The Need for Health Care Reform

A challenging problem facing the United States is the effect of rising health-related costs on the nation's long-term economic prosperity. In 1940 health care absorbed $4 billion, a mere 4 percent of our gross domestic product (GDP). In 1999 these costs were $1.211 trillion, or 13.0% of the GDP.

We can find the average percent rate of increase per year from these figures as follows. Let y represent the percent of GDP spent of health-related costs in year x.

Thus, on the average, each year since 1940 the percent of GDP spent of health costs has increased by an average of .15, or 15%.

Figure 1 shows U.S. health care costs as a percent of the GDP from 1960 to 1999. By reading figures for the percent of GDP from the graph for selected years, we can find a function that will give the approximate percent of GDP expended in any year. The graph can be approximate reasonably well for prediction purposes by a straight line. Suppose we choose x = 60 (for 1960), with y = 5.1% (approximately) and x = 99 (for 1999), with y = 13.0% (approximately). This gives the ordered pairs (60, 5) and (99, 13). The slope is

Now we will use the point-slope form to get the equation of the line that will define the function.

y - 5 = .20(x - 60)
y - 5 = .20x - 12
y = .20x - 7

To verify that this equation will give values of y that are reasonable, let us find y for x = 99 and compare with the figures given at the beginning of the application

If x = 99, y = .20(99) - 7 = 12.8

This result is reasonably close to the given value.

Using the function to predict the percent of the GDP that will be spent of health costs in 2010, let x = 100 in the equation.

If x = 110, y = .20(110) - 7 = 15.0.

If the linear trend continues, about 15% of the GDP will be spent on health care in 2010. Notice, however, that health care costs as a percent of the GDP has decreased in recent years, so it may not be accurate to use this equation for years beyond 1999.

Exercises