Unbiased Analysis of Today's Healthcare Issues

ESD: Mathias Kifmann

Written By: Jason Shafrin - Jul• 16•07

Below is a summary of some of the interesting points in the lecture of Mathias Kifman.

Gouveia model

This is a topping up political economy model. First, we have individuals who get utility from consumption and health care. There are two types: high risk πh and low risk πl. There are also two incomes, yi: rich yr and poor yp. Individuals have the following utility function:

  • max u(c) + πiv(h)
  • c=yi-Πt(y)g
  • h=g

Π is equal to the average risk of the population. The first order condition is:

  • u’Πt(yi)+πiv’

The comparative statics show that dg/dπi is positive (sicker people prefer more government health care), but the sign of dg/dy is unknown. Rich sick people prefer to have some government provided insurance since they can purchase the insurance at a lower rate, but since progressive or proportional taxation finances the system, they dislike the redistribution aspects of this program.

Topping up
We now allow individuals to buy additional medical care, m, even after paying for the public insurance program. For instance, if the government covers 5 doctors visits per year, and individual can buy additional insurance to pay for additional visits. Here, our model is:

  • max u(c) + &pii;v(h)
  • c=yi-Πt(y)g-πmi
  • h=g+m

The first order condition for the choice of m is:

  • -u'(yi-Πt(yi)g-πm)+v'(g+m)=0

The comparative statics reveal the following:

  • dm/dg is negative. More public health insurance will reduce the quantity of private health insurance purchased. This makes perfect sense since in the model public and private health insurance are perfect substitutes.
  • dm/dy is positive. Richer people have higher demand for all goods so it is sensible that they wish to purchase more private health insurance.
  • dm/dπi is negative. Sicker people purchase less private health insurance since the price of private health insurance is based on their risk level. Thus, high risks pay much more for private health insurance than low risks, while in public health insurance the price of health insurance is based on income rather than risk level.

Opting out vs. Topping up
While the topping up model shown above gives a compelling arguement for allowing private health insurance to be purchased in addition to some basic level of public health insurance, one can not always ‘top up’ with medical care. For instance, individuals may wish to avoid public health services altogether in order to avoid waiting list or in order to meet with higher quality doctors. Dr. Kifmann notes the following:

  • If the quality of public services is low, the typical individual prefers private services. Increasing public services (and raising taxes) decreases utility as long as private services are consumed.
  • Once quality is sufficiently high, however, individuals prefer public services. Increasing the quality of public health further can make individuals better off until their preferred qualitz is reached

Of course, it is difficult to ensure quality in a government monopolized system where there is no competition.

Political Economy
The political economy analysis reveals an ‘ends against the middle’ phenomenom. Individuals poorer than the median voter and the wealthiest voters prefer lower services. The poor have a high marginal utility of income and would rather spend their money on themselves rather than a public health care system, while the rich dislike the redistributionary aspect of social health insurance. The middle class, however, generally supports public health insurance. Thus, if the middle class makes up a large proportion of your society, it is more likely that government provided health insurance will be approved by the median voter.

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