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 Define the risk premium p = c – Cce where č = TCH + (1 – T)CL 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 7" > n' > T. Using a single diagram, plot the risk premium for each of these three lotteries. Does the risk premium increase or — с — Ссе decrease as we increase T across these three lotteries? Provide the intuition for your result.
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 Define the risk premium p = c – Cce where č = TCH + (1 – T)CL 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 7" > n' > T. Using a single diagram, plot the risk premium for each of these three lotteries. Does the risk premium increase or — с — Ссе decrease as we increase T across these three lotteries? Provide the intuition for your result.
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.7P
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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
Transcribed Image Text:Define the risk premium p = c – Cce where č = TCH + (1 – T)CL 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 7" > n' > T. Using a single diagram, plot the
risk premium for each of these three lotteries. Does the risk premium increase or
— с —
Ссе
decrease as we increase T across these three lotteries? Provide the intuition for
your result.
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