Question

In: Economics

There are two individuals, Scooter and the Big Man. There are two different streets in which...

There are two individuals, Scooter and the Big Man. There are two different streets in which each

individual can choose to live: Tenth Avenue and Thunder Road. It costs nothing to live or move

into each location. However, the probability of getting sick (and losing $100 to medical bills) on

Tenth Avenue is 0.25, while the probability of getting sick on Thunder Road is 0.5. Each individual

is endowed with $100 and faces a utility function of

U

=

√

w

where w is wealth. Scooter values living

on Thunder Road at $80 and living on Tenth Avenue at $40. The Big Man values living on Tenth

Avenue at $80 and living on Thunder Road at $40. Each person can choose where he wants to live

only once.

(a) Assuming each individual only cares about maximizing expected utility, where will each indi-

vidual want to live?

(b) Scooter and the Big Man can buy insurance for their medical bills from a firm. The firm can

break even, but cannot expect to make a positive profit because of perfectly competitive markets

and entry and exit. Due to a failure to collect accurate information, the firm hedges its bets

and assumes each individual will choose to live on the risky Thunder Road and values living on

Thunder Road at $80. What is the premium (p) the firm will charge each individual?

(c) Assume the firm charges each individual the premium as found in part b. Still assuming Scooter

and the Big Man only care about maximizing their expected utilities, what will each individual

choose to do? That is, where will they live? Will they choose to buy insurance?

(d) What is the name of the market failure that takes place in part c? How does it apply here?

(e) The firm hires a consultant who is good at acquiring accurate market information. Assume the

firm knows that Scooter values living on Thunder Road at $80 and the Big Man values living

on Tenth Avenue at $80. What premium should the firm charge each individual?

(f) Assume the firm charges the premiums found in part e. Still assuming Scooter and the Big

Man only care about maximizing their expected utilities, what will each individual choose to

do? That is, where will they live? Will they choose to buy insurance?

(g) Did the results from parts e and f solve the market failure identified in part e? If so, how? If

not, why not?

Expert Solution

Utility function of Scooter and the Big Man: U = √w

Scooter’s utility from living on Tenth Avenue = √(initial endowments+ value of living at Tenth Avenue - expected loss of living at Tenth Avenue) = √(100 + 40 – (0.25× 100)) = √115 = 10.72

Scooter’s utility from living on Thunder Road = √(initial endowments+ value of living at Thunder Road - expected loss of living at Thunder Road) = √(100 + 80 – (0.5× 100)) = √130 = 11.4

Big Man’s utility from living on Tenth Avenue = √(initial endowments+ value of living at Tenth Avenue - expected loss of living at Tenth Avenue) = √(100 + 80 – (0.25× 100)) = √155 = 12.45

Big Man’s utility from living on Thunder Road = √(initial endowments+ value of living at Thunder Road - expected loss of living at Thunder Road) = √(100 + 40 – (0.5× 100)) = √90 = 9.49

Scooter will live on Thunder Road as he gets higher utility from living on it. Big Man’s utility from living on Tenth Avenue is higher than his utility from living at Thunder Road. Therefore, he will live on Tenth Avenue.
Assuming that each person will live at Thunder Road and value living on it at $80, the insurance company will expect everyone to live on Thunder Road and will charge a premium of $50 (assuming that the firm has no other cost than the insurance claim).

Scooter’s utility from living on Tenth Avenue with insurance = √(initial endowments+ value of living at Tenth Avenue – insurance premium) = √(100 + 40 – 50) = √90 = 9.49

Scooter’s utility from living on Thunder Road = √(initial endowments+ value of living at Thunder Road - insurance premium) = √(100 + 80 – 50) = √130 = 11.4

Big Man’s utility from living on Tenth Avenue = √(initial endowments+ value of living at Tenth Avenue - insurance premium) = √(100 + 80 –50) = √130 = 11.4

Big Man’s utility from living on Thunder Road = √(initial endowments+ value of living at Thunder Road - insurance premium) = √(100 + 40 – 50) = √90 = 9.49

A comparison between the utility of living on Tenth Avenue and Thunder Road shows that Scooter will still prefer to live on Thunder Road and Big Man on Tenth Avenue. The comparison of Scooter and Big Man’s utilities with and without insurance shows that Scooter is indifferent between buying insurance. However, given that the utility function is concave (i.e. he is risk-averse), he may buy the insurance. Big Man, on the other hand, will not buy insurance as his utility from buying insurance will be lower.

The name of market failure in part c is adverse selection. Since insurance company does not know about the individuals, they keep their premium based on the worst outcome. However, it drives out the people choosing safer options from the market. In the present case, it means that Big Man will not buy the insurance.

Rahul Sunny answered 1 year ago

From 1985 to approximately 1993 a mentally ill man roamed the streets of Manhattan. His name...

From 1985 to approximately 1993 a mentally ill man roamed the streets of Manhattan. His name is Larry Hogue and he become notorious for scaring residents of the upper west side at 96th street. He soon became known as the "The Wild Man of 9th Street". His case is landmark as it applied to civil commitment and an individuals right to refuse medication. He had been arrested many times, in and out of Psychiatric facilities, became troublesome to the neighbor...

A standardized examination was given to the individuals who are trained at two different centres to...

A standardized examination was given to the individuals who are trained at two different centres to evaluate the difference in education quality between them. Let µ1 =The mean examination score for the population of individuals trained at center A µ2 =The mean examination score for the population of individuals trained at center B A B Sample Size 30 40 Sample Mean 82 78 Standard deviation 10 10 (Based on previous studies) Can we conclude using a = .05...

Your company assembles five different models of a motor scooter that is sold in specialty stores...

Your company assembles five different models of a motor scooter that is sold in specialty stores in the United States. The company uses the same engine for all five models. You have been given the assignment of choosing a supplier for these engines for the coming year. Due to the size of your warehouse and other administrative restrictions, you must order the engines in lot sizes of 1,240 units. Because of the unique characteristics of the engine, special tooling is...

A firm uses two factors of production: individuals with tattoos and individuals without tattoos, which have...

A firm uses two factors of production: individuals with tattoos and individuals without tattoos, which have different MPs and assume wage of tattooed is < wage of non-tattooed. The firm can hire as many tattooed individuals and non-tattooed individuals as they want at their respective wages. Also, assume that tattooed individuals and non-tattooed individuals are not perfect substitutes for each other in production. First, show on a diagram the optimal amount of tattooed individuals and non-tattooed individuals the firm would...

The answer needed is only for part C. A) Willow and Stevens are two-way streets in...

The answer needed is only for part C. A) Willow and Stevens are two-way streets in an urban area. A four-phase operation is used for the intersection of Willow and Stevens with a cycle time of 110 seconds, including 15 sec Green for the left turn (LT) vehicles on each street. If the green time for the through (TH) vehicles on Willow is 30 sec, determine the green time for the through (TH) vehicles on Stevens and construct the signal...

Two individuals invest in a project which takes two periods to complete. At the start of...

Two individuals invest in a project which takes two periods to complete. At the start of period one, individual A invests 4.5 and individual B invests 1.5. At the end of period one, each of the investors has a chance to withdraw her investment. The decisions whether to withdraw from the project or not are made simultaneously. If either investor withdraws, the project is scrapped and the scrapped value is 4. If both investors withdraw, they shared the scrapped value...

1. Show all the different kinds of gametes which could be produced by the following individuals?...

1. Show all the different kinds of gametes which could be produced by the following individuals? a) Ff b) Gg c) YyZz d) AaBbCc e) CC *please draw out solution and write how to figure it out* :)

An insurance company offers car policies to individuals with two different characteristics. Those with characteristic of...

An insurance company offers car policies to individuals with two different characteristics. Those with characteristic of type A will make a claim with probability p1 and those with the characteristic of type B will make a claim with probability p2, where p1 =/= p2. The fraction of the policyholders that are classed as type 1 characteristic is a and those of type 2 is 1−a, where 0 < a < 1. A policyholder is chosen at random. Let Ai denotes...

STAT 13_2: Each of the individuals in a particular population are: -Mature man in probability 3.0...

STAT 13_2: Each of the individuals in a particular population are: -Mature man in probability 3.0 -Mature woman in probability 0.3 -Youth child in probability 0.3 It is known that the probability that an individual has an iPhone is: -Of the adult men 0.4 - Of the older women 0.3 -Also, the probability that an individual in the population has an iPhone is 0.25. 1. A Youth is randomly selected from the population. What is the probability of having an...

How can we use sensors to map the streets to check which street has parking?