Counterpoint: "Competition and value-of-service pricing in the residential real estate brokerage market." (response to Sharon O'Donnell and Tom Geurts in this issue, p. 327)(Point/Counterpoint)
In their "Point," O'Donnell and Geurts ( 1995) dispute the results of my analysis, arguing that an equilibrium of the sort I claim is inconsistent with the model's assumptions. My original analysis is correct, however, and in this "Counterpoint" I hope to demonstrate the fallacy of O'Donnell and Geurts' argument.
As O'Donnell and Geurts note, the simplest version of my model has sellers of just two types, high and low-time-value sellers, and brokers who specialize in serving sellers of one or the other type. O'Donnell and Geurts' analysis errs in that it assumes that the full prices of brokerage services would equilibrate across segments of the market (characterized by different seller time values) rather than merely within segments.(2) In fact, the equilibrium values of the full price of service will differ across market segments; a point that is made on page 34 of my paper and supported in note 16.
Consider the simple special case: two market segments distinguished by seller time values [v.sub.1] and [v.sub.2] > [v.sub.1]. Equilibrium will be characterized by vectors of values for the brokerage fee, p; the size of the listing pool, n; and the full price of service, P; for each of the segments:
[Mathematical Expression Omitted] Results from my paper include:
(equation (10)), [Mathematical Expression Omitted]
(equation (8)), [Mathematical Expression Omitted]
(footnote (16)). [Mathematical Expression Omitted]
The market force that tends to equalize full prices within market segments is provided by sellers' search for low-full-price brokers. Why doesn't this force operate to equalize full prices across segments too? First of all, as my paper's Appendix A shows, a broker who has specialized in listings associated with sellers of one time value has no incentive to open his/her listing pool to sellers of the other time value (even if it were possible to discriminate between the two with respect to the brokerage fee that is charged). But what if brokers were prohibited from barring listings of the unwanted type? That is, what if brokers were required by law to merely post a fee for brokerage services (a value for p) and then provide service to all comers? Even in this case, there would be no tendency for full prices to equalize between segments because, at equilibrium, there would be no incentive for sellers to cross market segment lines.
To see this, consider Figure l, which is a version of my paper's "Chart 2" labelled slightly differently and cleared of some of the unnecessary clutter. The curve labelled "R = c" is the locus of (p, n) combinations for which broker sales fee revenue per unit time is constant and equal to c, the opportunity cost of broker services.(3) The two concave lines on the graph are loci of (p, n) combinations for which full price is constant.(4) Note, however, that full price is calculated using different time values for the two loci.(5) In each case, (p, n) points above and to the right of the locus yield full prices higher than that associated with points on the locus. Applying this principle, the following inequalities obtain: [Mathematical Expression Omitted] and [Mathematical Expression Omitted]
The first of these says that a high-time-value seller who sought service from a broker specializing in low-time-value listings would incur a greater full price of service than is available from high-time-value brokers.(6) That is, a high-time-value seller has no incentive to shop for brokerage services among brokers who are low-time-value specialists. The second inequality, likewise, says that low-time-value sellers have no incentive to attempt to cross market segment lines. Thus the equilibrium described in my paper is a separating equilibrium in the sense that the segmentation of the market is consistent with individual incentives for both sellers and brokers.
A simple numerical example will aid in this demonstration. A showing rate function of the form g(n) = [ab.sub.b] will satisfy conditions Equations 1, 2, and 3 of my paper with a > 0 and -1 < b c 0. For this case, the model's Equations 4, 6, and 7 can be solved explicitly for the endogenous variables:
[Mathematical Expression Omitted]
Let m, the expected number of showings required for a sale, be 10. Let c, the opportunity cost of brokers' services, be $500/day. Assume that sellers fall into one of two groups: those with time values of [v.sub.1] = $125/day and those with time values of [v.sub.2] = $250/day. Finally, take a = 0.5 and b = -0.2. Evaluating the equations above, first with v = [v.sub.1], then with v = [v.sub.2], yields:
[Mathematical Expression Omitted] and
[Mathematical Expression Omitted] The market rewards high-time-value sellers with smaller broker listing pool sizes (and correspondingly prompter sales) but at the expense of a higher brokerage fee and full price of service.
The separating nature of equilibrium can also be illustrated in the context of this example. A high-time-value seller who lists with a low-time-value broker would pay a fee of [Mathematical Expression Omitted] and expect a 00wait of m/ g([Mathematical Expression Omitted]) before sale. This would entail a full price of:
[Mathematical Expression Omitted] Because this is greater than the full price offered by high-time-value brokers, 9473, a high-time-value seller would have no incentive to cross market segment lines. A similar argument demonstrates that low-time-value sellers could not benefit by attempting to list with high-time-value brokers:
[Mathematical Expression [Mathematical Expression
The example can also be used to demonstrate the claim of my paper's Appendix A: the optimality of broker specialization. A broker with listing pool size n who offered service to a high-time-value seller while meeting or beating the market determined full price of [Mathematical Expression Omitted] could charge no more than:
[Mathematical Expression Omitted] To obtain the broker's revenue per listing per day for service to high-time-value sellers, multiply the expression above by g(n) / m, the broker's rate of sales. The result is:
[Mathematical Expression Omitted] Likewise, a broker with listing pool size n could earn revenue per listing per day of:
[Mathematical Expression Omitted] for service to low-time-value sellers. Evaluating these expressions at [Mathematical Expression Omitted] and [Mathematical Expression Omitted] the following inequalities obtain:
[Mathematical Expression Omitted] and
[Mathematical Expression Omitted] The first inequality says that a low-time-value specialist, with pool size [Mathematical Expression Omitted], earns revenue at a faster rate per listing through service to low-time-value sellers than could be earned through service to high-time-value sellers. The second inequality, likewise, states that a high-time-value broker has no incentive to open his/her listing pool to low-time-value sellers.
Finally, while I believe that O'Donnell and Geurts' specific criticism of my analysis is without foundation, I would like to reiterate qualifications I mentioned in my paper: My model is a highly stylized one that makes no pretense of explaining the specific form of value-of-service pricing practiced by brokers, percentage-of-house-value pricing. Nor does my analysis make any claim of efficiency for the equilibrium of the model. For these reasons, I agree with O'Donnell and Geurts' conclusion that "further research is warranted in this area."
(*) Direct all correspondence to: John R. Schroeter, Iowa State University, Department of Economics, Heady Hall, Ames, IA 50011-1070.
(1.) This is the kind of environment described in DeVany and Savings' (1977, 1983) models of services for which waiting time is an important quality dimension.
(2.) Their "proof by contradiction" turns on the assumption that the "P"s appearing on both sides of their Equation 2 have the same value. In fact, Equation 2 does hold, but with the left-hand-side "P" greater than the right-hand-side "P."
(3.) O'Donnell and Geurts mistakenly describe this as an "iso-cost curve."
(4.) O'Donnell and Geurts characterize these as opportunity loci for high- and low-timevalue sellers. More properly, they are opportunity loci for brokers specializing in providing service to high- and low-time-value sellers.
(5.) To briefly review the figure's interpretation: Iso-revenue curves above and to the right of the one shown are associated with higher revenue rates; those below and to the left, with lower revenue rates. A broker serving low-time-value ([v.sub.1]) sellers, for example, would confront sellers with the market determined full price of [Mathematical Expression Omitted] by choosing any point on the [Mathematical Expression Omitted] opportunity locus. Among these, ([Mathematical Expression Omitted], [Mathematical Expression Omitted]) lies on the highest iso-revenue curve. The maximized value of revenue per unit time, moreover, is equal to c, brokers' opportunity cost per unit time of service. Hence ([Mathematical Expression Omitted], [Mathematical Expression Omitted]) gives the brokerage fee and listing pool size of a free-entry equilibrium in the market for brokerage services for low-time-value sellers. Similarly, ([Mathematical Expression Omitted], [Mathematical Expression Omitted]) corresponds to an equilibrium for the high-time-value segment of the market.
(6.) To simplify terminology, I use "a high-time-value broker" to mean "a broker who specializes in service to high-time-value sellers."
DeVany, Arthur S. and Thomas R. Saving. 1977. "Product Quality, Uncertainty, and Regulation: The Trucking Industry." American Economic Review, 67: 583-594.
--. 1983. "The Economics of Quality." Journal of Political Economy, 91: 979-1000.
O'Donnell, Sharon I. and Tom G. Geurts. 1995. "POINT: Competition and Value-of-Service Pricing in the Residential Real Estate Brokerage Market. " Quarterly Review of Economics and Finance, (this issue).
Schroeter, John R. 1987. "Competition and Value-of-Service Pricing in the Residential Real Estate Brokerage Market." Quarterly Review of Economics and and Business, 27:29-40.
|Printer friendly Cite/link Email Feedback|
|Author:||Schroeter, John R.|
|Publication:||Quarterly Review of Economics and Finance|
|Date:||Sep 22, 1995|
|Previous Article:||Point: "Competition and value-of-service pricing in the residential real estate brokerage market." (response to John R. Schroeter in Quarterly Review...|
|Next Article:||Risk dominance and coordination failures in static games.|