Simon has current wealth of 836, including $20 in cash. With probabil- ity Simon's money will be stolen (contingency 1), leaving him with only $16 to spend on consumption, and with probability his cash will not be stolen (contingency 2) so he can spend the entire $36 on consumption. Simon has utility function (9.9) = √5 + √ where c is consumption spending in contingency i. Show Transcribed Text 1. What is the expected value of Simons contingent consumption? 2. What is the expected utility of Simons contingent consumption? 3. What is Simons MRS at his current contingent consumption bundle 4. An insurance company offers to fully insure Simon against the risk of theft for a premium (price) of $P. That is, if Simon pays $P to the insurance company, then the insurer will replace Simons $20 in contingency 1. If Simon buys the insurance his contingent consumption bundle is therefore (36 P; 36 P). i. What is Simons MRS at the fully insured contingent consumption bundle? ii. At what value of P would the insurer make zero expected profit were Simon to buy the insurance? iii. Would Simon buy the insurance at the price you identified in (ii)? Be sure to explain your answer. iv. At what value of P would Simon be indifferent about buying the insurance or not? What is the insurances expected profit at this premium? v. Draw a CC diagram showing Simons contingent consumption without insurance and his contingent consumption with insurance at the premium you computed in (iv). Sketch Simons indifference curve through each point. Be as accurate as possible, and make sure your diagram is consistent with your answers to the previous parts of this question.
Simon has current wealth of 836, including $20 in cash. With probabil- ity Simon's money will be stolen (contingency 1), leaving him with only $16 to spend on consumption, and with probability his cash will not be stolen (contingency 2) so he can spend the entire $36 on consumption. Simon has utility function (9.9) = √5 + √ where c is consumption spending in contingency i. Show Transcribed Text 1. What is the expected value of Simons contingent consumption? 2. What is the expected utility of Simons contingent consumption? 3. What is Simons MRS at his current contingent consumption bundle 4. An insurance company offers to fully insure Simon against the risk of theft for a premium (price) of $P. That is, if Simon pays $P to the insurance company, then the insurer will replace Simons $20 in contingency 1. If Simon buys the insurance his contingent consumption bundle is therefore (36 P; 36 P). i. What is Simons MRS at the fully insured contingent consumption bundle? ii. At what value of P would the insurer make zero expected profit were Simon to buy the insurance? iii. Would Simon buy the insurance at the price you identified in (ii)? Be sure to explain your answer. iv. At what value of P would Simon be indifferent about buying the insurance or not? What is the insurances expected profit at this premium? v. Draw a CC diagram showing Simons contingent consumption without insurance and his contingent consumption with insurance at the premium you computed in (iv). Sketch Simons indifference curve through each point. Be as accurate as possible, and make sure your diagram is consistent with your answers to the previous parts of this question.
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.5P
Related questions
Question
![[**] Simon has current wealth of $36, including $20 in cash. With probabil-
ity Simon's money will be stolen (contingency 1), leaving him with
only $16 to spend on consumption, and with probability his cash
will not be stolen (contingency 2) so he can spend the entire $36 on
consumption. Simon has utility function
u (0₁.0₂) = √6 + 2√
where c is consumption spending in contingency i.
Show Transcribed Text
1. What is the expected value of Simons contingent
consumption?
2. What is the expected utility of Simons contingent
consumption?
3. What is Simons MRS at his current contingent
consumption bundle
4. An insurance company offers to fully insure Simon
against the risk
of theft for a premium (price) of $P. That is, if Simon
pays $P
to the insurance company, then the insurer will
replace Simons
$20 in contingency 1. If Simon buys the insurance his
contingent
consumption bundle is therefore (36 P; 36 P).
i. What is Simons MRS at the fully insured contingent
consumption bundle?
ii. At what value of P would the insurer make zero
expected profit were Simon to buy the insurance?
iii. Would Simon buy the insurance at the price you
identified in (ii)? Be sure to explain your answer.
iv. At what value of P would Simon be indifferent
about buying the insurance or not? What is the
insurances expected profit
at this premium?
v. Draw a CC diagram showing Simons contingent
consumption without insurance and his contingent
consumption with
insurance at the premium you computed in (iv).
Sketch Simons indifference curve through each point.
Be as accurate as possible, and make sure your
diagram is consistent with your answers to the
previous parts of this question.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9cf8151b-bf9b-4f36-935f-8859cb70c986%2F07154b5e-ca74-4d9b-90c1-6b9b57c3badc%2Fvasvx6n_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[**] Simon has current wealth of $36, including $20 in cash. With probabil-
ity Simon's money will be stolen (contingency 1), leaving him with
only $16 to spend on consumption, and with probability his cash
will not be stolen (contingency 2) so he can spend the entire $36 on
consumption. Simon has utility function
u (0₁.0₂) = √6 + 2√
where c is consumption spending in contingency i.
Show Transcribed Text
1. What is the expected value of Simons contingent
consumption?
2. What is the expected utility of Simons contingent
consumption?
3. What is Simons MRS at his current contingent
consumption bundle
4. An insurance company offers to fully insure Simon
against the risk
of theft for a premium (price) of $P. That is, if Simon
pays $P
to the insurance company, then the insurer will
replace Simons
$20 in contingency 1. If Simon buys the insurance his
contingent
consumption bundle is therefore (36 P; 36 P).
i. What is Simons MRS at the fully insured contingent
consumption bundle?
ii. At what value of P would the insurer make zero
expected profit were Simon to buy the insurance?
iii. Would Simon buy the insurance at the price you
identified in (ii)? Be sure to explain your answer.
iv. At what value of P would Simon be indifferent
about buying the insurance or not? What is the
insurances expected profit
at this premium?
v. Draw a CC diagram showing Simons contingent
consumption without insurance and his contingent
consumption with
insurance at the premium you computed in (iv).
Sketch Simons indifference curve through each point.
Be as accurate as possible, and make sure your
diagram is consistent with your answers to the
previous parts of this question.
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