Maximising Health and Financial Security: Understanding John's Income and Insurance Choices
Answer
Introduction
In today's fast-paced world, unexpected health issues can have a significant impact on one's financial stability. To navigate these uncertainties, individuals often turn to insurance plans. In this blog post, we'll delve into John's monthly income uncertainties, his utility function, and various insurance scenarios. Let's explore the insights and decisions that can help John secure his financial well-being.
Understanding John's Income and Utility
John's monthly income is subject to two states: Sick and Healthy, with corresponding probabilities and income levels. His utility function \(U = Y^{0.5}\) helps us gauge the satisfaction he derives from his income.
1. **Expected Income (EY)**:
- John's expected income is $3640, reflecting the average income he can anticipate across states.
2. **Expected Utility (EU)**:
- With a utility function of \(U = Y^{0.5}\), John's expected utility is approximately 62.00, showcasing his contentment with his anticipated income levels.
3. **Risk Aversion**:
- John's preference for a certain income over a risky one with the same expected value indicates that he is risk averse.
---
**Assessing Risk and Risk Premium**
1. **Risk Premium**:
- John's willingness to pay $144 to avoid the risk of income loss highlights his desire for financial security.
2. **Changing Circumstances**:
- In a scenario where John's income in the sick state decreases, his risk premium remains at $144, indicating his commitment to minimizing financial uncertainty.
---
**Insurance and Risk Mitigation**
When it comes to insurance, different plans offer varying levels of protection and incentives:
1. Indemnity Benefits vs. Service Benefits:
- Indemnity Benefits provide a fixed amount for a specific service, offering predictable coverage. Service Benefits, covering a percentage of out-of-pocket expenses, may lead to overutilization.
2. Government Intervention and Universal Coverage:
- Direct public provision of insurance coverage proves most efficient in achieving universal coverage while minimizing deadweight loss.
3. Private vs. Public Insurers:
- Private insurers are more inclined to adopt loss prevention programs due to their profit-driven nature, focusing on reducing claims payouts for chronic diseases.
4. Free-rider Private Insurance:
- Indemnity Benefits health insurance plans are more likely to face challenges related to free-rider behavior, potentially leading to higher premiums.
Conclusion
In John's pursuit of financial security, understanding the nuances of income uncertainties, utility functions, and insurance options is crucial. By evaluating risk, preferences, and the nuances of different insurance plans, individuals like John can make informed decisions to safeguard their financial well-being. Balancing risk aversion with potential gains is the key to a secure financial future.
Note: The answers provided are based on the given scenarios and are for illustrative purposes only.
---
Question 1
What is John's expected income EY (that is, what is the expected value of his income across states)?
Answer: John's expected income EY is: $3,640
---
Question 2
Let John's utility function be U = Y ^ 0.5 , where Y is John's monthly income. Calculate John's expected utility EU (that is, expected value of utility across states) rounded to 2nd decimal point.
Answer: 62.00
---
Question 3
Compare the utility of John's expected income and the expected utility of his income. Based on this comparison. John is found to be risk averse.
True
False
Answer: True
---
Question 4
Calculate the maximum amount that John is willing to pay to avoid the risk of income loss resulting from becoming sick: i.e.. what is John's risk premium?
Answer: $144
Question 5
Calculate the new maximum amount that John is willing to pay to avoid the risk of income loss resulting from becoming sick; ie., what is John's risk premium?
Answer 5: $100
Question 6
Now that the probability of being in the sick state has increased, John is more likely to buy health insurance than before.
True
False
Answer 6: true
---
Question 7
Calculate the new maximum amount that John is willing to pay to avoid the risk of income loss resulting from becoming sick now that he is earning less in that state; i.e., what is John's risk premium?
*Answer: $144*
---
There are two states:
- Sick (p = 0.4): Income is now U(900)
- Healthy (p = 0.6): Income remains U(4,900)
John's utility function is still U = Y^0.5
To find the risk premium:
1. Calculate John's expected utility E(U):
- \(E(U) = (0.4 \cdot E[U(900)]) + (0.6 \cdot E[U(4,900)])\)
- \(E[U(900)] = \sqrt{900} = 30\)
- \(E[U(4,900)] = \sqrt{4,900} = 70\)
- \(E(U) = (0.4 \cdot 30) + (0.6 \cdot 70) = 54\)
2. Calculate utility of expected income U(E(Y)):
- \(E(Y) = (0.4 \cdot 900) + (0.6 \cdot 4,900) = 3,060\)
- \(U(E(Y)) = \sqrt{3,060} = 55.28\)
3. Find risk premium \(X\) such that:
- \(U(E(Y) - X) = E(U)\)
- \(\sqrt{3,060 - X} = 54\)
4. Solving this:
- \(X = 3,060 - 2,916 = 144\)
*With the lower sick state income, John's maximum risk premium is now $144.*
---
Question 8
Now that the income in the sick state has decreased, John is more likely to buy health insurance than before.
True
False
Answer: True
---
Question 9
Which type of private health insurance plan is more likely to become a free-rider private insurance?
- Indemnity Benefits health insurance plan
- Service Benefit health insurance plan
Answer: Indemnity Benefits health insurance plan
---
Question 10
Which type of private health insurance plan can provide better protection against the risk of financial loss when the insured is sick?
- Indemnity Benefits health insurance plan
- Service Benefit health insurance plan
Answer: Indemnity Benefits health insurance plan
---
Question 11
If the goal of government intervention is to achieve universal coverage, which strategy is the most efficient in terms of minimizing the deadweight loss?
Public subsidy
- Mandated insurance benefits
- Direct public provision of insurance coverage
Answer
- Direct public provision of insurance coverage
---
Question 12
As mentioned in this chapter, some insurers operate disease management programs that seek to promote prevention and screening in order to reduce adverse health outcomes of chronic disease and the associated expense. Does the incentive for such loss prevention differ between private insurers and public insurers?
YES
NO
Answer: YES
---
Question 13
As mentioned in this chapter, some insurers operate disease management programs that seek to promote prevention and screening in order to reduce adverse health outcomes of chronic disease and the associated expense. Which type of insurer is more likely to and stands to gain the most from adopting a loss prevention program?
Public Insurer
Private Insurer
---
Question 14
Please, upload your work for partial credit if an algebraic error caused a misspecification of the parameters above.
Upload
Choose a File
No comments:
Post a Comment