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.

ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
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Chapter1: Making Economics Decisions
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Only answer a, b, and c

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.
Transcribed Image Text: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.
(c) Draw the corresponding budget set with axes corresponding to
consumption in state 1 and in state 2. In addition, make sure to
label the point where the individual purchase no insurance, and
the point where the individual purchases full insurance.
(d) Assuming that the expected utility function u: [0, 40000] → R is
strictly concave, give the formula for the corresponding expected
utility, 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 1
and 2 (₁ and ₂).
(f) Draw the indifference curves to illustrate this solution, making
sure to mark in the slope on the 45-degree line of any indifference
curves drawn.
Transcribed Image Text:(c) Draw the corresponding budget set with axes corresponding to consumption in state 1 and in state 2. In addition, make sure to label the point where the individual purchase no insurance, and the point where the individual purchases full insurance. (d) Assuming that the expected utility function u: [0, 40000] → R is strictly concave, give the formula for the corresponding expected utility, 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 1 and 2 (₁ and ₂). (f) Draw the indifference curves to illustrate this solution, making sure to mark in the slope on the 45-degree line of any indifference curves drawn.
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