revision of an assignment for economics

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4430 Project

Question 1
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)
AFI=E(payout)==100000*0.05
5000
E(u) of risky choice
E(u)=∑Uf(U)
=(400000-5000)^1\2(0.95)+(100000-5000+100000)^1\2(0.05)
192,500
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)
E(I)=∑if(I)
E(I)=400000(0.95)+100000(0.05)
385000
E(u)=∑Uf(U)
E(u)=400000^1/2*0.95+100000^1/2*0.05 20000
192500
=632*0.95+316*0.05
616.2 438.7482193696
E(u)=√Is
616.2=√Is
616.2^2=Is
379702.44
Risk premium=E(I)-Is
=385000-379702
5,298
c)                  Provide an example utility function for a risk-averse, a risk-neutral, and risk-lovingindividual. You may use a graph or mathematical formula.
Risk-loving
Risk-averse Risk-neautral
income 0 10 15 20 30 40
utility 0 45 55 65 75 78
risk-neutral
income 0 10 20 30
utility 0 40 80 120
Risk-Loving
income 0 10 20 30 35
utility 0 20 43 83 140
Question 2
a)HHI for insurance in this state
30^2+20^2+20^2+5^2+5^2+5^2+5^2+5^2+5^2
1,850
b) What does this say about the level of competition?
Any market which has a HHI that is less than 1500 is a competative marketplace.
Any market that has HHI which is between 1500-2500 is said to have a moderate
concentration. Any market which has a HHI that is above 2500 is said to be highly
concentrated. This market is therefore moderately concentrated since it has a HHI
of 1850.
c) Calculate thenew HHI after the split.
15^2+15^2+20^2+20^2+5^2+5^2+5^2+5^2+5^2+5^2
1,400
This indicates a competitive marketplace. Since the split lowers the market
concentration, this lowers the competition which may allow space for increasing price/
cost and lowering the quality of Insurance offered.
Question 3.
a)   What is the cost of blood testing per year of life saved? how many people x life saved
25*3500 25x20
87,500
b)   What is the cost of blood testing per QALY?
4000*3500 500/.75
14,000,000
c)   Does a cost-benefit analysis support running the blood test on each patient at Seattle Grace?
without the test/treatment 25 patients will suffer from tumor and only enjoy a quality of 0.75 QALY
where 1 QALY is valued at 50,000
50,000*0.75*25
937,500 under 50thousan cost itll be worth it
If tested and treated, 25 lives will be saved 20 QALY which is valued at $50,000 added to their lives
25*20*50,000
25,000,000
from number a) above, the test cost 14 millions.
therefor total benefit =25million less 14 million
11,000,000
the benefit of testing and removing tumor surpasses that of not testing.
It is therefore worthy running the blood test.
Question 4
a)   Perform a cost-benefit analysis of the flu shot. Does it favor the vaccination?
if there is no vaccine, 30% get the flu
30%*5,000 1500
If there is vaccination, 15% won't suffer the flu
15%*5000 750
cost of the flu shot for 5000 patients
20*5000 100,000
By giving the flue 750 people will be saved at a benefit of 250
250*750 187,500
benefit
187,500-100,000 87,500
It is therefore worth giving the shot.
b)   What is the cost of the flu shot per case avoided?
15% probable cases means 750 cases 500x20
750*20 15,000 divide by 750
c)   Now consider that the benefit of not getting the flu is $200. Does this change your answer from part a? Explain.
750*200 150,000
it would still be worth giving the flu shot
Question 5
(a)  What are the expected costs for survivors of each option? For decedents (assuming death occurs right after treatment)?
Current (TTT) New Option A New Option B New Option C
Initial Treatment Cost 5000 12000 20000 22000
Follow-up costs-year 1 2500 5000 4000 5000
Mortaility Rate 0.1 0.1 0.06 0.03
Life Expectancy for Survivors (Years) 25 27 30 32
Annual Follow-up costs, subsequent years 1000 1500 2000 2500
follow up cost 8500 18500 26000 29500
total cost for survivors only 7,650 16,650 24,440 28,615
(b)  What are the expected costs from each option? Remember to take the mortality rate into consideration for both this and part c.
Initial Treatment Cost 5000 12000 20000 22000
Follow-up costs-year 1 2500 5000 4000 5000
Mortaility Rate 0.1 0.1 0.06 0.03
Life Expectancy for Survivors (Years) 25 27 30 32
Annual Follow-up costs, subsequent years 1000 1500 2000 2500
follow up cost 3500 6500 6000 7500
considering mortality rate 3150 5850 5640 7275
Expected costs for all options 8,150 17,850 25,640 29,275
(c)  Calculate the expected QALY's of each option.
Life Expectancy for Survivors (Years) 25 27 30 32
Expected Survivor Quality of Life (QALY scale) 0.8 0.8 0.85 0.75
QALY 20 22 26 24
(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.
total cost for survivors only 7650 16650 24440 28615
QALY 20 21.6 25.5 24
(a)  Calculate the ICER's in terms of additional costs per QALY gained.
total cost for survivors only 7650 16650 24440 28615
QALY 20 21.6 25.5 24
ICER 383 771 958 1,192

4430 Project

QALY
Cost
Effectiveness
utility
income
Utility
utility
Income
Utility
utility
Income
Utility