Medicine Worse than the Malady: Cure Rates, Population Shifts, and Health Insurance

We examine the welfare effects of the interaction of three types of technological progress in medicine and health insurance; some paradoxes emerge. The model specifies three types of people: W (well); H (sick with high cure rate if treated); and L (sick with low cure rate if treated). There are four insurance modes: Indemnity (I): fully covered treatments for Hs, cash bribes for Ls to forgo treatment); Deductible (D): partially covered treatments for Hs, no treatments for Ls); Zero (Z): no insurance and no treatments); and Full (F): fully covered treatments for Hs and Ls). The three types of technological progress are represented as population shifts from sicker to healthier classes of people; for brevity, we call the shifts L—>W, H—>W, and L—>H, and describe each as follows:L—>W: Improved ability to prevent illness among Ls- unambiguously improves welfare and seems to yield intuitive mode sequences.H—>W: Improved ability to prevent illness among Hs- unambiguously improves welfare but sometimes yields surprising mode sequences. Examples: F-Z (full insurance when there are many Hs, no insurance when there are fewer Hs); and D-F-D (Hs partially covered, then fully covered, then only partially covered once again. Ls not treated, then treated, then not treated once again.).L—>H: Some would-be Ls become more highly treatable Hs. Here, technological progress not only yields surprising mode shifts (e.g., D-Z-I-Z), but the welfare effects of progress are ambiguous. This is because L—>H may lead to more people being treated and cured (a welfare gain), but at a cost of higher premiums for all subscribers (a welfare loss).The paradoxical results are in part explained by the fact that utility is a concave function of wealth and a linear function of health.The three shifts could also be interpreted as autonomous demographic changes rather than as technological progress.