Quality choice in a health care market: a mixed duopoly approach

Abstract

We investigate a health care market with uncertainty in a mixed duopoly, where a partially privatized public hospital competes against a private hospital in terms of quality choice. We use a simple Hotelling-type spatial competition model by incorporating mean–variance analysis and the framework of partial privatization. We show how the variance in the quality perceived by patients affects the true quality of medical care provided by hospitals. In addition, we show that a case exists in which the quality of the partially privatized hospital becomes higher than that of the private hospital when the patient’s preference for quality is relatively high.

Appendix

Substituting $\sigma_{{q_{0} }}^{2} - \sigma_{{q_{1} }}^{2} = 0$ into Eqs. 9–12, we can reformulate q ₀, q ₁, x and the difference between qualities as:

$$ q_{0} = M - \frac{((4 - \theta ) - 3(1 - \theta )\alpha )t}{\alpha ((2 + \theta ) - (1 - \theta )\alpha )}, $$

$$ q_{1} = M - \frac{(3 - 2(1 - \theta )\alpha )t}{\alpha ((2 + \theta ) - (1 - \theta )\alpha )}, $$

$$ x = \frac{1}{2} - \frac{(1 - \theta )(1 - \alpha )}{2((2 + \theta ) - (1 - \theta )\alpha )}, $$

$$ q_{0} - q_{1} = - \frac{(1 - \theta )(1 - \alpha )t}{\alpha ((2 + \theta ) - (1 - \theta )\alpha )}. $$

(19)

Using Eq. 19, we obtain Eq. 17 under θ ∈ [0, 1) and Eq. 18 under θ = 1.