“The Demand for Health Care, Organ Sales,
and the Optimal Amount of Sick Time”
Raymond J. Ballard
Texas A&M University-Commerce
Recently a medical center affiliated with Harvard Medical School refused to do Kidney Transplants for two very sick patients (Forbes, June 5, 2006).Why did they refuse? The kidneys were directed donations from strangers rather than anonymous donors or relatives. Many hospitals refuse to support directed donation programs. This despite the fact that more than sixty-six thousand are on a waiting list for kidneys. About forty thousand have been waiting for more than a year. The most common way to get off the list is to die. The United Network for Organ Sharing provides a running total of people waiting for an organ transplant. Today the number is over ninety eight thousand. The Average waiting time for a kidney in the U.S is 5 years. Kidneys are scarce because the Federal Law prohibits buying and selling organs. Allowing the sale of Kidneys from living donors would greatly increase the supply and save lives. The National Organ Transplant Act of 1984 prohibits such sales.
Traditional demand theory is not directly applicable to the demand for health care since healthcare services are not desired directly. Health care demand is a derived demand, since the underlying demand is for health. Health care is an input to the production of health. It is important to distinguish between the concepts of “need” and “demand”. Need is defined by the medical profession as the amount of care that experts believe an individual should have to remain or become healthy, based on medical knowledge. The implication of using the concept of need as the basis for health care policy is that need itself should be the main determinant of physician and hospital use. We note that the concept “need” is independent of the price, the price of substitutes, the price of compliments, income and other demand factors. We note that changes in these factors would not change need as medically defined. However we assert that planning based on the concept of demand rather than the concept of need alone, will avoid the potential misallocation of health care resources. Further using demand analysis does not mean that medical need is disregarded but only that other factors should be included in an effort to estimate what the use level of health care services will be. Everyone may not place the same value on satisfying all or even a percentage of their medical needs. Some may not be willing to pay the price or spend the time to receive all the health care that experts believe they need. We assert that a higher level of health allows the individual to gain more utility from the consumption of non-health related goods and services than would be gained if the individual had a lower level of health. We assert that health care is a normal good and that given prices of all goods and services and his income, the individual attempts to choose that combination of goods and services, including health care that maximizes utility. We expect the demand for health care to depend on the price of health care, real income, prices of compliments (e.g. Obstetric or Pediatric services), substitutes (e.g. physician services and hospital outpatient services). Additionally, transactions costs such as waiting time and travel time measured by their opportunity costs will affect the demand for health care services within the context of maximizing behavior on the part of the individual, where the individual is viewed as choosing an optimal amount of sick time through the purchase of health care.
Below we offer a simple model of the individuals’ maximizing behavior. In choosing an optimal amount of sick time we assume that the individual may buy or sell organs in an effort to maximize utility. That is the individual can sell one of his kidney and use the money to buy non-health related goods and services in order to maximize utility. Additionally we assume that the individual may buy a kidney and forgo some non health related goods and services in order to maximize utility.
Model
The individual’s decision to purchase healthcare is viewed as a part of the utility maximizing process. Individuals have a preference function based upon their stock of knowledge and life experience. Additionally, they face budget and time constraints. The individual’s utility function is represented by (1):
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U = U(G,S,L),
Where U is total utility attainment, G represents the quantity of non-health related goods and services, where G is considered to be a composite good and UG > 0, S represents sick time and US < 0 and L is leisure time and UL > 0. Sick time(S) is defined here as time lost from work for which a wage would have been earned or as loss of leisure time. The probability density function for sick time can be represented as (2).
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p = f(S/A, θ, Hi , h),
where p is the probability of a particular amount of sick time which is a function of age(A), the individual’s share of public expenditures on health care (θ), the quantity of various types of health care purchased (Hi ) and the individual’s current level of health (h).
Health care is viewed as the mode by which the individual chooses the optimal amount of sick time. In this sense health care is preventative in that the individual, given the constraints faced, can choose his optional sick time within a range determined by the sick time which would be experienced in the absence of any health care and the sick time experienced if all of the individual’s resources (time and money) were expanded on health care. Sick time can be expressed in terms of its expected value in (3)
3.  =  [f(s)/A,θ,Hi,h] ds
which can be written as (equation four:)
4. S = S(A,θ, Hi),
where the individual’s state of health h is subsumed into the sick time function (S). The derivatives are assumed to be SA> 0 (i.e, sick time is positively related to age, SHi < 0 (health care reduces sick time). The individual attempts to maximize (1) subject a budget constraint (5) and a time constraint (6).
5. w[1-L-S(A, θ, Hi )] - PGG – Pi Hi , where,
(w) is the wage rate, (L) is labor time (i.e., time for which a wage is paid), (PG) is a price index for non-health related goods and (Pi) is the price of the ith type of health care and Hi is the ith type of health care. Equation (6) indicates that a given time period can be separated into leisure (l), labor (L) and sick time (S). Note, leisure time is viewed here as the residual of time which is not used working or being sick.
6. l = L + l + S. note, L(labor time) = 1 – l – S
Given, wage (w), the price index of non-health related goods (PG), age (A), and the individual’s share of public health expenditure S(θ), the individual attempts to maximize utility attainment by choosing, G, L, Hi. The function to be maximized is represented by (7)
7. γ = u[ G, S(A,θ, Hi), l] + λ {w[1-l-S(A,θ, Hi)] – PGG-  Pi Hi a Lagrangian-type function.
Necessary conditions for utility maximization are given in (8 a-d).
8. (a) U – λ ( Pi + wSi) = 0
(b) UG – λ PG = 0
(c) UG – λ w = 0
(d) w [1- l- S (A, θ,Hi)] – PGG -  Pi Hi =0
Equations (8a-d) indicate that in equilibrium the marginal utility of the composite good (G) is proportional to its price index, and the marginal utility of health care (Hi) is proportional to (Pi + wSi). Since SHi, the marginal sick time return on the ith type of health care is assumed to be negative; the effective price of health care is lower than Pi. Note, that wSi may be thought of as the value of expenditures on health care in terms of income opportunity gained resulting from decreased sick time. Therefore, (Pi – wSi) is the net cost of health care. Equations (8a-d) yield a solution for the unknown in terms of the parameters. Solving for Hi, the ith type of health care a demand function may be written as (9).
9. Hi = Hi (w, PG, PH, A, θ)
The signs of the derivatives of the function Hi can be determined by the necessary condition for utility maximization (i.e. totally differtiting egs. 8a-d).
10. (a) λ + 
(b) λ + 
(c) λ + λ - 1-l-S(A,θ, Hi)
Equation (10a) is a slutsky-type equation with a substitution term λDij/D and an income term HiDyj/D. The substitution term must be negative in the own price case, since conditions for a maximum require Dij/D < 0. The income term can not be signed without additional assumptions. Assuming health care is a normal good then, Dij/D is negative. So an increase in the price of health care reduces the quantity demanded. If the various types of health care are technical substitutes or to the extent they are substitutes in the sick time function, then (b) above is positive or negative depending on whether λDij/D<>hiDyj/D. Equation (c ) consists of three terms, the first two are substitution terms and the last is an income term. The two substitution terms result from a change in the wage rate. In the usual case where prices are independent of the wage rate, the substitution effect shows the impact on demand for health care produced by a change in the price of leisure (the wage rate), the second term in the (10c),changes in the wage rate(w) alters the relative prices of health care and produces a substitution effect among various types of health care, we would therefore expect that an increase in wage rate would cause the individual to switch to less time consuming types of health care. The last term in (10c) is an income effect produced by a change in wage rate. Since Dij/D is negative (health care is a normal good), so the last term in (10c) is positive. The other substitution term in (10c) can be signed if leisure time and sick time reduction are assumed to be substitutes. An increase in wage rate (the price of leisure) causes expenditures on health care to increase. So, Dλj /D> 0.
The impact of age on the demand for health care depends on the preference among goods, leisure, sick time, and the technical relation among various types of health care and the impact of age on the marginal productivity of health care. Intuitively, as age increases, sick time increases so that work time diminishes and income falls by the change in work time multiplied by the wage rate. Given that health care is a normal good, as income falls, ceteris paribus, the demand for health care falls, however, with third party payers, insurance, Medicare, etc., the optimal choice is changed, and the demand for health care tends to increase after age 65.
It should be noted that if the individual is constrained by law so he can not buy or sell an organ optimal choices can not be made and utility attained will be less than optimal.
The notion of owning one’s own body seems odd to some, but if we don’t own it ourselves, who does? Historically, after death, bodies were the property of the deceased’s relative, like the rest of the deceased’s estate or as part of a family’s right to bury their dead. Inherent in this traditional approach is the notion of ownership, either by the deceased or the family. But that isn’t how the government sees it.
The President’s Council on Bioethics, the U.S. Dept. of Health and Human Services, and the New York State Legislature are discussing presumed consent as a possible solution to the organ shortage. Presumed consent really is no consent at all. Presumed consent is a form of “conscription”. Unless individuals make their contrary wishes clearly known, the government will take possession of their organs and use them as they see fit. It seems rather undemocratic for the government to presume anything regarding my wishes, let alone the notion that the government has the authority to presume what I want to do with my body while alive or after death.
If not conscription, perhaps the proper analogy is eminent domain, in which case, fair compensation is due. Either way, the government is taking something of value from one set of citizens without their consent to benefit others, and those benefiting are not just the recipients dying on the organ donor waiting list. Doctors aren’t expected to harvest or implant organs for free. Hospitals aren’t expected to provide their surgical facilities and recovery rooms for free. Organs aren’t transported from one facility to another for free. Organ and tissue banks all make nice size profits, as do the companies that use donated bone and tissue to manufacture all sorts of medical products used in surgery. It is revealing that everyone is making money except for the people who provide the raw material. No wonder some patients feel cheated when what they give for altruistic reasons is used to make others millions.
The solution to the organ shortage is to allow a free market in all aspects of organ and tissue procurement. Let the market do what it does best – match those with goods and services with those who need them. It would be nice if altruistic motives were enough to provide all the organs and tissues needed, but why, in a society where the exchange of money for goods and services is the norm, should people be limited to the two options for giving their bodies away or having the government take them without asking?
The organ shortage kills more than just the people who die waiting on the organ donor list. Transplant surgeons argue that organs should be harvested earlier by reverting back to heart/lung indications for death instead of waiting for brain death; people get sick because organs are harvested without full medical screening; selling organs on the black market has caused multiple cases where people become ill due to contaminated bone and tissue transplants; and funeral homes steal and sell organs and other body parts on the black market.
To make a real dent in the organ shortage, states don’t need more laws, more police investigations, more active recruitment of donors, or more aggressive tactics to get families to donate; what they need is a legitimate market. Let people sell their kidneys while they are alive (most people have two), and let people stipulate in their wills that they want to sell their organs, bone and other tissues at death. Insurance companies can create real incentives- financial incentives-to get people to donate.
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