1 EO 364: Hospital 2 Hospitals in the Marketplace The last segment of our discussion has been on the hospital s structure and how it affects there choices. We will now examine in greater detail the hospitals place in both labor markets, and its choices in competition with each other. As before we will be using the structure of a ot-for-rofit Hospital as our base of consideration since it is straight forward to consider the decision process of a hospital as profiteering as opposed to one which maximizes the utility of its board of trustees or directors. Hospital in the Labor Market Labor Market for Medical taff ince the repute of a hospital is heavily dependent on the skills of its physicians, a primary concern is how to attract a good or potentially skillful physician. ote that we have used attract good doctors as opposed to hiring since as we have noted, hospitals do not hire doctors since they are subsumed under very different laws. The structure is similar in anada as it is in the.. This is quite unlike hospitals in other countries such as the.k. and Germany. The manner in which hospitals attract doctors has been through direct competition with one another through better provision of facilities so as to permit the doctor better opportunities for profit maximization. The manner this is done, as noted from our discussion of residual claimant is through the board of trustees acquiescing on their needs, and consequently our belief that doctors are the most likely, and strongest residual claimants. It should also be noted that not all doctors are made equal in the eyes of the board of trustees since some may bring both repute and disrepute, while others are cash cows to the hospital on account of the skills. The exact mix is ultimately dependent on the utility of the board of trustees. What do you think is the optimal mix to a public hospital? However, if we think about it, in truth both the hospitals and doctors need each other, since the doctor cannot practice without the facilities provided by the hospital. The equilibrium in service and equipment provided to the doctors in each hospital differs depending on the equilibrium bargaining outcome (if both parties has a credible position should an agreement fail, the threat would lead both to the attainment of a ash Bargaining equilibrium.). The difference in equilibrium as has been noted is due to the preferences of the board of trustees and in turn the strongest lobbying group of doctors. It has been suggested that the competition for physicians as been costly in so far as virtually all hospitals have technologically advanced treatment facilities including those in smaller hospitals, and consequently the diffusion of doctors into smaller communities. However, should we really think of this as detrimental to the general welfare, or is it a good thing, since it does reduce/eliminate accessibility problems.
2 EO 364: Hospital 2 Hospitals and atients The primary aim of a hospital in attracting good doctors is to attract patients, but are patients really drawn to a hospital on account of good doctors?. To the extent that some patients are not responsive to treatment cost due to full insurance coverage, attracting patients is not diametrically opposed to attracting good Doctors. This type of patients would be more concerned with quality of care from Doctors, service quality of ursing staff, and even quality of food. 2. However, there is another segment of the market that is price sensitive due to lack of full coverage, or no coverage at all. In that instance, better equipment that attracts doctors would be opposed to the objective of attracting patients. Further recall an earlier finding that hospital can and do past on all cost increases to patients. How then can we model the competition among hospitals? How do we think about the demand that the hospital faces? How is the effectiveness of the hospital at attracting patients and doctors affected? As noted before, the likely model would be monopolistic competition. sing the idea of ournot competition, the elasticity of demand would be proportional to a hospital s share of the total market. Feldmand and Dowd (986) using data on Minneapolis-t. aul found that the price elasticity for different segments of patients were close to what the ournot model suggested; where private pay patients had a price elasticity of -4; for Blue ross patients about This is suggestive evidence that hospitals have some market power as we have discerned before. Given this, this has implications on how effective a hospital would be able to attract good doctors and patients. Model of Equilibrium Quality and rice sing ewhouse s model (976), a hospital is characterized by a single utility function (think of that as the median voting Board member). Let the hospital choose between size/quantity of patients () and quality of service () for simplicity first (though it is not difficult to think about the two facets as being vectors of features the hospital finds important). The hospital then maximizes its utility, (,). Let the inverse demand for patients be (,), where price is decreases with respect to but increases with respect to. Let the cost of running the hospital be (,) and that it is increasing in both and. Further since we are trying to depict the choices of a not-for-profit hospital, we have an additional constraint of breakeven point, [(,)(,)]. This essentially says that the not-for-profit hospital will not make any profit. Given this last constraint we can depict the set of combinations for and that would satisfy the constraint.
3 EO 364: Hospital 2 A of given Equilibrium ombinations of and Demand for given ote that the equilibrium points are the lower of the intersection between the demand and the average cost curve. The higher intersection is not a reasonable choice since the hospital can always do better by increasing the quantity choices. Anything in the middle violates the constraint that they are not-for-profit. Where there is only a single point, it is because it is a tangency. ote that each demand and average cost above is drawn for a given level of quality. You can just as well draw the diagrams in terms of quality, and have them dependent on. These choices then give us the usual concave production possibility frontier in this case, and the optimal choice of the board of trustees is the point of tangency of the indifference curve of the not-for-profit hospital and their production possibility frontier.
4 EO 364: Hospital 2 * * Mathematically, the solution to the problem is as follows; olve the lagrangian, L (, ) [ (, ) (, )] which gives the following first order conditions (ote that the term is interpreted as the implicit price of meeting the constraint. ince it is a price it will always have a positive value), 0 ( ) ( ) 0 (, ) (, ) 0 The above first order conditions can be rewritten as,, ( ) (, ) Equating the first two conditions yield the condition that says that the ratio of Marginal tility over cost for both quantity and service must be the same. ote that this is not the same as saying and shares the same weight since the weight is ultimately decided by the level of utility either one gives to the board of trustees. If the utility is weighted towards, then for the two ratios to equate, the service rendered must be high so that the marginal utility from it begins to fall substantially (due to diminishing marginal utility), and rising marginal cost of an additional unit of service.
5 EO 364: Hospital 2 Implications of the imple Model: First note that when the marginal utility from quantity choice is 0, ( ) 0 0 M This means that when the hospital ignores considerations of quantity, in the sense that quantity does not affect the utility of the board of trustees, then the problem reduces to a monopolist s problem, and we should then expect higher prices. To see this, when the ot-for-rofit hospital does consider quantity an important component of the Board s utility, then the first order conditions gives us the following pricing strategy. ( ) 0 The comparison of the two equations yields the following insight.. If quantity choices are an important element to the hospital, prices should be lower than under the monopolist case. 2. Another way to look at the above is to ask ourselves, does the hospital produce at the elastic or inelastic portion of the demand, or how is that affected by the quantity choice;
6 EO 364: Hospital 2 ote that all that will differ between the elasticity of a monopolist and a caring hospital is that the denominator of the elasticity formulation would be larger. First to see that prices are indeed higher for a caring not for profit hospital, note from the pricing equation that such a hospital would need to raise the marginal cost, which is attained at higher level of quantity choice, and at the same time, due to diminishing marginal utility, the marginal utility of quantity would start to fall substantially enough. It is when quantity is high, than would you get the hospital producing at a lower elasticity level. Essentially, there would be a trade off between raising prices by raising quantity, but realizing that as elasticity tends towards, they would be producing at too high a level. This essentially hint at the idea that a not for profit hospital would typically price lower, and produce at a greater quantity. 3. Another issue that may be studied pertains to the ability of a hospital to transfer changes in cost (particularly cost increases directly to patients). The argument is regardless of the fact that the cost of treatment for various sub-group of patients (identified say by insurance groups, full insurance, partial insurance etc.), it is optimal for the hospital to past on cost asymmetrically to patients by their elasticity, i.e. the greater the elasticity the lower the price, and the lower the elasticity, the greater the price charged. ee page 36 of your text. Insurance and ompetition in the Hospital s Decision We can use the above model and analysis to understand how changes in the proportion of the populace becoming insured affect the overall quantity and quality of treatment, and care. What we have done with the model up till now, is to treat the action of the not for profit hospital as a single entity to the exclusion of how they might behave in response to other hospitals. onsider the following, from the diagram below (which is exactly the same as the one in the earlier page), note that at some levels of production, the not for profit hospital is producing at the increasing average cost portion of the average cost curve. uppose as a result of high demand still available in the market, other not for profit hospitals choose to enter into the various segments of the quantity market, such as mid size hospitals etc. What entry does is to cause a fall in the demand of the incumbent hospital that is already serving that segment of the market.
7 EO 364: Hospital 2 A of given Equilibrium ombinations of and Demand for given On the limit, what occurs is that the reduction in demand causes a shift in the collection of equilibrium points for the entire market such that at all levels, optimal quantity is characterized by tangencies, and since the demand curve is downward sloping, all these tangencies would be occurring on the downward sloping portion of the average cost curve. The implication of which is that these hospitals would then be operating with excess capacity in the sense that it would be optimal to raise their production, but would not be able to since they would be making losses in that instance. A of given Equilibrium ombinations of and Demand for given What this means when we think about the increasing trend of private insurance in the orth American health market is that it causes an increase in the slope (because demand has become less responsive to changes in prices due to insurance) of the respective
8 EO 364: Hospital 2 demand, thereby raising the excess capacity that we see in hospitals. But yet at the same time, this causes an outward shift in the production possibility curve facing the hospitals, thereby allowing the health sector, and particularly hospitals to produce greater patient visits, and greater quality in treatment. Further, we know that this phenomenon would increase increased competition for doctors, which entail attractive the best doctors with the best equipment, thereby raising the average cost of the hospital as well. Interactions between Hospitals and Doctors To understand the decision of a doctor s choice of entering into a particular health market, we could treat each doctor as if they were a monopolistically competitive firm or agent. Each physician as we have noted faces the cost of their practice, and in competing for physicians, a hospital attempts to attract them by providing the use of equipment. We can think of this strategy as a cost reduction strategy from the hospital to the doctor. uppose the hospital is in initial equilibrium A, where every doctor in the market is currently making zero profit. Fall in A to attract new doctor B A Fall in demand facing each doctor as a result of new entry. Q When hospital attract new doctors into the market, and particularly their hospital, that is tantamount to a downward shift to the A curve of the relevant doctors in the hospital, and not just for the new doctor alone (externalities of equipment that is for all doctors within a particular specialty in a hospital). When the doctor enters, it shifts the demand facing all the relevant doctors down since they have to share some of the overlapping patient market. I have drawn the new equilibrium as a zero profit point, though that needn t be true since it depends on how great the shift in the A is. For a substantial downward shift in the A, all doctors may in fact earn zero profits. (ote that I have assumed that doctors are profit maximizers which we have from the beginning surmised that it needn t be true, and should not be true. But the structure of this simple discussion allows us to understand how hospital and doctor entry choices are related.
9 EO 364: Hospital 2 Hospitals in the Labor Market We will now examine the interactions between hospitals and the various types of labor market besides that for Doctors/hysicians. Hospitals in their provision of services would need to obtain factor inputs in the various respective markets, and in economics we have typically segregated them into either capital and labor markets. The principal problem which is not unlike that of other firms in other industries depends on how specialized those needs are. We will discuss those differences in relation to the factor market for labor, and more specifically between specialized labor in the form of therapists, nurses etc, as against secretaries, and janitors etc. The principal difference between the two is that in the former, the industry determines the wages paid, while in the latter, it is largely out of the hands of the industry, and its constituents. As in your text, we will refer to the latter as the demand for nurses, and in the former that for secretaries. We can think of the supply curve for the nurses as upward sloping, thus creating the increase in wages should the industry expand its needs, while in the latter, because the labor is not specialized, consequently the labor force is able to move between industries with little to no friction, which in turn implies a flat demand. It is easy to see then that the latter should have a flat or if not a very elastic supply. ursing hortages eriodically over the decades, most countries has realized a shortage of nurses, and in the, the most recent occurrence took place during the 80s. When we think of shortages, of something constricting the wage rate or the supply to prevent the re-equilibrating of the market, since when we know that when an excess demand occurs market forces would drive the equilibrium wages up. An explanation that has been bandied about the shortages is a result of the market power that hospitals exercise in the nursing market. This means that the hospitals behaves like in sole buyer within the industry (and this characterization is not exactly untrue given that in some cities, only a few firms own a large share of the hospitals in the market. The diagram for a monopsonist would be as follows;
10 EO 364: Hospital 2 Wage Marginal Factor ost upply w* Labor hortage/ nfilled Vacancies L* Demand Labor/urses Yet on the flip side, there is also the increased unionization of nurses. If we then think of nurses in each market (for a city) as a monopoly, that could similarly explain the higher wages that is driving the cost of health care, and the constriction in the supply of nurses, i.e. the shortage that we see bandied around so often. Wage upply w* L* MR Demand for nurses by nions Labor/urses But given the anecdotal evidence that enrollment in nursing programs has been falling, it would seem the economic gains to entering the profession hasn t been great enough to encourage entry into the profession which suggests that this argument might not have bite. However, if both sides to the story did indeed obtain some form of bargaining power by being a monopsonist and a monopoly, the solution would largely be dependent on which party has the greater bargaining power, as determined by the greater threat. For example, if similarly accredited foreign nurses could enter the market, then the monopsonist would have the greater bargaining power within the market.
11 EO 364: Hospital 2 Appendix The following is an abbreviated discussion on ash Bargaining. ash Bargaining The ash Bargaining solution must follow essentially four axioms,. areto Efficiency: Only areto Efficient Outcomes can be solutions. 2. ymmetry: If the feasible set of solutions is symmetric, each party will get equal share of utility. 3. Invariance: Linear Transformations of either party will not affect the solution. 4. Independence of Irrelevant Alternatives: Exclusions of outcomes that is not the solution in the solution set will not affect the solution. The problem is structured as follows:. A bargaining problem is a pair (,d), where is a set of couplets (pairs of numbers) that are payoffs to agreements and d is a couplet that describes the payoff to disagreement. 2. d 3. For some couplets in, such as ( v,v 2 ) we have v > d and v 2 > d is a convex set. 5. is bounded (it is a subset of a larger set), and closed (every convergent sequence of members of is in. The solution to such a problem is the maximization of ( v d )( v ). 2 d 2 I repeat the example I gave you earlier: Let the total profit that is being bargained over between the union and firm be π. And let the threat of each party be T and T respectively. Then the ash Bargaining solution is the solution to the following problem, max π T Then u π f ( ) ( ) ( π ) f T u (( ) π T ) π ( π T ) ( T T ) f 2 2π Where describes the share of total profits. u u f 0