PROFIT RATIO AND MARKET STRUCTURE


 Jeremy Holmes
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1 POFIT ATIO AND MAKET STUCTUE By Yong Yun Introducton: Industral economsts followng from Mason and Ban have run nnumerable tests of the relaton between varous market structural varables and varous dmensons of performance. The most popular one, however, has been the usng of proft rates to measure the concentraton and barrers to entry. In general, ths type of studes tend to confrm the expectaton that, other thngs beng equal, profts wll tend to be hgher n ndustres n whch structural condtons depart substantally from those of the compettve model. But these studes has not always been clearly based on a welldefned theoretcal model. So when a theoretcal model s spelled out t becomes obvous that some nterndustry relatonshps of ths sort are meanngless because of the certan omtted varables. A prme example s the omsson of the ndustry prce elastcty of demand. Ths means that the former studes have all assumed that the prce elastcty of demand across ndustres wthn the crosssecton are the same. Ths s defntely wrong because n fact these s few chances for the prce elastcty of even two ndustres to be the same. In ths paper, a explct theoretcal model wth varable η whch represents the prce elastcty of demand s gven out. Ths supposed to be able to examne the relatonshp between two dfferent ndustres wth dfferent prce elastcty of demand. However, t s too complcated. Here my suggest s: Snce the prce elastcty wthn one ndustry s always more steady than that of dfferent ndustres, why can't we use tme
2 seres data to analyss a sngle ndustry? Maybe the results that ths ntrandustry study wll yeld s more meanngful. The Basc Model: Consder an ndustry wth n frms producng a homogenous product. We can wrte down the proft equaton for the th frm as: = pq c( q ) F (1) Where Π s proft, p s prce, q s output, c s varable cost and F s fxed cost, assumng that for the moment the same cost condtons for each frm. The nverse market demand functon s: p = f ( q) = f ( q1 + q q n ) () Now assumng proftmaxmzng behavor and neglectng the problem of potental entry at present, we get: Where d p q f q = + ( ) c '( q ) = 0 (3) d j q = 1+ = 1+ β j Multplyng (3) by q and summng over the n frms, we have: pq q q f q q + c q q '( )( 1+ β ) ' ( ) = 0 (4) Or we can rewrte t as :
3 pq pq c ' ( q ) q t q f '( q) q = ( ) ( 1 + µ ) (5) q pq Where n n / = 1 = 1 µ = β q q (see ader, 197, pp.71~7). If we assume the frms have constant margnal cost equal to average varable cost, then the left sde of the equaton s the rato of proft plus fxed cost (Π+F) to revenue( ). On the rght sde the frst term s the HrschmannHerfndahl ndex of concentraton ( H ),so the equaton can be rewrte as: + F H = ( 1 + µ ) (6) η Where η s the prce elastcty of demand. We therefore have the predcton that the proftrevenue rato s related postvely to the Hrschmannherfndahl ndex of concentraton and nversely to the prce elastcty of demand. The problem wth testng ths predcton s the that t s always hard to measure the prce elastcty of a ndustry. So here a good approach s to change the focus of analyss away from explanng nterndustry dfferences to explanng ntrandustry changes over tme. Thus, assumng that all prce elastcty wthn a sngle ndustry durng a certan perod s constant. It s also reasonable to assume that µ s constant. Now for perod t we have:
4 t + Ft t Ht = ( 1 + µ ) (7) η For perod t' we have: t' + Ft t ' ' Ht ' = ( 1 + µ ) (8) η Take the rato of equaton (7) and (8), we get: + F ( ) t + F ( ) t' = Ht Ht' (9) We assume that the fxed cost s constant durng the perod of tme, so though the magantude of F wll nfluence the absolute rato of HHI, t won't change the relatve rato. So here fxed cost s possbly to be omtted. Thus we get the new equaton: ( ) t Ht = ( ) Ht' t ' (10) Appled to a sngle ndustry: Industry Select and Data arrangement From the above mentoned analyss we know that the most reasonable ndustry for ths model s an ndustry wth a sgnfcant change n the concentraton rato durng a perod of years. Thanks for professor Looms, he gave me some advce on the selectng of the telecommuncaton ndustry as the objectve and also help me by gvng me the quarterly revenue and concentraton rato data of the ndustry through year 1984 to year However, the proft data have really taken me some tme.
5 (1) Concentraton rato Our model defnes the HrschmannHerfndahl measure as the relevant one, but unfortunately, the HHI of the telecommuncaton ndustry s not publshed. I am grateful to professor Looms for gvng me the revenue of the major companes also the whole ndustry durng these years so I can roughly calculate out the market share of each company then the HHI of the whole ndustry. However, because I ddn t take some trval companes nto account, we should note that ths method of estmaton wll a lttle understate the true level of HHI. But, anyway, ths won t do much matter. () evenue Fortunately, as mentoned above, I got both the revenue of each company and the total revenue of the whole ndustry drectly from the quarterly toll revenue reported to shareholders. (3) Proft Wthn the three varables n the equaton, defntely proft s the one that I have done much more effort. At frst I want to use equaton (9) to do the analyss because by usng ths method the results should be more precse. In order to do ths, the sum of proft and fxed cost must be fnd out. The frst way I have thought about s to fnd drectly the proft and the fxed cost of the ndustry then sum them up. But I can t fnd anythng about the fxed cost. Even the proft I can only fnd a sngle company s wthn a sngle year. It s mpossbly complcated for me to sum them all out. Then I want to try another way, to measure the sum of proft and fxed cost as gross output mnus raw materals purchases and wages and salares. However,ths s also tested to be too complex. At last,i have to change equaton (9) to equaton (10). Ths only need us to fnd the proft, revenue and the
6 HHI, I have menton above how to fnd revenue and the HHI, so the only varable left s proft. As aforesad, t s also too complex to fnd all years total proft, so I wll just use three years proft data, that s year 1984,1990 and Data Partcpaton and the esult (1) evenue Data: for year 1984: (dollar amounts show n mllons) Frst quarter: AT&T 8,684 MCI 475 SPINT 30 WOLDCOM 0 OTHE 405 TOTAL 9,866 Second quarter: AT&T 9,169 MCI 485 SPINT 317 WOPLDCOM 0 OTHE 43 TOTAL 10,394 Thrd quarter: AT&T 9,097 MCI 478 SPINT 307 WOLDCOM 0 OTHE 44 TOTAL 10,34 Forth quarter: AT&T 9,7 MCI 51 SPINT 30 WOLDCOM 0 OTHE 46 TOTAL 10,574 So AT&T yearly total: 36, MCI yearly total: 1,959 SPINT yearly total: 1,46 Industry yearly total: 41,158 for year 1990: Industry yearly total: 56,98
7 for year 1996: Industry yearly total: 94,331 () Concentraton Data: Usng the revenue data, we can calculate out the concentraton rato: for year 1984: HHI=7, for year 1990: HHI=4, for year 1996: HHI=3,34.5 (3) Proft Data: I get the proft data from the annual report: for year 1984: ndustry total proft: 10,80.5 for year 1990: ndustry total proft: 1,487.7 for year 1996: ndustry total proft: 14,51.5 Substtute these data nto equaton (10), we can test the theory that as the rato of proft to revenue declnes, so wll the concentraton rato. Concluson: Untl recently, the analyss of frms performance wth respect to the market structure has generally been based on an ndustrybyndustry descrptve approach. A recent study by Mller analyzed the mpact of the dstrbuton of ndustry shares among successve groups of frms top four, next four, and so forth whch he descrbed as the margnal concentraton, ntroducng an ntrandustry study.
8 However, n ths paper, the spelled out model s able to both support the analyss of an nterndustry study and also the analyss of an ntrandustry study. Especally, we should say, t s more effcent for us to do an ntrandustry study. ths s because: (1) The prce elastcty s more steady wthn the same ndustry than n dfferent ndustres. () The product wthn the same ndustry s lkely to be homogenous. So we don t have to consder the product dfferentaton. In general, n the analyzng of the performance and market structure, our statstcal results speak rather drectly themselves. HHI appears to be sgnfcantly assocated wth ntrandustry proft rato to the total revenue. Data won t be attached. eferences: (1) prcecost margns and ndustry structure Norman. Collns and Lee E. Preston the revew of economcs and statstcs 71~86. () Ban s concentraton and rates of return revsed Brozen Y. journal of law and economcs 14,351~369. (3) profts, varablty of profts and frm sze Samuels J.M. and Smyth D.J. economca 35,17~139. (4) concentraton and prcecost margns n food manufacturng ndustres Collns N.. and L. E. Preston journal of ndustral economcs (July 1996),6~4.
9 (5) concentraton ratos n manufacturng ndustry U.S. Congress Washngton: U.S. government Prntng offce,196. (6) prcecost structure and behavor of proft margns Sato K. Yale economc essays, fall 1961,361~418.
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