Community Rating in the Market for Private Health Insurance: A simple analysis of why it can’t work
Community Rating in the Market for Private Health Insurance: basic A simple analysis of why it can’t work
Source: Rothschild and Stiglitz,  1976
<ul><li>Consider the following contingent commodities diagrams: </li></ul><ul><li>High Risk </li></ul><ul><li>Individuals ...
<ul><li>Consider the following contingent commodities diagrams: </li></ul><ul><li>High Risk </li></ul><ul><li>Individuals ...
<ul><li>Consider the following contingent commodities diagrams: </li></ul><ul><li>High Risk </li></ul><ul><li>Individuals ...
<ul><li>Consider the following contingent commodities diagrams: </li></ul><ul><li>High Risk </li></ul><ul><li>Individuals ...
<ul><li>Consider the following contingent commodities diagrams: </li></ul><ul><li>High Risk </li></ul><ul><li>Individuals ...
<ul><li>Insurance companies can fragment the market and offer different risk premiums to different groups. </li></ul><ul><...
C 2 C 1 45 ° H
C 2 C 1 45 ° H L
C 2 C 1 45 °
<ul><li>L  -> fair insurance line for low risk people </li></ul><ul><li>H -> fair insurance line for high risk people </li...
<ul><li>L  -> fair insurance line for low risk people </li></ul><ul><li>H -> fair insurance line for high risk people </li...
<ul><li>Mapping the three diagrams together: </li></ul>C 2 C 1
<ul><li>Mapping the three diagrams together: </li></ul>IC 1   ->  indifference curve if high-risk individuals are offered ...
<ul><li>Mapping the three diagrams together: </li></ul>IC 1   ->  indifference curve if high-risk individuals are offered ...
<ul><li>Mapping the three diagrams together: </li></ul>A  ->  insurance line for pooled (community rated) contracts IC 1 I...
<ul><li>Mapping the three diagrams together: </li></ul>A  ->  insurance line for pooled (community rated) contracts IC 1 I...
<ul><li>Mapping the three diagrams together: </li></ul>IC 3   ->  indifference curve if high-risk individuals are offered ...
<ul><li>Mapping the three diagrams together: </li></ul>IC 3’   ->  indifference curve for high-risk who cannot over insure...
<ul><li>Mapping the three diagrams together: </li></ul>IC 3’   ->  indifference curve for high-risk who cannot over insure...
<ul><li>Mapping the three diagrams together: </li></ul>We see that: IC 3’  > IC 1   ⇒ high-risk people are on a higher ind...
<ul><li>If the market is competitive is this a stable equilibrium? </li></ul>C 2 C 1
<ul><li>In a competitive market other firms may enter the market and offer insurance. </li></ul><ul><li>Another firm may o...
L  -> fair insurance line for low-risk group L C 2 C 1
Any contract in the shaded area makes low risk people better off but is not attractive to high risk people.  C 2 C 1
Point  X  represents a better contract for the low risk individuals if the bad state of the world occurred. At  X  the new...
Point  X  represents a better contract for the low risk individuals if the bad state of the world occurred. At  X  the new...
The original company will find p a  = r a  < p h and will be making a loss. X C 2 C 1
The original company will find p a  = r a  < p h and will be making a loss. To counter this the company may  start to char...
The original company will find p a  = r a  < p h and will be making a loss. To counter this the company may  start to char...
The original company will find p a  = r a  < p h and will be making a loss. To counter this the company may  start to char...
The original company will find p a  = r a  < p h and will be making a loss. To counter this the company may  start to char...
As they have all high risk people this company may increase it price to  the fair price for those people. X C 2 C 1
However at this price even high risk people will find contract  X attractive and will switch. X C 2 C 1
However at this price even high risk people will find contract  X attractive and will switch. This is not what the company...
C 2 C 1 As a result of this the company will have to start increasing the price.
C 2 C 1 As a result of this the company will have to start increasing the price.
This is where we started. And we already know that this is not a stable equilibrium. C 2 C 1
<ul><li>It is  not  possible to have a stable equilibrium in a competitive insurance market with community rating. </li></ul>
<ul><li>It is  not  possible to have a stable equilibrium in a competitive insurance market with community rating. </li></...
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Community Rating In The Market For Private Health Insurance

  1. 1. Community Rating in the Market for Private Health Insurance: A simple analysis of why it can’t work
  2. 2. Community Rating in the Market for Private Health Insurance: basic A simple analysis of why it can’t work
  3. 3. Source: Rothschild and Stiglitz, 1976
  4. 4. <ul><li>Consider the following contingent commodities diagrams: </li></ul><ul><li>High Risk </li></ul><ul><li>Individuals </li></ul><ul><li>Low Risk </li></ul><ul><li>Individuals </li></ul>C 2 C 1 45 ° C 2 C 1 45 °
  5. 5. <ul><li>Consider the following contingent commodities diagrams: </li></ul><ul><li>High Risk </li></ul><ul><li>Individuals </li></ul><ul><li>Low Risk </li></ul><ul><li>Individuals </li></ul>C 2 C 1 45 ° C 2 C 1 45 °
  6. 6. <ul><li>Consider the following contingent commodities diagrams: </li></ul><ul><li>High Risk </li></ul><ul><li>Individuals </li></ul><ul><li>Low Risk </li></ul><ul><li>Individuals </li></ul>C 2 C 1 45 ° C 2 C 1 45 °
  7. 7. <ul><li>Consider the following contingent commodities diagrams: </li></ul><ul><li>High Risk </li></ul><ul><li>Individuals </li></ul><ul><li>Low Risk </li></ul><ul><li>Individuals </li></ul>C 2 C 1 45 ° C 2 C 1 45 °
  8. 8. <ul><li>Consider the following contingent commodities diagrams: </li></ul><ul><li>High Risk </li></ul><ul><li>Individuals </li></ul><ul><li>Low Risk </li></ul><ul><li>Individuals </li></ul>C 2 C 1 45 ° C 2 C 1 45 °
  9. 9. <ul><li>Insurance companies can fragment the market and offer different risk premiums to different groups. </li></ul><ul><li>The slopes of the indifferences curves are: </li></ul><ul><li>The slopes of the budget constraints are: </li></ul><ul><li>For fair insurance </li></ul><ul><li>p = r </li></ul><ul><li>With two groups this can be a separating equilibrium </li></ul><ul><li>p h = r h </li></ul><ul><li>p l = r l </li></ul>
  10. 10. C 2 C 1 45 ° H
  11. 11. C 2 C 1 45 ° H L
  12. 12. C 2 C 1 45 °
  13. 13. <ul><li>L -> fair insurance line for low risk people </li></ul><ul><li>H -> fair insurance line for high risk people </li></ul>C 2 C 1 H L
  14. 14. <ul><li>L -> fair insurance line for low risk people </li></ul><ul><li>H -> fair insurance line for high risk people </li></ul><ul><li>A -> average of the two </li></ul>C 2 C 1 H A L
  15. 15. <ul><li>Mapping the three diagrams together: </li></ul>C 2 C 1
  16. 16. <ul><li>Mapping the three diagrams together: </li></ul>IC 1 -> indifference curve if high-risk individuals are offered fair insurance IC 1 C 2 C 1
  17. 17. <ul><li>Mapping the three diagrams together: </li></ul>IC 1 -> indifference curve if high-risk individuals are offered fair insurance IC 2 -> indifference curve if low-risk individuals are offered fair insurance IC 1 IC 2 C 2 C 1
  18. 18. <ul><li>Mapping the three diagrams together: </li></ul>A -> insurance line for pooled (community rated) contracts IC 1 IC 2 A C 2 C 1
  19. 19. <ul><li>Mapping the three diagrams together: </li></ul>A -> insurance line for pooled (community rated) contracts IC 1 IC 2 C 2 C 1
  20. 20. <ul><li>Mapping the three diagrams together: </li></ul>IC 3 -> indifference curve if high-risk individuals are offered pooled insurance contract IC 1 IC 2 IC 3 C 2 C 1
  21. 21. <ul><li>Mapping the three diagrams together: </li></ul>IC 3’ -> indifference curve for high-risk who cannot over insure with pooled contract IC 1 IC 2 IC 3’ C 2 C 1
  22. 22. <ul><li>Mapping the three diagrams together: </li></ul>IC 3’ -> indifference curve for high-risk who cannot over insure with pooled contract IC 4 -> indifference curve if low-risk individuals are offered pooled insurance contract IC 1 IC 2 IC 4 IC 3’ C 2 C 1
  23. 23. <ul><li>Mapping the three diagrams together: </li></ul>We see that: IC 3’ > IC 1 ⇒ high-risk people are on a higher indifference curve IC 2 < IC 4 ⇒ low-risk people are on a higher indifference curve IC 1 IC 2 IC 4 IC 3’ C 2 C 1
  24. 24. <ul><li>If the market is competitive is this a stable equilibrium? </li></ul>C 2 C 1
  25. 25. <ul><li>In a competitive market other firms may enter the market and offer insurance. </li></ul><ul><li>Another firm may offer insurance at a different price (insurance line) to the incumbent. </li></ul>C 2 C 1
  26. 26. L -> fair insurance line for low-risk group L C 2 C 1
  27. 27. Any contract in the shaded area makes low risk people better off but is not attractive to high risk people. C 2 C 1
  28. 28. Point X represents a better contract for the low risk individuals if the bad state of the world occurred. At X the new insurance company will only attract low risk individuals. X C 2 C 1
  29. 29. Point X represents a better contract for the low risk individuals if the bad state of the world occurred. At X the new insurance company will only attract low risk individuals. X C 2 C 1
  30. 30. The original company will find p a = r a < p h and will be making a loss. X C 2 C 1
  31. 31. The original company will find p a = r a < p h and will be making a loss. To counter this the company may start to charge a higher price. X C 2 C 1
  32. 32. The original company will find p a = r a < p h and will be making a loss. To counter this the company may start to charge a higher price. X C 2 C 1
  33. 33. The original company will find p a = r a < p h and will be making a loss. To counter this the company may start to charge a higher price. X C 2 C 1
  34. 34. The original company will find p a = r a < p h and will be making a loss. To counter this the company may start to charge a higher price. X C 2 C 1
  35. 35. As they have all high risk people this company may increase it price to the fair price for those people. X C 2 C 1
  36. 36. However at this price even high risk people will find contract X attractive and will switch. X C 2 C 1
  37. 37. However at this price even high risk people will find contract X attractive and will switch. This is not what the company the entered the market and offered X wants. X C 2 C 1
  38. 38. C 2 C 1 As a result of this the company will have to start increasing the price.
  39. 39. C 2 C 1 As a result of this the company will have to start increasing the price.
  40. 40. This is where we started. And we already know that this is not a stable equilibrium. C 2 C 1
  41. 41. <ul><li>It is not possible to have a stable equilibrium in a competitive insurance market with community rating. </li></ul>
  42. 42. <ul><li>It is not possible to have a stable equilibrium in a competitive insurance market with community rating. </li></ul><ul><li>Unless............. </li></ul>
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