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
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Chapter22: Frontiers Of Microeconomics
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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
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)*
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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