Uwe E. Reinhardt is an economics professor at Princeton. He has some financial interests in the health care field.

My previous post, on the shortage of primary-care doctors, brought forth a set of illuminating comments. As many readers pointed out correctly, the issue has many facets, not only an economic one.

Although economists are fully aware of the complexity of career choices, in their Op-Ed piece on the subject that inspired my initial post, Drs. Peter Bach and Robert Kocher used what economists call the human-capital approach to occupational choice.

That approach styles a career choice as an ordinary investment project, focused mainly on alternative cash flows or, in their more sophisticated forms, monetary equivalents of costs and benefits. Drs. Bach and Kocher focus purely on cash flows.

To recap their proposal, they would make attending medical school free of tuition for all students and pay that substantial cost by eliminating the salaries currently paid to residents not in a primary-care residency.

Making tuition free will not increase the overall number of medical school graduates –- because their number is constrained by the limited supply of medical-school places in the United States.

There is already huge excess demand for medical education in the United States, which denies access to thousands of qualified American college graduates every year, then covers the resulting physician shortage by importing large numbers of medical graduates from abroad.

Drs. Bach and Kocher believe that eliminating the salaries of residents in the specialties will drive many among an artificially limited supply of medical school graduates into primary care. Frankly, I doubt it.

To follow my reasoning, let us build the human-capital model that economists would use in the classroom to this end.

The Baseline Human-Capital Model
To illustrate the human-capital approach, I begin with what I shall call the baseline case, using numbers from Drs. Bach and Kocher. Currently, residents in both primary care and in a non-primary-care specialty (hereafter just “specialty”) are paid salaries starting at $50,000 and assumed here to be rising at an annual rate of 3 percent.

We imagine a 26-year-old medical-school graduate who is choosing between a career in primary care and a higher-paying medical specialty that does, however, require two added years of residency. We assume that primary-care physicians serve a three-year residency and residents in the non-primary specialty serve a five-year residency.

Upon completion of their residencies, we assume that primary-care physicians will start practice at a pretax income of $190,000 and specialty physicians will earn 70 percent more in every year of their career, as suggested by Drs. Bach and Kocher. Thus, we assume that specialists start at an annual income of $323,000. Our assumption, as noted, is that specialists start practice two years later than primary-care physicians.

Finally, we assume that the incomes of both categories of physicians grow at 5 percent a year until age 55 and a bit more slowly thereafter. That rate may be higher than current growth rates in annual physician incomes; the higher rate reflects an impending overall shortage of physicians in the United States, as is now widely anticipated by the experts. In fact, a rate of 5 percent may turn out to be low.

Many physicians may not recognize their own experience in this hypothetical example, because there is considerable variance among physician incomes. I merely seek to be illustrative here with reasonably realistic central tendencies.

The chart below illustrates the alternative future cash flows that our hypothetical baseline case implies over the physicians’ careers, starting with their first year of residency. For ease of calculation, we make the assumption that all salaries and incomes are received by the physician at the end of the year in one lump sum.

The red line in the chart represents our hypothetical primary-care physicians and the blue line the specialist.

Let us now look at the purely financial investment implied by a medical-school graduate’s decision to train for a specialty rather than pursue a primary-care career, other things being equal.

Basically, the investment here is the primary-care income that the specialists forgo during the extra two years of residency, minus the residency salary they will earn in those two years. The return on that investment is the much higher income the specialist earns thereafter.

The next chart depicts the differential cash flow implied by this investment decision. From a monetary perspective, training for a specialty tends to bring a large payoff on a relatively small investment outlay, certainly for the higher-paying specialties.

The two most widely used metrics in the classroom and in modern business practice to evaluate future cash flows from investments are the net present value of the cash flow, known as N.P.V., and the internal rate of return on the decision, known as I.R.R.

(This is not the place to explain these two economic concepts in detail. For readers who would like to know a bit more about them, see the lecture notes from my freshman economics course.)

In a nutshell, the net present value of an investment is the algebraic sum of the future periodic cash flows it yields, with each future year’s cash flow converted to present-value terms. In this case “present” means the beginning of the first year of residency.

The idea is that if one can earn, say, 6 percent on $1,000 invested for one year, one would end up with $1,060 at the end of the year. The $1,000 is thus the present value of the $1,060 receivable one year hence. By the same reasoning, at an interest rate (also called discount rate) of 6 percent, a $350,000 receivable, say, 12 years hence would have a present value of only $173,939 = $350,000/(1.06)¹².

Practically, we can think of the N.P.V. as the amount by which the investor’s (here the specialist’s) wealth is expected to increase, as of the moment when the investment decision is made, by choosing the investment rather than forgoing it. Think of it as instant wealth creation, but wealth measured in N.P.V. terms.

The I.R.R. is a more difficult concept. It can be thought of as the rate of return the investment project yields, in any given year, on the amount invested in the project and not yet returned by past cash inflows as of the beginning of that year.

In their textbooks on corporate finance, economists regularly warn against relying on the I.R.R. to evaluate investment decisions, because that metric can be quite treacherous. Ironically, when applying the human-capital model to occupational choice in their theoretical or empirical work, economists have focused mainly on the I.R.R.

In what follows, I shall focus mainly on the N.P.V. criterion.

For our baseline case — in the absence of the Bach-Kocher proposal — where both types of physicians are paid salaries during their residencies, the net present value of an investment in becoming a specialist rather than a primary-care physician, calculated at an annual discount rate of 6 percent, is $2.1 million. (If we had looked just as the algebraic, undiscounted sum of the differential cash flow in the second chart it would be $9.3 million, but because $1 received 40 years hence is not the same as $1 received one year from now, the algebraic sum of long-term future cash flows has no useful meaning).

I note in passing that the corresponding I.R.R. to this investment is 39.22 percent. That rate of return may strike readers as very high, but even higher rates have been found in the empirical literature (see, for example, Pages 4-8 in this paper by Sean Nicholson, now of Cornell University, and Slide 18 in another of his papers).

The Bach-Kocher Proposal
Under this proposal, no medical student would pay tuition. Therefore we can disregard tuition altogether, because there is no difference between the two types of physicians.

In fact, the only small difference between this proposal and the current baseline is that specialty residents would not be paid a salary during their five years of residency. The algebraic sum of the foregone salaries is a mere $265,457. Its present value is $222,872, not even as much as the specialist’s first-year income. It represents a decline of about 3.3 percent in the $6.8 million N.P.V. of the specialist’s lifetime cash flow.

Put another way, the Bach-Kocher proposal would shrink the difference between the N.P.V.’s of the two physicians’ lifetime earnings to about $1.88 million, from $2.1 million.

If I were the medical school graduate and had to choose between a specialty career or a primary-care career, these small declines in the N.P.V. of my expected lifetime earnings certainly would not drive me into primary care.

An Alternative Proposal
An alternative proposal would be not to force specialists to forgo their residency salaries. Instead, we would alter the baseline case simply by raising the primary-care physician’s income by X percent in each year of practice, leaving the cash flow of specialists unchanged. In that case, one would not make medical school tuition-free, sparing the taxpayer the need to bear that cost.

For starters, let us ask how large X would have to be to achieve the same result as the Bach-Kocher proposal, in terms of a decline of the N.P.V. of the specialist’s cash flow relative to the primary-care physician’s.

The answer is that a 2.21 percent increase in every year of the primary-care physician’s income would have the same overall effect as withholding the salaries of the specialists during residency. That may seem a small increase, but it would, of course, be applied every year, and that will add up.

While the Bach-Kocher proposal is imaginary and novel, I conclude that is too timid to move the mountain.

If there really is a shortage of primary-care physicians in America — and one could have a debate on that issue — then more powerful policy tools must come into play, going beyond mere financial return, which is but one of many factors driving specialty choice.

Part of a better policy solution would be to inquire more deeply how medical graduates responds to income differentials in practice. Do they use the concepts taught in economics? Or do they just observe prevailing income differentials among the various specialties and base their choices on that information?”

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