- Could You Solve Question 3 For Me 1 (167.1 KiB) Viewed 30 times
could you solve question 3 for me?
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answerhappygod
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could you solve question 3 for me?
could you solve question 3 for me?
1 Question #1 dc dc Consider the lottery that assigns a probability a 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) = du(c) for the first derivative of the utility function with respect to du(c) du'c) consumption and u"(c) de to be the second derivative of the utility function (which is also the derivative of the first derivative of the utility function). 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 u(Cce-u(CL) expression for the ratio, uch)-u(CL) 3. Define the risk premium p = c – Cce where c = ach + (1 – 7 )c is the expected level of consumption from the lottery (c = E[c]). Consider the following exercise. There are three lotteries characterized by different probabilities of obtaining ch. Let these probabilities be given by 7" > T' > 7. 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.
1 Question #1 dc dc Consider the lottery that assigns a probability a 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) = du(c) for the first derivative of the utility function with respect to du(c) du'c) consumption and u"(c) de to be the second derivative of the utility function (which is also the derivative of the first derivative of the utility function). 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 u(Cce-u(CL) expression for the ratio, uch)-u(CL) 3. Define the risk premium p = c – Cce where c = ach + (1 – 7 )c is the expected level of consumption from the lottery (c = E[c]). Consider the following exercise. There are three lotteries characterized by different probabilities of obtaining ch. Let these probabilities be given by 7" > T' > 7. 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.