I'd say there should be a "Health Care System" issue, which would affect how fast would both hospitals work.
The University Hospital (or equivalent paid institutions) would provide fast and efficient services at a price (which would rise, the more liberal health care laws become), while the Free Clinic would provide less effective (if not L+) services for free. (Of course, this runs under an assumption that non-sleeping LCS members, having no official job, wouldn't have health insurance. I may be wrong, as I'm not an American.)
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C+: The health care system is fully privatized, with no government benefits.
The Free Clinic doesn't work at all.
C: The health care system mostly relies on private insurance.
The Free Clinic provides basic care, twice as slow.
M: While some benefits are in order, health care is still expensve for most.
The Free Clinic works 1.5 times as slow as paid hospitals.
L: An extensive set of benefits provides affordable health care for those in need.
The Free Clinic works _almost_ as effectively as the paid hospitals. (1.25 times as slow)
L+: A universal single payer health care system is in order.
The paid hospitals disappear, while the Free Clinic finally catches up in quality.