Consider the lottery that assigns a probability T of obtaining a level of consumption CHand a probability 1-Tan individual facing such a lottery with utility function u(c) that has the properties thatmore is better (that is, a strictly positive marginal utility of consumption at all levels ofc) and diminishing marginal utility of consumption, u"(c) < 0. As usual, we are usingthe shorthand u'(c) =T of obtaining a low level of consumption CL with CH > CL. Considerdu(c)for the first derivative of the utility function with respect todcdu(c)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 functiondcdc21. Provide a definition for the certainty equivalent level of consumption for the simplelottery described above.

Certainty Equivalent is defined as a return that is guaranteed that an individual would accept now,…

Consider the lottery that assigns a probability r of obtaining a level of consumption CH and a probability 1– 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) = consumption and u"(c) = -T of obtaining a low level of consumption CL with cH > CL. Consider du(c) for the first derivative of the utility function with respect to dc du(c) dc2 du' (c) dc to be the second derivative of the utility function %3D (which is also the derivative of the first derivative of the utility function).

Consider the lottery that assigns a probability r of obtaining a level of consumption CH and a probability 1– 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) = consumption and u"(c) = -T of obtaining a low level of consumption CL with cH > CL. Consider du(c) for the first derivative of the utility function with respect to dc du(c) dc2 du' (c) dc to be the second derivative of the utility function %3D (which is also the derivative of the first derivative of the utility function).

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.7P

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