Health Economics Final Set 5

Front 1

Medicare:
Discuss how features of the pricing/reimbursement structures in Parts A and D, which we discussed in class, could be used to identify the presence of moral hazard.

Back 1

In part A, nonlinearities exist in hospital care pricing. First 20 days are free, 21-80 days cost 180 per day, days over 80 days arenít covered. If individuals leave right after day 21, or right after day 81, it would be evidence of moral hazard.

Part D has the donut hole. The first 2500 dollars or so are covered at 75 percent (depending on the year in discussion), after that, there is no coverage until a large amount is spend (4600 in 2006, higher in more recent years) is spent. If people stop using drugs at the low cutoff and increase usage sharply age at the high cut off, it would be evidence of moral hazard.

Front 2

Suppose an individual has the Expected utility function

U(π, c1, c2)= π( (c1)^2 - 75π^2) + (1-π) ( (c1)^2 - 75π^2)

Suppose c1 = 250; 000, and is the state of the world where you are healty. π refers to your probability of being healthy. Suppose c2 = 160; 000; as getting sick costs you 90,000

What maximizes your utility?

Back 2

EU=π(〖250,000〗^(1/2)-75π^2 )+(1-π)(〖160,000〗^(1/2)-75π^2)

=500π-75π^3+(1-π)(400-75π^2)

=500π-75π^3+400-75π^2-400π+75π^3

=100π+400-75π^2

∂EU/∂π=100-150π

100=150π

π=2/3, so 2/3 maximizes your utility.

Front 3

Suppose full insurance is introduced reducing the cost of being sick to 0. What is the new optimal ? Is this an example of adverse selection or moral hazard, and why?

GIVEN:

Suppose an individual has the Expected utility function

U(π, c1, c2)= π( (c1)^2 - 75π^2) + (1-π) ( (c1)^2 - 75π^2)

Suppose c1 = 250; 000, and is the state of the world where you are healty. π refers to your probability of being healthy. Suppose c2 = 160; 000; as getting sick costs you 90,000

What maximizes your utility?

Back 3

We need to find π:
EU=π(〖250,000〗^(1/2)-75π^2 )+(1-π)(〖250,000〗^(1/2)-75π^2)

=〖250,000〗^(1/2)-75π^2

δEU/∂π=150π

π=0. Moral hazard, the presence of insurance reduces incentives to invest in health.

Front 4

Suppose someone suggests charging a higher medical premium (which would happen in both states of the world) would encourage individuals to behave in more healthy way (choose a larger ): Based on the model, is this a good policy mechanism?

Given:
Suppose an individual has the Expected utility function

U(π, c1, c2)= π( (c1)^2 - 75π^2) + (1-π) ( (c1)^2 - 75π^2)

Suppose c1 = 250; 000, and is the state of the world where you are healty. π refers to your probability of being healthy. Suppose c2 = 160; 000; as getting sick costs you 90,000

What maximizes your utility?

Back 4

EU=π((〖250,000〗^(1/2)-pr)-75π^2 )+(1-π)((〖250,000〗^(1/2)-pr)-75π^2)

=〖(250,000〗^(1/2)-pr)-75π^2

δEU/∂π=150π

π=0

The presence of higher premiums does not affect of relative prices as they are charged in both states, so there is no effect on

Front 5

What about instituting a copay (a payment which you make only when sick). How big would the copay need to be to cause an individual to choose the same they did in part A?

GIVEN:
Suppose an individual has the Expected utility function

U(π, c1, c2)= π( (c1)^2 - 75π^2) + (1-π) ( (c1)^2 - 75π^2)

Suppose c1 = 250; 000, and is the state of the world where you are healty. π refers to your probability of being healthy. Suppose c2 = 160; 000; as getting sick costs you 90,000

What maximizes your utility?

Back 5

EU=π((250,000-cp)^(1/2)-75π^2 )+(1-π)((250,000-cp)^(1/2)-75π^2)
=500π-75π^3+(250,000-cp)^(1/2)-75π^2-π(250,000-cp)^(1/2)+75π^3
=500π+(250,000-cp)^(1/2)-75π^2-π(250,000-cp)^(1/2)
δEU/∂π=500+150π-(250,000-cp)^(1/2)
Set π equal to 2/3:
=500+150(2/3)-(250,000-cp)^(1/2)
400=(250,000-cp)^(1/2)
160,000=250,000-cp
cp=90,000

A co pay will change behavior. In order to choose = 2=3; the copay would need to be 90,000 so the same financial trade offs are faced

Front 6

Suppose you are interested in assessing whether or not health insurance markets are competitive. Consider two states:

WA
Company 1 .37
Company 2 .36
Company 3 .20
Company 4 .05
Company 5 .02

OR
Company 1 .39
Company 2 .20
Company 3 .16
Company 4 .15
Company 5.10

What is the Herfandahl index for Oregon?

Back 6

0.2502

Front 7

Suppose you are interested in assessing whether or not health insurance markets are competitive. Consider two states:

WA
Company 1 .37
Company 2 .36
Company 3 .20
Company 4 .05
Company 5 .02

OR
Company 1 .39
Company 2 .20
Company 3 .16
Company 4 .15
Company 5.10

What is the Herfandahl index for Washington?

Back 7

0.3094

Front 8

Suppose you are interested in assessing whether or not health insurance markets are competitive. Consider two states:

WA
Company 1 .37
Company 2 .36
Company 3 .20
Company 4 .05
Company 5 .02

OR
Company 1 .39
Company 2 .20
Company 3 .16
Company 4 .15
Company 5.10


What market is more competitive? Why?

Back 8

Oregon has a lower herfandal index, which indicates more competition, and less market concentration. Both markets are between perfect competition, and a monopolistic market.

Front 9

What are the first and second welfare theorem's of economics?

Back 9

1. Competitive markets are pareto efficient
2. Any pareto e¢ cient outcome is achievable via a wealth transfer and letting a competitive market take over

Front 10

What are some factors that might contribute to ine¢ ciency of health care markets, and prevent them from being Pareto efficient based on our classroom discussion?

Back 10

Could be several observations. Missing markets. Prices far higher than marginal costs. Just to a couple.
Large fixed costs prevent entry into competitive markets. Also markets arenít complete (I can't sell my kidney to pay off my student loans!!). Imperfect/incomplete information abounds everywhere.

Front 11

Suppose two hospitals are competing in a market with the demand curve P = 140 Q: Each hospital has the cost function C(Q) = 1000 + 20 Q: Assume the two firms move simultaneously in a Cournot fashion

Show that firm 1 has the reaction function (a function that describes form 1's best response to firm 2's quantity). Q1 = (120 - Q2)/2

Back 11

π1 = (140 - Q1- Q2)*Q1 - 1000 - 20Q1

dπ1/d1 = 140- 2Q1 - Q2- 20 = 0

120 - Q2 = 2Q1 or (120-Q2)/2 = Q1

Front 12

Suppose two hospitals are competing in a market with the demand curve P = 140 Q: Each hospital has the cost function C(Q) = 1000 + 20 Q: Assume the two firms move simultaneously in a Cournot fashion

Knowing firm 1's reaction function above, and deriving firm 2's reaction function, what is the optimal quantity for firm 1, and firm 2, and knowing those, what is the market price which emerges in the market. What is the total profits for each company?

Back 12

(120-Q2)/2 = Q1 and (120-Q1)/2 = Q2 plug one into the other:

Q1= (120-((120-Q1)/2))/2

Q1=60 - 30+ Q1/4

3/4Q1= 30

Q1= 40

Pluginto firm 2's reaction; andQ2= 40:

P=140-Q1- Q2 = 60

Profits=40*60-1000-20*40=600

Front 13

Suppose two hospitals are competing in a market with the demand curve P = 140 Q: Each hospital has the cost function C(Q) = 1000 + 20 Q: Assume the two firms move simultaneously in a Cournot fashion

Suppose firm 1 and 2 announce a plan to merge hospitals.
They suggest this will make consumers better off because now the new combined cost function is C(Q) = 1000 + 10Q.

As they are merging, they new hospital will profit maximize as a monopolist. Knowing this, as an expert witness for the Federal Trade Commission, what is your expert testimony on the merits of such a merger.

Will the total profits for the hospital go up?
What happens to the market price and quantity of health care provided? Are consumers better off?
Why or why not?

Back 13

π= (140- Q)Q - 1000 - 10Q

dπ/dQ= 140 - 2Q - 10 = 0

130=2Q; Q=65

π= 75*65 - 1000 - 10*75 = 3225

Price goes up to 75, quantity falls to 65. Consumers are worse off.


Company profits go from 600*2 (there are two companies) to 3225 when they merge. Company is much better off, both due to lower costs, and less competition.

Front 14

Consider a utility function where Utility in period t if a person exercises is 2, and utility in period t+1 if they exercise is 8. On the other hand if they don’t exercise, their utility in period t is 6, and their utility in period t+1 is 4. Consider two scenarios. If the person has discounts geometrically across future utilities, with β = .8, how does the person feel about exercising today. What about exercising 7 days from now?

Back 14

Viewing the decision of exercising today U=2+8*.8=8.4
Viewing the decision of not exercising today U=6+4*.8=9.2
Don't exercise as 8.4<9.4

Viewing the decision of exercising a week from now
U=2*.8^7 +8*.8^8 =1.76
Viewing the decision of not exercising today
U=6*.8^7 +4*.8^8 =1.92
Today they would state they wouldnít exercise 7 days from now as 1.76<1.92

Front 15

GIVEN:
Consider a utility function where Utility in period t if a person exercises is 2, and utility in period t+1 if they exercise is 8. On the other hand if they don’t exercise, their utility in period t is 6, and their utility in period t+1 is 4.

Suppose an individual hyperbolically discounts, so the discount factor applied to period t is (1/t+1).
How does the person feel about exercising today?
What about exercising 7 days from now?

Does this person have time-consistent or time-inconsistent choices?

Back 15

Viewing the decision of exercising today
U=2+8*(1/2)= 6
Viewing the decision of not exercising today
U=6+4*(1/2) =8
Don't exercise as 6<8

U=2*(1/(1+7)) +8*(1/(1+8)) =1.14
Viewing the decision of not exercising today
U=6*(1/(1+7)) +4*(1/(1+8)) =1.19
Today they would state they wouldnít exercise 7 days from now as 1.14<1.19

Even with hyperbolic discounting they prefer to not exercise. In order to have individuals prefer to exercise, there needs to be a long term gain in utility, even if there is a short-term cost, but in this case, there was no long term gain in utility which is why even with hyperbolic discounting people prefer to not exercise.