San José State University
Department of Economics

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Thayer Watkins
Silicon Valley
USA

 The Economic Effects of the Subsidization of a Monopolized Commodity: How Subsidized Healthcare May Bankrupt the Nation

## The Nature of the Issue

Although this webpage addresses the general problem of the effect of subsidization of consumers in a protected monopoly market, the specific issue isthe healthcare industry. The trade organization of physicians, the American Medical Association (AMA), around 1900 got control of the accreditation of medical schools in the U.S. For more on how this was achieved see The Medical Cartel. The AMA used this power to cut the admissions to medical about in half, which is generally the effect of the monopolization of a previously competitive industry. Over time this artifical restriction of supply raised the price of physicians' services enormously. In effect, physicians had formed a cartel. For many years the AMA ran the cartel so as to maintain such things as pricing based upon patient incomes. These were lost over time but as long as the artificial limitation on medical school admission stayed in place the healthcare industry was subject to monopoly pricing.

The policy of government has been to ignore the artificial restriction on the supply of physicians which is the source of the problems of healthcare in the U.S. and instead promote ways to subsidize the consumers who cannot afford the monopoly pricing. Most consumers coped with the monopoly pricing by purchasing medical insurance which spread the payment for medical services over time. Usually the payment for medical services involve the consumer paying a portion of the cost, called the co-payment and the insurance company or the government program paying the rest.

## The General Character of Monopoly Pricing

First consider the problem of monopoly pricing without any subsidization. Let p be the price the consumer pays and the monopolist received. The quantity sold q is a function of this price; i.e., q=f(p). The cost of production is a function of the quantity sold; i.e., C=g(q). The profit π of the monopolist is then

#### π = pf(p) − g(f(p))

The effect of an increase in price on profit is given by

#### dπ/dp = f(p) + pf'(p) + g'(q)f'(p) = f(p) + (p-g'(q))f'(p)

The effect of a price increase on quantity demanded, f'(p), is generally negative. The monopolist keeps increasing the price until the negative effect of a price increase on the quantity sold outweighs the revenue from the price increase. If for some reason a price increase has no effect on the quantity sold then the monopolist increases price until it does. For a commodity such as medical services consumers need a limited amount but over a range of prices the quantity per consumer is not much affected. Therefore for medical services f'(p) becomes negative only when some consumers drop out of the market because they cannot afford the price. Government policy is usually directed at preventing any block of consumers from dropping out of the market because they cannot afford the price. The effect of this policy is then to allow the monopolist be raise the price still further.

## A Simple Linear Model

Let the demand function for the commodity be

#### q(p) = qmax − bp

The cost function for the commodity is

#### C(q) = cq

The diagram below shows the essential elements of monopoly pricing for this special case.

If the industry is competitive then the market price would be equal to the unit price c and the quantity produced and consumed would be equal to the quantity demand at a price c. This is the socially optimum level of consumption, qopt. The monopoly, in this case, produces one half of the socially optimum level; i.e., qmon=½qopt. The price that is established is the price such that the quantity demanded is equal to qmon. In happens, for this case, that the monopoly price is the average of pmax and c.

Now the effect of subsidization in this market can be considered.

Let the price paid by the consumer, called the co-payment, be denoted as pco. The co-payment share of the full price p is α. Thus

#### pco = αp

The quantity demanded is functon of the co-payment pco rather than the full price p. Thus the profit of the monopolist is

#### π = pq(pco) − cq(pco)

The monopolist chooses p and pco simultaneously to maximize profits. It is simplest to let pco be the variable chosen; i.e.,

#### π = (pco/α)q(pco) − cq(pco) or, equivalently π = (pco/α)(qmax−bpco) − c(qmax−bpco)

The maximization of profit requires that dπ/dpco=0. This means that

#### (1/α)(qmax)−2bpco) + cb = 0 which reduces to pco = ½(qmax/b + αc)

The expression (qmax/b) is the intercept of the demand function with the price axis and thus represents the maximum price that would be paid for any of the commodity, pmax. Thus the profit-maximizing co-payment and full price are:

#### pco = ½(pmax+αc) and, since p=pco/α p = ½(pmax/α + c)

Since the the insurance share or the subsidy is paid out of insurance premiums or taxes by the consumers, the true price paid by consumers is p rather than pco. Note that as α→0 the full price p→∞. Thus the economy would be bankrupted trying to pay for the monopolized commodity and its subsidy. Consider the extreme case in which the commodity is free to the consumers and they demand qmax no matter how high of a price charged to the insurance company or the government. The monopolist can then charge an unlimited price. In effect the profit maximizing price becomes infinite. Obviously the economy would be bankrupted under such a regime.

There is an interesting result from the model concerning what happens to the prices p and pco. The limit of pco as α→0 is not zero. Instead the limit pco as α→0 is ½pmax. This is because the full price is a function of the co-payment share α. Thus

#### pco = αp(α)

and when the effect of a decrease in α on the full price p is taken into account pco does not necessarily go to zero as α goes to zero. As stated above,if α is equal to zero this means the consumers want qmax no matter what the full price is and hence the monopolist increases the full price without bound.

## The Effect of Subsidization on the Profits of the Monopolist

Now consider the profit of the monopolist as a function of the co-payment share α. The profit of the monopolist is π=(p−c)q(pco). The difference between the full price p and the marginal cost c is

#### p−c = ½(pmax/α−c)

The quantity consumed is

Thus

#### π = ½αb(pmax/α−c)²

The dependence of π on α is of the form

#### π = ½b[pmax²/α − 2cpmax + c²α]

and hence as α→0, π→∞. Since the revenue of the monopolist comes from the consumers as insurance buyers or tax payers the infinite profits of the monopolist come from the infinite expense for the consumers. Thus a misguided effort to benefit the consumers by making the co-payment share as small as possible would bankrupt the economy.

This process of bankrupting the economy is operation and has been for decades. Consider the dramatic increase in the share that medical expenditures constitutes of the Gross Domestic Product (GDP).

The big question is, "At what share of GDP will medical expenditures bring about a collapse of the economy?" As the share gets larger and larger taxes will have to be greater and greater and hence the incentives for working and striving will become less and less. Suppose that share is 25 percent. A linear extrapolation of the trend indicates that a 25 percent level will be reached in 36.5, in 2043. But the trend is not strictly linear. It has an upward curvature that would indicate an exponential trend. With such an exponential trend the 25 percent level would be reached in 18 years, in 2025.

The only way to avoid the harm of monopoly pricing for the consumers is to break the monopoly. In the case of healthcare this means training twice as many physicians and other health professionals. If the existing medical schools cannot accommodate the admission of twice as many students then additional medical schools should be created.