the insurance actuarially fair or actuarially unfair? (b) Give the formula for consumption in each state if insurance paying out $Y in state 1 is purchased.

Brief Principles of Macroeconomics (MindTap Course List)

8th Edition

ISBN:9781337091985

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter9: The Basic Tools Of Finance

Section: Chapter Questions

Problem 5PA

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