Table 2.

Conditions for Implementing Efficient Care and Fairness When Taste is Unavailable as a Basis of Payment

Conditions for Efficiency

General Case

Health Plans Can Finance Efficient Care

Silver:

π_{s} + π_{h} = x_{s p}^{*} + x_{h p}^{*}

π_s + π_h = 4 + 1 = 5

Gold:

π_{s} + π_{h} + 2 y = x_{s r}^{*} + x_{h r}^{*}

5 + 2y = 9 + 2.25
y = 3.125

Low-taste Choose the Silver Plan

Sick:

v_{s p} (x_{s r}^{*}) - y - t_{s}^{G} < v_{s p} (x_{s p}^{*}) - t_{s}^{S}

12 - 3.125 - t_{s}^{G} < 8 - t_{s}^{S}

.875 < t_{s}^{G} - t_{s}^{S}

Healthy:

v_{h p} (x_{h r}^{*}) - y - t_{h}^{G} < v_{h p} (x_{h p}^{*}) - t_{h}^{S}

3 - t_{h}^{G} < 2 - t_{h}^{S}

High-taste Choose the Gold Plan

Sick:

v_{s r} (x_{s r}^{*}) - y - t_{s}^{G} \geq v_{s r} (x_{s p}^{*}) - t_{s}^{S}

18 - 3.125 - t_{s}^{G} \geq 12 - t_{s}^{S}

Healthy:

v_{h r} (x_{h r}^{*}) - y - t_{h}^{G} \geq v_{h r} (x_{h p}^{*}) - t_{h}^{S}

4.5 - 3.125 - t_{h}^{G} \geq 3 - t_{h}^{S}

- 1.625 \geq t_{h}^{G} - t_{h}^{S}

Conditions for Fairness

Strong solidarity: Equal payments for Sick and Healthy

t_{s}^{S} = t_{h}^{S}, t_{s}^{G} = t_{h}^{G}

Weak solidarity:

t_{s}^{S} \leq t_{h}^{S}, t_{s}^{G} \leq t_{h}^{G}