1. Provide a definition for the certainty equivalent level of consumption for the simple lottery described above.
1. Provide a definition for the certainty equivalent level of consumption for the simple lottery described above.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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![Consider the lottery that assigns a probability 7 of obtaining a level of consumption C
and a probability 1-7 of obtaining a low level of consumption c1, with CH > C1. Consider
an individual facing such a lottery with utility function u(c) that has the properties that
more is better (that is, a strictly positive marginal utility of consumption at all levels of
c) and diminishing marginal utility of consumption, u"(c) < 0. As usual, we are using
the shorthand u'(c) = du@ for the first derivative of the utility function with respect to
du' (c) to be the second derivative of the utility function
consumption and u"(c) = Puc)
(which is also the derivative of the first derivative of the utility function).
de
1. Provide a definition for the certainty equivalent level of consumption for the simple
lottery described above.
2. Using the definition of the certainty equivalent level of consumption provide an
expression for the ratio,
u(Cce) u(€L)
u(cH) u(c1)*
3. Define the risk premium p = č – Cee where č = rCH + (1 – 7)c, is the expected
level of consumption from the lottery (7 = E[c]). Consider the following exercise.
There are three lotteries characterized by different probabilities of obtaining cH -
Let these probabilities be given by a" > n' > a. Using a single diagram, plot the
risk premium for each of these three lotteries. Does the risk premium increase or
decrease as we increase a across these three lotteries? Provide the intuition for
your result.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe7a1c65f-28b5-42a1-ba29-b0e05a0006b8%2F5b98177e-a140-4ecf-bffe-e146d4a5836a%2Fv5cwj28_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the lottery that assigns a probability 7 of obtaining a level of consumption C
and a probability 1-7 of obtaining a low level of consumption c1, with CH > C1. Consider
an individual facing such a lottery with utility function u(c) that has the properties that
more is better (that is, a strictly positive marginal utility of consumption at all levels of
c) and diminishing marginal utility of consumption, u"(c) < 0. As usual, we are using
the shorthand u'(c) = du@ for the first derivative of the utility function with respect to
du' (c) to be the second derivative of the utility function
consumption and u"(c) = Puc)
(which is also the derivative of the first derivative of the utility function).
de
1. Provide a definition for the certainty equivalent level of consumption for the simple
lottery described above.
2. Using the definition of the certainty equivalent level of consumption provide an
expression for the ratio,
u(Cce) u(€L)
u(cH) u(c1)*
3. Define the risk premium p = č – Cee where č = rCH + (1 – 7)c, is the expected
level of consumption from the lottery (7 = E[c]). Consider the following exercise.
There are three lotteries characterized by different probabilities of obtaining cH -
Let these probabilities be given by a" > n' > a. Using a single diagram, plot the
risk premium for each of these three lotteries. Does the risk premium increase or
decrease as we increase a across these three lotteries? Provide the intuition for
your result.
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