## Healthcare Economist

Unbiased Analysis of Today's Healthcare Issues

## A simple model giving some justification for Medicaid

Written By: Jason Shafrin - Mar• 11•06

While many poor people do not have insurance, a great majority have access to some type of care.  For instance, all people have access to emergency room services.  I currently volunteer at one of the many free clinics located in San Diego county.  Thus, lack of insurance is not equivalent to absence of medical care.

A brief model I have created may help explain how poor individuals choose their optimum number of work hours and amount of health care consumption.

Individuals are utility maximizers and maximize the following function:

U(C,h,l), s.t.:

• C+p*s+=I+wL;   if p*s
• C=c; if p*s>I+wL-c
• h=f(s);
• l+L=N
• p=P+t

C‘ is total consumption, ‘h‘ is a person’s health which is a function of health care spending ‘s‘.  ‘l‘ is leisure and ‘L‘ is hours of work; these two variables must sum to the total hours in a year ‘N‘.  ‘I‘ is non-wage income.  ‘c‘ is the lower bound of consumption.  ‘p‘ is the price of health care.

A middle class or wealth person will generally want a C>c and will maximize subject to the first budget constraint.  The first order conditions for them are:

• U_c = (U_l)/w = ((U_h)*f)/p

Poor individuals will generally choose another option.  I assume that one can get as much medical services as one pleases by going to free clinics or the emergency room; by doing so, however, one is relegated to a minimal consumption level since a hospital or medical services provider will be able charge a patient for its services, unless the person is extremely poor.  The provider could not collect an amount which would lower a person’s consumption below ‘c‘.

Thus, people using the second budget constraint (generally the poor), will have:

• C=c; L=0; s=infinity.

Since any money earned by the poor individual will simply be used to pay medical bills, this person has no incentive to work.  Further, since health care is free, the person will want to consume an infinite amount of services.  In reality, medical care is not completely free to an individual since there are travel and time costs so ‘s‘ will be finite.

Nevertheless, this simple model would provide some rational for the Medicaid program.  I am not generally in favor of government administered health insurance, however, if the poor are able to force suppliers of medical services to provide their services free of charge, this will imply a higher price for those able to pay for the services.  Another option would be to not offer the poor medical services unless they paid.  Fortunately for the disadvantaged, our society has rejected this notion.

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