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## 09 Apr Project – Suppose that an individual has the following utility function

4430 Project

1. Suppose that an individual has the following utility function, ????=????., where U stands for utility and W for Wealth. The individual currently has a net wealth of \$400,000. The individual believes there is a 5% chance they will get into a car accident this year. It is expected that a car accident would cost them \$100,000 (dropping their overall wealth to \$300,000).

a) How much would it cost to purchase an actuarially fair insurance policy to cover all lossesfrom a car accident? (In other words, what are the expected losses)

b) How much would the individual be willing to pay for this policy? (What are the maximumloading fees that an insurance company could charge for this policy)

c) Provide an example utility function for a risk-averse, a risk-neutral, and risk-lovingindividual. You may use a graph or mathematical formula.

2. In one state, 9 insurance companies have at least a five percent share of the market. One firm controls a 30% share, two each have a 20% share, and the remaining six firms each have a 5% share.

a) Calculate the HHI for insurance in this state.

b) What does this say about the level of competition? Provide a 2-3 sentence explanation.

c) Suppose the largest firm decides to split into two firms (each has a 15% share). Calculate thenew HHI after the split. Using economic theory, identify and explain how the split may affect the cost and quality of insurance.

3. Suppose that of the 4,000 patients that are treated for stomach pains at Seattle Grace Hospital each year, 25 of them have an undiagnosed tumor that will cause them to die in one year if not treated. A blood test that can correctly identify all tumors costs \$3,500 per test. However, all patients treated for stomach pains must be tested in order to identify the 25 patients with a tumor. Individuals who have the tumor removed are expected to live for 20 more years. On average, individuals with a tumor (with or without receiving treatment) will enjoy a quality of life of 0.75 on a QALY scale while they are alive. A year in perfect health (1 QALY) is valued at \$50,000.

a) What is the cost of blood testing per year of life saved?

b) What is the cost of blood testing per QALY?

c) Does a cost-benefit analysis support running the blood test on each patient at Seattle Grace?

4. A study finds benefit in giving patients the flu shot while they visit the doctor for routine check-ups. Specifically, the probability of getting the flu drops from 30% for those not treated to 15% for those who receive the vaccine. We consider the costs and benefits of a clinic providing the flu shot for its 5,000 patients when:

-The cost of the flu shot is \$20

-The benefits from getting the flu shot last for one year

-On average, individuals place a benefit on not getting the flu at \$250

a) Perform a cost-benefit analysis of the flu shot. Does it favor the vaccination?

b) What is the cost of the flu shot per case avoided?

c) Now consider that the benefit of not getting the flu is \$200. Does this change your answer from part a? Explain.

5. Dragon Pox is a contagious disease that mainly occurs in older witches and wizards. St. Mungos hospital has a cure for this disease, called the TTT (tried and true technique), but it is not without drawbacks. Recently, the hospital has been testing three new alternate treatments, brilliantly titled New Options A, B, and C. You are tasked with performing a costutility analysis to compare the new alternatives to the current treatment.

Current (TTT) New Option A New Option B New Option C

 Mortaility Rate 10% 10% 6% 3% Life Expectancy for Survivors (Years) 25 27 30 32 Expected Survivor Quality of Life (QALY scale) 0.8 0.8 0.85 0.75 Initial Treatment Cost \$5,000 \$12,000 \$20,000 \$22,000 Follow-up costs-year 1 \$2,500 \$5,000 \$4,000 \$5,000 Annual Follow-up costs, subsequent years \$1,000 \$1,500 \$2,000 \$2,500

(a) What are the expected costs for survivors of each option? For decedents (assuming death occurs right after treatment)?

(b) What are the expected costs from each option? Remember to take the mortality rate into consideration for both this and part c.

(c) Calculate the expected QALY’s of each option.

(d) Graph the effectiveness and costs of each option. In Excel, this can be done using an XY Scatter plot.

Effectiveness should be on the Y axis and Costs should be on the X axis.

(e) Calculate the ICER’s in terms of additional costs per QALY gained.

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