RENT: Notes on Efficiency Pricing, Rent Control and Monopolistic Landlords. June, Abstract

Transcription

1 ENT: Noes on Efficiency Pricing, en Conrol and Monopolisic Landlords Kaushik Basu Deparmen of Economics Cornell Universiy Parick M. Emerson Deparmen of Economics Cornell Universiy and Deparmen of Economics Universiy of Colorado a Denver June, 2000 Absrac We consider a model of enancy ren conrol where landlords are no allowed o raise he ren on siing enans nor o evic hem, hough hey are free o se he nominal ren when aking on a new enan. If here is any inflaion in he economy, landlords prefer o ake shorsaying enans. Assuming ha here is no way for landlords o ell a enan s ype, an adverse selecion problem arises. If in his conex, landlords have monopoly power which, as we argue, is indeed pervasive--hen he housing marke equilibria can exhibi some unexpeced properies. Mos srikingly, landlords may prefer no o raise he ren even when here is excess demand for housing. Such rens are labeled efficiency rens in his paper and heir exisence shows ha enancy ren conrol can give rise o equilibria which look as i here were radiional ren conrol in which he ren of each uni has a fla ceiling. In oher words, enancy ren conrol may no achieve he flexibiliy, which i was expeced o impar, o he sysem of radiional ren conrol. (JEL classificaion numbers: D40, K10, L12, L51, 31) (Keywords: en Conrol, en egulaion, Asymmeric Informaion, Adverse Selecion, Monopoly)

2 1 ENT: Noes on Efficiency Pricing, en Conrol and Monopolisic Landlords I. Inroducion Sandard ren conrol places a ceiling on he rens ha a landlord can charge. Hence under sandard ren conrol, excess demand for housing is common. Arguably, more common han sandard ren conrol is enancy ren conrol, which allows a landlord o se he ren freely when leasing o a new enan (subjec o, of course, he enan s righ no o accep), bu hereafer he landlord is no allowed o raise he ren, nor can he evic he enan. I will be shown in his paper ha enancy ren conrol can, hrough he workings of he marke, resul in an oucome which looks as if here is sandard ren conrol. Tha is, in equilibrium i may be in he landlord s ineres o keep he ren for new enans so low ha here is excess demand for housing a ha ren. The landlord volunarily behaves as if here was a legal ceiling on he renal rae. This surprising resul has analogues in he heory of efficiency wage (Leibensein, 1957; Shapiro and Sigliz, 1984) or he heory of efficiency ineres rae (Sigliz and Weiss, 1981). I should be clarified here ha our model is one where here is enancy ren conrol and landlords have monopolisic power. In fac wha we consider in his paper is he case of a monopolis landlord which is he oher polar exreme o he case modeled in Basu and Emerson (2000). The sandard resul of monopoly where price is raised above he marke clearing level and some of he produc (housing, in his case) remains unsold (vacan) arises in our model. Bu, wha is surprising is ha under cerain

3 2 parameric condiions, we can have he opposie case where he landlord ses he ren so low as o give rise o excess demand for housing. The assumpion of perfecly compeiive or monopolisically compeiive housing suppliers is a common one in he heoreical lieraure on ren conrol (see Arno,1995, for a houghful review of he lieraure). Bu here is a large amoun of empirical evidence ha suggess ha renal housing markes are far from compeiive. Cronin (1983), for example, noes ha in he Washingon, D.C. suburbs of Virginia, on average 70% of all unis in each submarke are conrolled by one owner and ha he average number of renal housing firms in each submarke is slighly over four. Mollenkopf and Pynoos (1973) noed ha in Cambridge, Massachuses 6% of he ciies households conrolled 70% of he renal housing unis. In addiion, hey esimaed ha 90% of he aparmen owners in he ciy belong o an associaion of propery owners 700 srong, and ha wihin ha organizaion 20 owners accoun for 40% of he renal housing sock. Hence even when here are many landlords here is scope for monopoly behavior hrough collusion. Appelbaum and Glasser (1982; as cied in Gilderbloom, 1989) found ha, in Isla Visa, California, 27 owners conrolled 50% of he renal housing sock. Close by in Sana Barbara, Linson (1978; as cied in Gilderbloom, 1989) repored ha over 50% of he renal housing was owned by only 60 owners and ha seven of hem could accoun for 20% of he renal sock. Finally, Gilderbloom and Keaing (1982; as cied in Gilderbloom, 1989) found ha in Orange, New Jersey, jus en owners conrol close o one hird of he renal housing and ha in Thousand Oaks, California, jus one owner conrols over 30% of he renals. In an empirical sudy of supply side concenraion of

4 3 he renal housing marke in Boson, Cherry and Ford (1975) find ha housing prices are significanly deermined by concenraion of wihin marke segmens. Thus here are many reasons o believe ha housing markes are less han perfecly compeiive; he concenraion of renal propery in he hands of only a handful of major owners and he collusive opporuniies from he presence of landlord s associaions are wo. This, of course, does no mean ha a model ha assumes landlords are monopoliss is any closer o realiy han one ha assumes ha hey are perfec compeiors, he rue model likely lies somewhere in beween he wo. Wha we are aemping o do in he presen paper is o examine he oher exreme ha has been negleced in he lieraure and poin ou he aspecs ha are paricular o he monopoly case so ha we may beer undersand he rue naure of ren conrolled housing markes. II. The Algebra of en In his paper we will consider he effecs of ren conrol when he supply of ren conrolled housing is limied. New York, inner-ciy Mumbai and Delhi are examples of his. en conrols can however be of many kinds. I can ake he form of a ren fixed by a ren conrol auhoriy or governmen (see Olsen, 1998, for a discussion of he differen forms of ren conrol) or of a law ha gives landlords some or full freedom o adjus rens when leasing ou propery o new enans bu hen requiring he ren o be held consan (or adjused upward only wihin limis) as long as a enan remains he lessee (and wih he landlord having no righ o arbirarily evic a siing enan). This laer form of ren conrol, called enancy ren conrol, (see, e.g., Basu and Emerson, 2000; Nagy, 1997; Arno, 1995; Börsch-Supan, 1986) is quie pervasive and is he subjec maer of his paper.

5 4 Given enancy ren conrol, he presence of even a small posiive inflaion gives rise o an adverse selecion problem. Landlords now prefer shor-saying enans o longsaying enans, bu hey have no way of elling ypes apar. Long-saying enans know heir ype bu have no ineres in revealing his informaion o prospecive landlords. Curiously, he relaion beween ren conrol and inflaion remains a negleced subjec. We ried o develop he building blocks of a model for analyzing his in Basu and Emerson (2000). In he presen paper, we develop some of he basic heory in a coninuous-ime model and build ino our model some elemens of realiy o wi, limied supply and monopolisic power on he par of landlords which has no been modeled hus far. 1 Each (poenial) enan has an exogenously given duraion of enure (>0). When we say ha a enan is of ype we mean ha he enan will move from an aparmen afer periods. There is a coninuum of enans and heir densiy funcion on he enure duraion,, is given by f(), wih F() being he corresponding disribuion funcion. All agens are supposed o have he same discoun facor δ [0,1). We denoe he oal number of enans in he renal marke by N. Hence: F = o ( ) = f ()d N. Suppose a landlord leases ou o enans of only ype (ha is, ges a ype enan, afer every periods), and each ime a new enan comes he fixes he ren so ha is real value is $1. Thereafer he nominal value of he ren remains fixed so long as he enan does no leave. Le he inflaion rae be such ha he value of each dollar erodes in each 1 Some monopoly elemens were considered in a model of enancy by Basu (1989), bu he focus of ha paper was enirely on innovaions and he conex was ha of a backward agrarian economy.

6 5 period a he rae of 1 β, where β ( 0,1). Under hese circumsances he presen value of he landlord s income is denoed by v(). Clearly hen, v() = ( β+δ)x δ ( β+δ)x 2δ e dx + e e dx + e e ( β+δ)x dx + L = 0 e ( β+δ)x 1 e δ dx ( β+δ) 1 e = (1) δ ( β + δ)(1 e ) The process of adverse selecion ensures ha, for each renal rae, only enans of a cerain ype and above will seek housing in he ren conrolled marke. Hence, he cenral mahemaical characer in such an analysis is vˆ () - he presen value of rens (in real erms) earned by a landlord who manages o ren ou his house o a enan seleced randomly from a enan pool wih enure ime x, a a ren which is equal o 1 real dollar o sar wih and hereafer kep fixed nominally (so i erodes each period by 1 β ), and each ime a enan leaves he landlord repeas he above procedure. vˆ () is given by he following expression: vˆ () x f (x) ( β+δ)k δx = e dk e vˆ() dx N F() +. (2) 0 To undersand his, observe ha f(x)/(n-f()) is he probabiliy of picking a ype x enan, condiional on enans of ype and above being available. The expression in he square bracke is he presen value of rens earned when he firs enan is of ype x. Now we are ready o sae and prove he one echnical resul on which we will build our economic analysis.

7 6 Proposiion 1: If >, hen vˆ ( ) < vˆ ( ). Proof: To prove his, firs noe ha vˆ () can be simplified using (1) and (2) o be wrien as: vˆ() = f (x)(1 e N F() δx )v(x)dx f (x)e δx dx (3) From (3) i is clear ha vˆ () is he weighed average of he differen values of v(x), as x ranges from o. This is obvious from he fac ha if v(x) is removed (i.e. se equal o 1, for all x) from he righ-hand side of (3), hen he righ-hand erm equals 1. The proposiion is now proved in hree seps. Sep 1: We will show ha v() rises as falls. In oher words, v () < 0, for all. To prove his noe ha: ( ) βx δx βx δx δ βx δx δ v = + + ( 2 e e dx e e dx e e e dx e ) + L 0 1 e ( β+δ) = ( )( δ β + δ 1 e ) Then: v ( ) = v ( ) ( ) ( β+δ) δ 1 e 1 e β + δ e ( β+δ) 0 Noe ha v ( ) is posiive. We mus now show ha he erm in parenheses is negaive, rearranging and collecing erms under a common denominaor reduces our problem o showing he numeraor, or δe δ 0 δ ( β+δ ) ( β + δ) e β δe X(), is negaive.

8 7 We need o prove his for all 0. To see his noe ha δ β ( β + δ) δe [1 e ] X () =. Hence X () = 0 if = 0, and X () < 0 if > 0. I follows ha if X(0) 0, hen X () < 0, > 0. Finally, noe ha X (0) ( β + δ) β δ = 0 This esablishes Sep 1. =. Sep 2: As falls from o, he weigh on each v(x), for x given by: To prove his, suppose x, in (3) falls.. The weigh on v(x) in (3), denoed by w(x,), is w(x,) f (x)(1 e N F() δx ) f (x)e δx dx. Noe ha: w(x, ) < w(x, ) (4) δ iff N F( ) f (x)e x dx > N F( ) f (x)e δ x dx or δ f (x)e x dx < f (x)dx (5) (5) is obviously rue. Hence (4) is rue, which esablishes Sep 2. Sep 3: Since he weighs on v(x) in (3) always sum o 1, a decline in he weighs on v(x), for all x implies posiive weighs on v(x), for all x [, ]. Hence we know from Sep 2 ha as falls from o, he weighs ge ransferred from values of v(x),

9 8 where x o values of v(x) where x [, ] x,y such ha x [, ] and y >.. From Sep 1 we know v(x) > v(y) for all I follows ha vˆ ( ) < vˆ ( ). Wih his echnical resul in he background, i is now easy o describe a full model of ren conrol. When enans make he decision wheher o lease a ren-conrolled aparmen he alernaive hey have o keep in mind is for hem o find housing in a nonren conrolled area or o buy a house. Le us assume ha his alernaive housing arrangemen coss C dollars (in presen-value erms). For simpliciy, we assume ha C is independen of he enan s ype. This seems reasonable as well. In buying a house he cos will clearly be independen of wheher he person is a long-sayer or a shor-sayer. Likewise in rening an aparmen in a non-ren conrolled area, he enan s ype is unlikely o maer because he ren can be inflaion indexed or be made coningen on he lengh of he enan s say. Now suppose ha he ren (per period) in he ren conrolled housing is. The life-ime renal cos o a enan of ype is clearly given by v(). ecall ha v() is he presen-value of life-ime paymen made by a enan of ype if he real ren a he sar of enure is se each ime a 1. Consider now a monopoly landlord, who ses he real (saring) ren equal o. Clearly only hose ypes of enan,, will accep his for whom v() C. Since from Sep 1 of Proposiion 1 we know v () < 0, for all, i follows ha all enans ypes such 1 ha v ( C ) will accep he offer. I follows from he definiion of vˆ ( ) ha he

10 9 landlord s expeced presen-value of renal earned from each aparmen ha is leased ou is given by: 1 ( v ( C ) V() vˆ. From Sep 1 of Proposiion 1 we know ha as rises, v ( C ) 1 1 Proposiion 1 we know ha as rises vˆ ( v ( C ) rises, V() may rise or fall. Figure 1 represens a possible picure of V(). rises. Hence, from falls. I is now ransparen ha as Earnings per aparmen C V() ~ en per period, Figure 1 Define ~ o be he supremum of he se { f () 0} >. In oher words, ~ is such ha here are no enans of ype > ~, and for all > 0, here exiss enans of ype [ ~, ~ ]. Now define ~ such ha v 1 C ~ = ~. Then if ren goes above ~, here are no furher akers among he enans. Hence V() is no defined for > ~. A ~, he

11 10 only akers are of ype ~. Hence V( ~ ~ ) = ~ vˆ( ) = ~ v( ~ ) = ~ C / ~ = C. I is easy o see ha for all < ~, V() < V( ~ ). This explains he shape of V() in Figure 1. I is also eviden ha V() can fall over some sreches. This is especially ransparen if enan ypes are finie. Then over some increases in, large numbers of shor-sayers can decline he renal offer, leaving he pool of enans suddenly worse from he landlord s poin of view. This is he classic adverse selecion problem (Akerlof, 1970). III. Excess Supply, Excess Demand and Efficiency en The resuls are he oucome of he landlord s opimizaion problem when confroned wih an earnings curve, V(). The case of many landlords who drive profis down o zero was analyzed in Basu and Emerson (2000). Here we ake on he oher polar end: he case of limied supply and monopoly. en conrol applied o a fixed sock of housing, such as in New York, and he evidence supporing he conenion ha renal housing markes are no compeiive, make i worhwhile invesigaing his polar case. To begin his analysis, le us derive he demand for ren-conrolled housing as a funcion of he (per-period) ren,. From secion 2, we know ha given, all enans of 1 ype v ( C ) will wan o lease ren-conrolled housing. Hence, he demand for housing, D, is given by 1 D() = ()d N F( v ( C ) 1 v f. ( C )

12 From Sep 1 of Proposiion 1, v ( C ) 1 11 rises as rises. Hence, D() declines, as rises. Such a demand curve is illusraed in he lower panel of Figure 2. The upper panel is a reproducion of Figure 1. Earnings per aparmen C A B E V() 0 * ^ ' ~ en, S Supply Demand D(), Demand and Supply Figure 2 Nex, draw he supply curve in he lower panel. The landlord, i is assumed, owns S unis of propery. For simpliciy, i is assumed ha he opporuniy cos of leasing ou

13 12 propery is zero. Hence he supply curve is perfecly inelasic hrough he poin marked S. Le ˆ be he ren which equaes demand and supply. To locae he landlord s opimum ren, consider all rens less han ˆ, and locae he ren (lef of ˆ ) which maximizes V(). This, in Figure 2, is given by *. Since V() is no necessarily monoonic, here is no reason why * will coincide wih ˆ. Observe ha, if he landlord was resriced o selecing a ren less han or equal o ˆ, she would choose *. This is because for all ˆ, she manages o lease ou he same number of aparmens, o wi, S, and a * he per-aparmen earnings are maximized. Hence, he oal earnings are maximized a *. Nex consider rens greaer han or equal o ˆ. As is raised saring from ˆ, he earnings of he landlord mus evenually (weakly) rise (since V( ~ ) = C V(), for all ). However even if V() rises, he oal earnings need no rise, since demand falls below S and so more and more aparmens remain vacan as is raised. Le be he ren where oal earnings are maximized (subjec o ˆ ). Le E be he same heigh as A and he projecion of E on he horizonal axis., The landlord s chosen ren will clearly be eiher * or. If [ ˆ, ) clearly, her earnings are greaer a *, since a such an, per aparmen earning is smaller and fewer aparmens are aken. Even if >, oal earnings may be smaller a since a such a ren, he landlord will be unable o find enans for all her aparmens.

14 13 If he opimum urns ou o be a, hen his is a fairly ypical monopoly equilibrium. The monopolis holds back supply in order o push up he price and her earnings. The ineresing case occurs when * urns ou o be he opimum. Here demand for housing exceeds supply (see lower panel of Figure 2). Neverheless he landlord prefers no o raise he renal. This is because a higher ren worsens he qualiy (from he landlord s poin of view) of he enan. This is raher like in models of efficiency wage (e.g. Sigliz, 1974; Mirrlees, 1975) or efficiency ineres raes (e.g. Sigliz and Weiss, 1981). We shall herefore call * he efficiency ren. Usually, we would expec his kind of a ren o prevail on he marke if ren conrol ook he form of an exogenous ceiling on ren. In such a case demand exceeding supply is compaible wih equilibrium. Wha our model illusraes is ha even if here is no ceiling on rens, enancy ren conrol can resul in behavior such ha he marke equilibrium mimics a ren ceiling. IV. Conclusion Well meaning urban policy makers of he 70 s and 80 s, aemping o correc he glaring problems of old-syle ren conrols ha placed ceilings on rens (problems ha had been illusraed quie vividly by economiss), urned o a form of ren conrol ha was more of a enan s proecion legislaion han a uni-by-uni ren resricion. This ype of enancy ren conrol simply resriced landlord s abiliy o raise rens on siing enans and prohibied mos side paymens and arbirary evicion. This was seen o be a more

15 14 flexible program and one ha was less suscepible o he inefficiencies of he old ren conrol laws. Wha we showed in Basu and Emerson (2000) is ha his new ype of ren conrol brings abou differen kinds of inefficiencies due o he adverse selecion problem brough abou by he asymmeric naure of informaion in hese markes. Wha he presen paper illusraes is; in he presence of monopolisic landlords, enancy ren conrol can cause landlords o operae in such a way ha mimics he old syle ren conrol. To wi, hey hold down price, even wih excess demand, o arac a beer qualiy enan (i.e. one ha will no say oo long). We call his efficiency ren. Assuming renal housing markes o be monopolisic may be an absracion from realiy, bu wih all of he evidence o sugges large amouns of concenraion and possible collusion (hrough landlord s associaions) in renal housing markes, i is cerainly no more of an absracion han models ha assume perfec compeiion (as is he norm in he lieraure). Given he pervasiveness of enancy ren conrol, i is imporan o undersand fully he naure of he inefficiencies i creaes. Wha he presen work illusraes (as does Basu and Emerson, 2000) is ha cerain ypes of enans are helped by his policy while oher ypes are hur. In addiion, i illusraes a ype of sraegic behavior on he par of monopolisic landlords ha has no been previously explored in he lieraure.

16 15 eferences Akerlof, George. The Marke for Lemons : Qualiy Uncerainy and he Marke Mechanism. Quarerly Journal of Economics 84 (1970): Appelbaum, ichard P., and Todd Glasser. Concenraion of Ownership in Isla Visa. (1982) San Francisco: Foundaion for Naural Progress. Arno, ichard. Time for evisionism on en Conrol? Journal of Economic Perspecives 9 (Winer 1995): Basu, Kaushik. Technological Sagnaion, Tenurial Laws, and Adverse Selecion. American Economic eview 79 (March 1989): Basu, Kaushik and Parick M. Emerson. The Economics of Tenancy en Conrol. The Economic Journal. Forhcoming, Ocober Börsch-Supan, Axel. On he Wes German Tenans Proecion Legislaion. Journal of Insiuional and Theoreical Economics 142 (1986): Cherry,. and E. J. Ford, Jr. Concenraion of enal Housing Propery and enal Housing Markes in Urban Areas. American eal Esae and Urban Economics Associaion Journal 3 (Spring 1975): Cronin, Francis J. Marke Srucure and he Price of Housing Services. Urban Sudies 20 (1983): Gilderbloom, John I. Socioeconomic Influences on enals for U.S. Urban Housing. American Journal of Economics and Sociology 48 (July 1989): Gilderbloom, John I., and Dennis Keaing. An Evaluaion of en Conrol in Orange. (1982) San Francisco: Foundaion for Naural Progress, Housing Informaion Cener.

17 16 Leibensein, Harvey. Underemploymen in Backward Economies. Journal of Poliical Economy 65 (1957): Linson, Neal. Concenraion of Ownership in Sana Barbara. (1978) Sana Barbara, California: Sana Barbara Tenans Union (mimeo.). Mirrlees, James A. Pure Theory of Underdeveloped Economies. in L. G. eynolds, ed. Agriculure in Developmen Theory (1975) New Haven: Yale Universiy Press. Mollenkopf, John, and Jon Pynoos. Boardwalk and Park Place: Propery Ownership, Poliical Srucure and Housing Policy a he Local Level, in Jon Pynoos, ober Schaffer and Cheser Harman, eds., Housing in Urban America. (1973) Chicago: Aldine, pp Nagy, John. Do Vacancy Deconrol Provisions Undo en Conrol? Journal of Urban Economics 42 (1997): Olsen, Edgar O. Economics of en Conrol. egional Science and Urban Economics 28 (1998): Shapiro, Carl; Sigliz, Joseph E. Equilibrium Unemploymen as a Worker Discipline Device. American Economic eview 74 (June 1984): Sigliz, Joseph E. Alernaive Theories of Wage Deerminaion and Unemploymen in LDC'S: The Labor Turnover Model. Quarerly Journal of Economics 88 (May 1974): Sigliz, Joseph E. and Andrew Weiss. Credi aioning in Markes wih Imperfec Informaion. American Economic eview 71 (June 1981):