San José State University
Department of Economics
& Tornado Alley
This material is an analysis to a simple model of a monopoly to obtain an estimate of the magnitude of the social costs of the cartel arrangement that artificially restricts the number of physicians and other medical professionals trained each year.
A monopoly which does not have to worry about competing entrants to its market maximizes its profits by restricting output and raising its price. Its production is less than the social optimum production and that restriction of production has a social cost.
Where there is a market price for a commodity consumers increase their consumption up to the point where the marginal benefit of another unit of consumption is equal to the market price. Thus if consumption is reduced by one unit the decrease in consumer benefit is equal to the market price. As consumption is further reduced the price increases.
The demand function for a commodity is the relation between the quantity demanded and the market price. The inverse demand function is the price as a function of the quantity consumed. In effect, the inverse demand function is the marginal benefit to consumers as a function of the quantity consumed.
Consider a demand function which is a straight line. Algebraically such a demand function is of the form
The inverse demand function is then
where pmax=(a/b) is the price that reduces the quantity demanded to zero. In effect, pmax is the maximum price that would be paid for any of the commodity.
The word monopoly means one seller but if there is only one seller in the market because the price is so low that there are no other firms willing to enter then there is no social costs to there being only one seller in the market. It is the protected monopoly that is the social problem.
The protected monopoly maximizes profit by finding a level of production and corresponding market price such that the marginal revenue from another unit of production is equal to the marginal cost to it of another unit of production.
For a straight line demand function the marginal revenue is given by
In the analysis which follows the marginal cost is assumed to be a constant c. Furthermore there are no externalities so the marginal social cost of production is the same as the marginal private costs. For social efficiency analysis the relevant marginal cost is the minimum average cost of the marginal production unit. Since the ultimate purpose of this analysis is the analysis of cartels it is appropriate to presume a constant marginal cost.
The socially optimum level of consumption is where the market price is equal to the marginal cost; i.e.,
A protected monopolist chooses a level of output qmon where MR=MC; i.e.,
This means that
When the AMA got control of the accreditation of medical schools in the U.S. the number of functioning medical schools was cut in half and the total enrollments were correspondingly reduced to about half of what they were before. The admissions were cut from 4400 per year to 2000. This lends credence to the above relation.
Further support for the notion comes from the statistics on the ratio of practicing physicians to the overall population in various countries. These are shown for the OECD countries:
|The Number of Practicing
Physicians per 1000 Population
for the OECD countries,
per 1000 pop
The Anglo-Saxon countries have a low ratio of physicians to population in the range 2.2 to 2.4 except for Australia which is slightly above that range. Apparently in the United Kingdom, Canada, New Zealand and Australia the physicians learned from their American brethren how to raise physicians' pay by restricting enrollments in their medical schools. In the wealthier states of Europe, such as Switzerland, France, Germany Italy, Norway, Sweden, Denmark, Austria, the Netherlands and Belgium, the ratios are in the range of 3.4 to 3.8. Luxembourg is the anomaly with a ratio of 2.5. Spain, Portugal and Czechia, although less affluent, are also in that upper range. This is probably what the ratio should be and what it would be in the Anglo-Saxon countries in the absence of medical cartels.
There are some countries such as Mexico, South Korea and Turkey, where the training of physicians may be limited by the resources available. Japan's ratio of 2.0 is a puzzle. It probably is due to an artificial restriction in the number of physicians trained, but possibly because of a healthier population there may be a less need for physicians' services.
The ratio of the midpoint of the lower 2.2 to 2.4 range (2.3) to the midpoint of the upper 3.4 to 3.8 (3.6) is 0.64. This is not too far off of the 0.5 ratio of cartel production to optimum production.
The statistics for practicing nurses shows a similar pattern.
|The Number of Practicing
Nurses per 1000 Population
for the OECD countries,
per 1000 pop
There is a set of high income, industrialized countries for which the ratio is in the range 9.4 to 10.6. The Anglo-Saxon countries are not grouped together with low ratios as in the case of physicians. There is a tier of countries, among which the United States is included, where the ratios are in the range of 7.0 to 8.1. The ratio of the midpoints of these ranges is about 0.75.
The statistics on nurses gives some perspective on the anomalous cases for physicians. Greece trains a high number of physicians but a low number of nurses. Japan makes up for its low physician ratio with a high ratio for nurses. Other countries such as Mexico, South Korea and Turkey have both a low ratio for physicians and for nurses.
The monopoly price pmon is determined from the inverse demand function and the level of monopoly output qmon; i.e.,
The above relationships are shown graphically as
The revenue received by the monopolist, Rmon, is then given by
The social cost, Smon, of the monopoly pricing is then the area under the demand curve as the consumption is reduced from qopt to qmon. This area is just that of the trapezoid with a base equal to (qopt−qmon) times the average of pmon and popt. Since qopt is 2qmon, (qopt−qmon) is qmon. Thus
Let the ratio Smon/Rmon be denoted as σmon. Then
This means that σmon is a function solely of the ratio c/pmax. The ratio c/pmax has to be between 0 and 1. If c>pmax there is no production.
If (c/pmax)=0 then σmon=½.
If c/pmax=1 then σmon=1. From the diagram below it is seen that as c/pmax approaches 1 the monopoly revenue and social cost become closer and closer.
The functional relationship between σmon and c/pmax is monotonic.
Thus the analysis reveals that the social cost of the reduced consumption resulting from monopoly pricing is somewhere between 50 and 100 percent of the revenue received by the monopolist.
It is true that as c/pmax approaches 1 the monopoly output qmon goes to zero and likewise with it the revenue Rmon and the social cost Smon of the monopolist go to zero. Nevertheless as Rmon and Smon both go to zero their ratio goes to unity.
The social cost be considered above is in the nature of a gross social cost. As production is reduced the production cost is also reduced. The net social cost of the monopoly is a different matter. Usually this amounts to the dead weight loss due to a monopoly. This is known to be positive but its magnitude difficult to estimate. Also the relationships of monopoly profit to the monopoly revenues and social costs are different matters. The important thing here is that the range gross social costs of monopoly pricing can be estimated from the observable data on revenues.
In the scheme of Cost Benefit Analysis the partially offsetting benefit of monopoly pricing is the reduced resource use. It may seem strange for there to be some benefit of monopoly pricing but consider the case when the OPEC (the Organization of Petroleum Exporting Countries) cartel raised the price of petroleum by collectively restricting production. Environmentalists hailed this monopoly pricing as a good thing because it reduced the depletion of petroleum.
There are cartels that are protected by government-enforced licensing arrangements. The most infamous of these is the cartel operated by the medical establishment that restricts to the number of physicians trained each year to about half of what it should be. Similar arrangements limit the number of dentists and other medical professionals trained.
|Estimates of the Social Costs
of the Medical Cartels in the U.S., 2007
The quotas on the number of physicians, dentists and other medical professionals trained each year have social costs on the order of a half trillion dollars per year for recent years. This is an enormous robbery of the American public. This figure does not include the loss to American young people who are denied the opportunity to pursue careers in medicine that they have the ability and motivation for.
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