Tom has an initial wealth of 100. His car may be stolen so he runs a...
Tom has an initial wealth of 100. His car may be stolen so he runs a risk of a loss of 40 dollars. The probability of loss is 0.2. It is possible, however, for Tom to buy insurance. One unit of insurance costs γ dollars and pays 1 dollar if the loss occurs. Thus, if α units of insurance are brought, the wealth of Tom will be 100-γα if there is no loss (a good state) and 100-γα-40+α if the loss occurs (a bad state). Tom is an expected utility maximizer with Bernoulli utility function u(x)=ln(x) where x is his wealth in a state.
(a)(10%) Write down Tom's expected utility if he buys α units of insurance. Different- iate it with respect to α to derive the first order condition which will be useful later.
(b)(10%) Suppose in 2016 insurance is actuarially fair in the sense that the insurance company breaks even on average. What should γ be? How much insurance (α) will Tom buy? What is his wealth in the good state? What is his wealth in the bad state? Does Tom face any risk after being insured?
(c)(10%) In 2017 insurance company decides to change the premium so now γ becomes 0.25 How much insurance (α) will Tom buy now? What is his wealth in good state? What is his wealth in the bad state?
(d)(10%) Facing the premium change from 2016 to 2017, what is the Slutsky substitution effect of Tom's wealth in the good state?
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Tom has an initial wealth of 100. His car may be stolen so he
runs a...
1. Tom has an initial wealth of 100. His car may be stolen so he runs...
1. Tom has an initial wealth of 100. His car may be stolen so he runs a risk of a loss of 20 Hollars. The probability of loss ik 0.2. It is also possible that someone breaks in Tom's home. In this case, he runs a risk of a loss of (80 dollars. The probability of loss is 0.1, These two probabilities (events) are independent. It is possible, however, for Tom to buy insurance. One unit of car insurance costs...
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Question3 An investor has utility function U(w) n(w) and initial wealth 100. The investor has the...
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Suppose the function u(x) = x0.5 , where x is consumption, represents your preference over gambles using an expected uti...
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expected utility function.
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and a probability 0.9 of getting xG (good state).
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(b, p), where b is the insurance benefit the company pays you if
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1. Tom has an initial wealth of 100. His car may be stolen so he runs a risk of a loss of 20 Hollars. The probability of loss ik 0.2. It is also possible that someone breaks in Tom's home. In this case, he runs a risk of a loss of (80 dollars. The probability of loss is 0.1, These two probabilities (events) are independent. It is possible, however, for Tom to buy insurance. One unit of car insurance costs...
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Suppose the function u(x) = x0.5 , where x is
consumption, represents your preference over gambles using an
expected utility function.
You have a probability 0.1 of getting consumption xB (bad state)
and a probability 0.9 of getting xG (good state).
An insurance company allows you to choose an insurance contract
(b, p), where b is the insurance benefit the company pays you if
the bad state occurs and p is the insurance premium you pay the
company regardless of...
wthout insunnce coverage? The text ook aplans inutvely why te risk-areธe consumer brys nsurance; tis homework assgment uses a simple numerical exampia.) If losses are uitrmy dstrbutad frm 0 to average loss, as we wored out oarier? The actuarial pure prem um is 1% of the awengo loss. This should bo haf the pure premium of the sconato whon al losses are total bsas) Microoconomics, Module 24, Risk and Uncortainty (Chapter 18) Hamowark The atadhed PDFfie has better formating-) Rek...
Hello, my name is Shady Slim. I understand you are going to help me figure out my gross income for the year... whatever that means. It's been a busy year and I'm a busy man, so let me give you the lowdown on my life and you can do your thing I was unemployed at the beginning of the year and got $2,000 in unemployment compensation. I later got a job as a manager for Roca Cola. I earned $57,500...
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