Consider the lottery that assigns a probability T of obtaining a level of consumption CH and a probability 1-7 of obtaining a low level of consumption cL with CH > CL. 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) dhue for the first derivative of the utility function with respect to dc du(c) dc2 du' (c) consumption and u"(c) = to be the second derivative of the utility function dc (which is also the derivative of the first derivative of the utility function)
Consider the lottery that assigns a probability T of obtaining a level of consumption CH and a probability 1-7 of obtaining a low level of consumption cL with CH > CL. 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) dhue for the first derivative of the utility function with respect to dc du(c) dc2 du' (c) consumption and u"(c) = to be the second derivative of the utility function dc (which is also the derivative of the first derivative of the utility function)
Principles of Microeconomics
7th Edition
ISBN:9781305156050
Author:N. Gregory Mankiw
Publisher:N. Gregory Mankiw
Chapter22: Frontiers Of Microeconomics
Section: Chapter Questions
Problem 6PA
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![Consider the lottery that assigns a probability r of obtaining a level of consumption CH
and a probability 1-T of obtaining a low level of consumption cL
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)
L with CH > CL. Consider
du(c)
for the first derivative of the utility function with respect to
dc
d²u(c)
dc2
du' (c)
consumption and u"(c)
which is also the derivative of the first derivative of the utility function).
to be the second derivative of the utility function
dc](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b714a0e-b01f-49d4-9d2a-b07b3adf1f36%2F800ad894-33a8-48cb-933b-8b8c05be7014%2Fahmc4ba_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the lottery that assigns a probability r of obtaining a level of consumption CH
and a probability 1-T of obtaining a low level of consumption cL
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)
L with CH > CL. Consider
du(c)
for the first derivative of the utility function with respect to
dc
d²u(c)
dc2
du' (c)
consumption and u"(c)
which is also the derivative of the first derivative of the utility function).
to be the second derivative of the utility function
dc
![2. Using the definition of the certainty equivalent level of consumption provide an
expression for the ratio,
u(Ссе) —и(ст)
u(сн)-и(сL)*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2b714a0e-b01f-49d4-9d2a-b07b3adf1f36%2F800ad894-33a8-48cb-933b-8b8c05be7014%2F19koe8v_processed.png&w=3840&q=75)
Transcribed Image Text:2. Using the definition of the certainty equivalent level of consumption provide an
expression for the ratio,
u(Ссе) —и(ст)
u(сн)-и(сL)*
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