196:
store operating in the same area. In supermarkets, the margin is usually 15-20%, and in convenience stores 25-30 %. This is due to the fact that supermarkets operate in a more competitive environment — during their operation, other outlets are also working at the same time to ensure a significant number of customers, it is necessary to offer attractive prices. Convenience stores charge a higher price than supermarkets because some of their customers fall at a time when there is not a large selection of outlets or for the sake of a minor purchase, it makes no sense to look for other options. The number of visitors to such stores is generally less dependent on prices than in supermarkets (less elastic demand). According to the Lerner coefficient, small stores have more monopoly power because they charge higher margins on the same product. But at the same time, such stores usually receive a much smaller amount of profit than a supermarket, since they have a much smaller sales amount, and the average unit cost is higher.
1214:
lending to small and medium-sized businesses, as well as to analyze the market power of various groups of commercial banks. As a research method, the Lerner index was chosen to determine which of the groups of banks (small, medium and large; partners and non-partners of various development banks) have higher market power and how it changes over time. This work made a significant contribution to the study of banking competition, adapting the indicator for assessing the competition of the entire banking services market to the assessment of the degree of competition in the market of a single product - lending to small and medium-sized businesses, as well as showing the presence of competition.
661:
1034:
During the period 2000–2005 the Lerner index computed for the credit market slightly increased. It means that there was a slight decrease in competition. Then, during 2006–2009, there was a decrease in the Lernex index. In 2010 the Lerner index significantly increased. The mean of the Lerner index
195:
It is very important to note that market power alone does not guarantee high profits, since profits depend on the ratio of average costs to price. A firm may have more market power than another firm, but still make less profit. As an example, let's compare an average supermarket and a convenience
1213:
In 2015, the article "Application of the Lerner index to the assessment of competition in small and medium-sized business in lending market of Russia" was published. They analyzed the period from 2010 to 2013. The objectives of this work were to assess the degree of competition in the segment of
186:
The Lerner index can never be greater than one. As a result, if the firm is maximizing profit, the elasticity of demand facing it can never be less than one in magnitude (|E|<1). If it were, the firm could increase its profits by raising its price, because inelastic demand means that a price
1204:
This table represents the estimation of the market power in the deposit market in Czech
Republic. During the period 2005–2009 the Lerner index computed for the deposit market slightly decrease, which means a slight increase in competition. In 2010, there was an increase in the Lerner index. It
112:
The Lerner Rule or Lerner
Condition is that if it is to maximize its profits, the firm must choose its price so that the Lerner Index equals -1 over the elasticity of demand facing the firm (note that this is not necessarily the same as the market elasticity of demand):
478:
1287:
The results of the study showed that the segment of lending to small and medium-sized businesses by structure is a monopolistic competition, the dominant position in which is occupied by state-owned banks. The monopoly power of this group is due to their use of
91:. The index ranges from 0 to 1. A perfectly competitive firm charges P = MC, L = 0; such a firm has no market power. An oligopolist or monopolist charges P > MC, so its index is L > 0, but the extent of its markup depends on the
187:
increase of 1% would reduce quantity by less than 1%, so revenue would rise, and since lower quantity means lower costs, profits would rise. Put another way, a monopolist never operates along the inelastic part of its demand curve.
282:
Under suitable conditions (that this is a convex maximization problem, e.g. P(Q) and C(Q) are linear functions), we can find the maximum by taking the derivative of profit with respect to Q and getting the first-order-condition:
403:
182:
A drawback of the Lerner Index is that while it is relatively easy to observe a firm's prices, it is quite difficult to measure its marginal costs. In practice, the average cost is often used as an approximation.
1292:, the low cost of funding, and the lower risks of loans issued. The effect of supporting the development banks of small and medium-sized banks is not significantly reflected in their market power.
656:{\displaystyle {\begin{aligned}{\frac {P-MC}{P}}&=-{\frac {dP}{dQ}}{\frac {Q}{P}}\\&\\&=-1/\left({\frac {dQ}{dP}}{\frac {P}{Q}}\right)\\&\\&=-{\frac {1}{E_{d}}},\end{aligned}}}
177:
102:
the price elasticity of demand for goods produced by the company — the smaller the fluctuations in demand under the influence of prices, the smaller the elasticity and the greater the value of L;
483:
1372:
1367:
467:
83:
277:
765:= -1/L, the elasticity of demand for industry A will be -2.5. We can use the value of the Lerner index to calculate the marginal cost (MC) of a firm as follows:
105:
the interaction with competitors — the more of them and the larger their size, the less the company's ability to maximize profits and the smaller the L;
208:
problem. A firm choosing quantity Q facing inverse demand curve P(Q) and incurring costs C(Q) has profit equalling revenue (where R = PQ) minus costs:
1368:
https://cyberleninka.ru/article/n/primenenie-indeksa-lernera-k-otsenke-konkurentsii-na-rynke-kreditovaniya-malogo-i-srednego-biznesa-v-rossii/viewer
289:
1035:
computed for the full sample is 53.58 %, which do not confirm either monopoly or perfect competition in the credit market of Czech
Republic.
95:(the price-sensitivity) of demand and strategic interaction with competing firms. The index rises to 1 if the firm has MC = 0.
1205:
signals a decrease in competition. However, the value of Lerner index haven't changed significantly in estimated 10 years.
119:
1397:
408:
which gives the standard rule of MR = MC. To get the Lerner Rule, switch to the notation dC/dQ = MC and rewrite as
108:
the degree of regulation — the more actively the state conducts an antitrust policy, the lower the value of L.
1387:
1306:
414:
44:
865:
Thus, industry B has the greatest monopoly power, and industry С is the closest to perfect competition.
773:
value of -2, we find that the Lerner index is 0.5. If the price is 30 and L is 0.5, then MC will be 15:
214:
92:
1316:
781:
should be -4 . Based on the results of the calculations, our table will take the final form:
777:
Industry C. For P=40 and MC=30, the Lerner index will be equal to 0.25 , and the value of E
8:
1357:
205:
1346:
1329:
Lerner, A. P. (1934). "The
Concept of Monopoly and the Measurement of Monopoly Power".
1289:
1392:
1338:
1311:
1301:
398:{\displaystyle {\frac {dProfit}{dQ}}=({\frac {dP}{dQ}}Q+P)-{\frac {dC}{dQ}}=0}
1381:
88:
28:
24:
1362:
1350:
1342:
1218:
Descriptive statistics of the Lerner Index for the banking system
769:
The missing values for industry B are found as follows: from the E
679:
Let's suppose we need to fill in the gaps in the following table:
87:
where P is the market price set by the firm and MC is the firm's
1208:
98:
The following factors affect the value of the Lerner index:
23:, formalized in 1934 by British economist of Russian origin
1038:
868:
1358:
https://journal.open-broker.ru/economy/indeks-lernera/
481:
417:
292:
217:
172:{\displaystyle {\frac {P-MC}{P}}={\frac {-1}{E_{d}}}}
122:
47:
655:
461:
397:
271:
171:
77:
1379:
666:using the derivative definition of elasticity.
1209:Lerner index in the lending market of Russia
190:
1044:Lerner index of the Czech deposit market
1039:Lerner index of the Czech deposit market
874:Lerner index of the Czech credit market
869:Lerner index of the Czech credit market
767:0.4 = (10 – MC) ÷ 10 ⇒ MC = 10 − 4 = 6.
462:{\displaystyle P-MC=-{\frac {dP}{dQ}}Q}
1380:
1328:
204:The Lerner Rule comes from the firm's
1363:https://www.cjournal.cz/files/91.pdf
775:MC = P − P × L = 30 — 30 × 0,5 = 15.
78:{\displaystyle L={\frac {P-MC}{P}}}
13:
14:
1409:
272:{\displaystyle Profit=P(Q)Q-C(Q)}
39:The Lerner index is defined by:
1331:The Review of Economic Studies
674:
363:
331:
266:
260:
248:
242:
16:Measure of firm's market power
1:
1322:
199:
34:
7:
1295:
669:
27:, is a measure of a firm's
10:
1414:
1317:Market segmentation index
1307:Amoroso–Robinson relation
1398:1934 in economic history
191:Market power and profit
1373:ru:Коэффициент Лернера
796:Elasticity of demand,E
694:Elasticity of demand,E
657:
463:
399:
273:
173:
79:
658:
464:
400:
274:
174:
80:
1388:Eponyms in economics
479:
415:
290:
215:
120:
45:
1229:Standard deviation
1219:
1045:
875:
472:Divide by P to get
206:profit maximization
1290:economies of scale
1217:
1043:
873:
653:
651:
459:
395:
269:
169:
75:
1285:
1284:
1202:
1201:
1032:
1031:
863:
862:
755:
754:
644:
605:
595:
545:
535:
505:
454:
387:
352:
326:
167:
142:
73:
1405:
1354:
1312:Herfindahl Index
1220:
1216:
1046:
1042:
876:
872:
793:Marginal cost,MC
784:
783:
691:Marginal cost,MC
682:
681:
662:
660:
659:
654:
652:
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643:
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630:
619:
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615:
611:
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487:
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404:
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401:
396:
388:
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353:
351:
343:
335:
327:
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317:
294:
278:
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275:
270:
178:
176:
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168:
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156:
148:
143:
138:
124:
84:
82:
81:
76:
74:
69:
55:
1413:
1412:
1408:
1407:
1406:
1404:
1403:
1402:
1378:
1377:
1343:10.2307/2967480
1325:
1298:
1211:
1041:
871:
802:Lerner index,L
799:
780:
776:
774:
772:
768:
766:
764:
760:
700:Lerner index,L
697:
677:
672:
650:
649:
638:
634:
629:
617:
613:
612:
597:
587:
579:
577:
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572:
567:
552:
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488:
486:
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379:
371:
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344:
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318:
295:
293:
291:
288:
287:
216:
213:
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202:
193:
161:
157:
149:
147:
125:
123:
121:
118:
117:
56:
54:
46:
43:
42:
37:
17:
12:
11:
5:
1411:
1401:
1400:
1395:
1390:
1376:
1375:
1370:
1365:
1360:
1355:
1337:(3): 157–175.
1324:
1321:
1320:
1319:
1314:
1309:
1304:
1302:Ramsey problem
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1294:
1283:
1282:
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15:
9:
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3:
2:
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1225:
1222:
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1215:
1206:
1197:
1194:
1192:
1189:
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1175:
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1168:
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1162:
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1132:
1129:
1127:
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1123:
1119:
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1111:
1110:
1106:
1103:
1101:
1098:
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1080:
1077:
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1067:
1064:
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1059:
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1054:
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1048:
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1036:
1027:
1024:
1022:
1019:
1018:
1014:
1011:
1009:
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1005:
1001:
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988:
985:
983:
980:
979:
975:
972:
970:
967:
966:
962:
959:
957:
954:
953:
949:
946:
944:
941:
940:
936:
933:
931:
928:
927:
923:
920:
918:
915:
914:
910:
907:
905:
902:
901:
897:
894:
892:
889:
888:
884:
881:
878:
877:
866:
858:
855:
852:
849:
847:
844:
843:
839:
836:
833:
830:
828:
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824:
820:
817:
814:
811:
809:
806:
805:
801:
795:
792:
789:
786:
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751:
749:
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734:
731:
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721:
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703:
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683:
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646:
639:
635:
631:
626:
623:
621:
608:
602:
599:
591:
588:
583:
580:
573:
568:
564:
561:
558:
556:
542:
539:
531:
528:
523:
520:
514:
511:
509:
502:
498:
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492:
489:
475:
474:
473:
456:
450:
447:
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439:
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430:
427:
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421:
418:
411:
410:
409:
392:
389:
383:
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375:
372:
366:
360:
357:
354:
348:
345:
340:
337:
328:
322:
319:
314:
311:
308:
305:
302:
299:
296:
286:
285:
284:
263:
257:
254:
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245:
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236:
233:
230:
227:
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218:
211:
210:
209:
207:
197:
188:
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162:
158:
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150:
144:
139:
135:
132:
129:
126:
116:
115:
114:
107:
104:
101:
100:
99:
96:
94:
90:
89:marginal cost
85:
70:
66:
63:
60:
57:
51:
48:
40:
32:
30:
26:
22:
1334:
1330:
1286:
1273:
1260:
1247:
1234:
1212:
1203:
1190:
1177:
1164:
1151:
1138:
1125:
1112:
1099:
1086:
1073:
1060:
1033:
1020:
1007:
994:
981:
968:
955:
942:
929:
916:
903:
890:
864:
845:
826:
807:
757:For L = -1/E
756:
739:
722:
705:
678:
665:
471:
407:
281:
203:
194:
185:
181:
111:
97:
86:
41:
38:
29:market power
21:Lerner index
20:
18:
675:Calculation
25:Abba Lerner
1382:Categories
1323:References
200:Derivation
93:elasticity
35:Definition
627:−
562:−
515:−
493:−
434:−
422:−
367:−
255:−
151:−
130:−
61:−
1296:See also
787:Industry
685:Industry
670:Examples
1393:Pricing
1351:2967480
1281:0,1405
1268:0,1341
1255:0,1337
1242:0,1274
1198:0.7355
1185:0.4880
1172:0.6328
1159:0.6776
1146:0.6806
1133:0.7100
1120:0.6482
1107:0.7204
1094:0.6692
1081:0.6959
1068:0.6898
1055:Median
1028:0.6582
1015:0.3289
1002:0.5029
989:0.5739
976:0.5457
963:0.6163
950:0.5371
937:0.6089
924:0.5530
911:0.5455
898:0.5486
885:Median
790:Price,P
688:Price,P
1349:
1278:0,3027
1265:0,2285
1252:0,2137
1239:0,3159
1195:0.7642
1182:0.5266
1169:0.6255
1156:0.6696
1143:0.6718
1130:0.6955
1117:0.6595
1104:0.7170
1091:0.6930
1078:0.6864
1065:0.5905
1025:0.6742
1012:0.3921
999:0.5109
986:0.5650
973:0.5673
960:0.5980
947:0.5430
934:0.6165
921:0.5723
908:0.5598
895:0.4438
1347:JSTOR
1226:Value
859:0.25
761:and E
1274:2013
1261:2012
1248:2011
1235:2010
1223:Year
1191:2010
1178:2009
1165:2008
1152:2007
1139:2006
1126:2005
1113:2004
1100:2003
1087:2002
1074:2001
1061:2000
1052:Mean
1049:Year
1021:2010
1008:2009
995:2008
982:2007
969:2006
956:2005
943:2004
930:2003
917:2002
904:2001
891:2000
882:Mean
879:Year
840:0.5
821:0.4
818:-2.5
717:0.4
19:The
1339:doi
31:.
1384::
1345:.
1333:.
856:-4
853:30
850:40
837:-2
834:15
831:30
812:10
747:30
744:40
732:-2
727:30
710:10
1353:.
1341::
1335:1
846:C
827:B
815:6
808:A
798:d
779:d
771:d
763:d
759:d
740:C
723:B
706:A
696:d
647:,
640:d
636:E
632:1
624:=
609:)
603:Q
600:P
592:P
589:d
584:Q
581:d
574:(
569:/
565:1
559:=
543:P
540:Q
532:Q
529:d
524:P
521:d
512:=
503:P
499:C
496:M
490:P
457:Q
451:Q
448:d
443:P
440:d
431:=
428:C
425:M
419:P
393:0
390:=
384:Q
381:d
376:C
373:d
364:)
361:P
358:+
355:Q
349:Q
346:d
341:P
338:d
332:(
329:=
323:Q
320:d
315:t
312:i
309:f
306:o
303:r
300:P
297:d
267:)
264:Q
261:(
258:C
252:Q
249:)
246:Q
243:(
240:P
237:=
234:t
231:i
228:f
225:o
222:r
219:P
163:d
159:E
154:1
145:=
140:P
136:C
133:M
127:P
71:P
67:C
64:M
58:P
52:=
49:L
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