Paradigm insurer

The Paradigm Insurer's future operating results depend on the variation in PI's Population Loss Ratio Estimates ($PLRE_{PI}$s), PI's standard error, $\sigma_{e_{1,000,000}}$ = $\sigma_{e_{PI}}$ = $\frac{\sigma}{\sqrt{1,000,000}}$ which I assume to be 0.0500. PI's Cumulative PLRE Distribution Function is normally distributed, $\Phi_{PI}$(0.7500, 0.0500). Insurance risk assuming health care providers are similar to insurers smaller than PI. PI's operating characteristics include:

• Issues 1,000,000 policies and charges each policyholder the $4,000 ``market premium'' collecting Earned Premiums totaling $4,000,000,000 (1,000,000 * $4,000)
• Bears ``risk'' because $PLRE_{PI}$ is unknown until policies expire and accounting is complete
• Operating results are functions of the PLRE ($PLRE_{PI}$)
• Expected[Population Loss Ratio Estimate] = Population Loss Ratio (0.7500)
• Incurs ``Underwriting Expenses'' of $0.15 per premium dollar ($600,000,000)
• Charges policyholders a market based ``Profit Margin'' of 5% ($200,000,000)
• Charges policyholders a market based ``Risk Premium'' of 5% ($200,000,000)
• Pays Claims Costs of $3,000,000,000 or less ($PLRE_{PI}$ $\leq$ 0.7500) from current revenues, earning profits of at least 10%, with probability 0.5000
• Pays Claims Costs of $3,200,000,000 or less ($PLRE_{PI}$ $\leq$ 0.8000) from current revenues, earning profits of at least 5%, with probability 0.8413
• Pays Claims Costs of $3,400,000,000 or less ($PLRE_{PI}$ $\leq$ 0.8500) from current revenues, and avoids net operating losses, with probability 0.9772
• Starts the year with Surplus of $200,000,000 protecting itself from Claims Costs up to $3,600,000,000 ( $PLRE_{PI} \leq 0.9000$)
• Becomes insolvent (Probability = 0.00135) when Claims Costs $>$ $3,600,000,000

Table 1 Column 4, highlights PI's future operating results. Before proceeding, I stress that all insurers, and all health care providers, operate as efficiently as possible. I will show that small insurers and small, clinically efficient, capitated health care providers must cut services below the level PI provides. Capitation cannot create more efficient health care (finance) systems because it cannot work in efficient health care (finance) systems.