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1 |
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2 654 164 217 211 236 212 217 164 236 |
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3 |
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4 THE 659 211 727 233 728 211 659 233 |
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5 AMERICAN 738 211 928 233 929 211 738 233 |
|
6 ECONOMIC 938 211 1131 233 1132 211 938 233 |
|
7 REVIEW 1142 212 1286 235 1287 212 1142 235 |
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8 |
|
9 SEPTEMBER 1557 217 1766 239 1768 217 1557 239 |
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10 1980 1781 220 1846 239 1847 220 1781 239 |
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11 |
|
12 dispersion 161 307 340 344 341 307 160 343 |
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13 and 356 307 418 336 419 307 356 336 |
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14 models 434 307 557 336 558 307 434 336 |
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15 of 574 307 608 336 609 307 574 336 |
|
16 temporal 624 308 780 346 781 308 623 344 |
|
17 price 796 308 882 346 883 308 794 344 |
|
18 dis 898 308 937 337 938 308 898 337 |
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19 - 938 317 959 337 960 317 938 337 |
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20 |
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21 persion. 161 355 296 393 297 355 160 392 |
|
22 Most 315 355 403 385 405 355 315 385 |
|
23 models 420 355 543 385 544 355 420 385 |
|
24 of 559 355 591 385 592 355 559 385 |
|
25 spatial 608 356 721 394 722 356 607 393 |
|
26 price 739 356 824 394 825 356 738 393 |
|
27 disper 840 356 937 394 938 356 839 393 |
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28 - 938 366 959 386 960 366 938 386 |
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29 |
|
30 sion, 161 400 240 429 242 400 161 429 |
|
31 such 259 400 336 429 337 400 259 429 |
|
32 as 355 409 388 429 389 409 355 429 |
|
33 the 407 400 457 429 458 400 407 429 |
|
34 Salop-Stiglitz 475 400 711 438 712 400 474 437 |
|
35 model 728 401 837 431 838 401 728 431 |
|
36 or 855 411 889 431 890 411 855 431 |
|
37 the 907 401 959 431 960 401 907 431 |
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38 |
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39 Wilde-Schwartz 160 445 439 474 440 445 160 474 |
|
40 model, 458 445 576 474 577 445 458 474 |
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41 have 597 446 675 475 676 446 597 475 |
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42 equilibria 695 446 864 484 865 446 694 483 |
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43 with 883 446 957 475 959 446 883 475 |
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44 |
|
45 specific 160 491 290 529 291 491 159 527 |
|
46 prices 314 491 414 529 415 491 312 527 |
|
47 being 439 491 535 529 536 491 438 527 |
|
48 charged 559 491 698 529 699 491 558 527 |
|
49 with 724 492 797 522 798 492 724 522 |
|
50 positive 823 492 957 530 959 492 822 529 |
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51 |
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52 probability 159 537 354 575 355 537 158 574 |
|
53 mass. 367 546 459 566 460 546 367 566 |
|
54 The 473 537 540 566 542 537 473 566 |
|
55 a 555 546 555 566 555 546 555 566 |
|
56 ? 555 546 575 566 576 546 555 566 |
|
57 bove 576 537 657 566 659 537 576 566 |
|
58 argument 672 538 840 576 842 538 670 575 |
|
59 shows 855 538 957 568 959 538 855 568 |
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60 |
|
61 that 160 583 227 612 229 583 160 612 |
|
62 such 253 583 330 612 331 583 253 612 |
|
63 strategies 357 583 517 621 518 583 356 621 |
|
64 cannot 544 583 664 612 666 583 544 612 |
|
65 be 690 584 729 614 731 584 690 614 |
|
66 profit-max 757 584 935 622 936 584 755 622 |
|
67 - 936 594 956 614 957 594 936 614 |
|
68 |
|
69 imizing 160 630 289 668 290 630 159 668 |
|
70 Nash 311 630 401 660 402 630 311 660 |
|
71 behavior 426 630 581 660 582 630 426 660 |
|
72 in 604 631 635 661 636 631 604 661 |
|
73 a 660 641 677 661 679 641 660 661 |
|
74 temporal 705 631 862 669 863 631 703 669 |
|
75 ran 888 641 936 661 937 641 888 661 |
|
76 - 937 641 957 661 959 641 937 661 |
|
77 |
|
78 domizing 160 677 322 715 323 677 159 715 |
|
79 model. 340 677 454 707 455 677 340 707 |
|
80 |
|
81 Since 203 724 294 753 295 724 203 753 |
|
82 there 322 724 407 753 408 724 322 753 |
|
83 are 434 733 485 753 486 733 434 753 |
|
84 no 513 733 555 753 556 733 513 753 |
|
85 point 582 724 673 761 674 724 581 761 |
|
86 masses 701 734 819 754 820 734 701 754 |
|
87 in 849 725 878 754 879 725 849 754 |
|
88 the 907 725 957 754 959 725 907 754 |
|
89 |
|
90 equilibrium 160 768 363 806 364 768 159 806 |
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91 density, 380 768 512 806 513 768 379 806 |
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92 the 531 768 582 798 583 768 531 798 |
|
93 cumulative 600 770 792 799 793 770 600 799 |
|
94 distribu 810 770 936 799 937 770 810 799 |
|
95 - 937 779 957 799 959 779 937 799 |
|
96 |
|
97 tion 161 814 226 844 227 814 161 844 |
|
98 function 248 814 394 844 395 814 248 844 |
|
99 will 415 814 475 844 477 814 415 844 |
|
100 be 497 814 535 844 536 814 497 844 |
|
101 a 557 824 572 844 574 824 557 844 |
|
102 continuous 594 814 788 844 790 814 594 844 |
|
103 function 811 816 957 845 959 816 811 845 |
|
104 |
|
105 on 159 870 201 890 203 870 159 890 |
|
106 (p 222 871 248 898 249 871 220 898 |
|
107 * 249 870 269 890 270 870 249 890 |
|
108 , 270 871 292 890 294 871 270 890 |
|
109 r). 308 871 348 890 349 871 308 890 |
|
110 Let 370 861 425 890 426 861 370 890 |
|
111 F(p) 445 863 530 898 531 863 444 898 |
|
112 be 551 861 589 890 590 861 551 890 |
|
113 the 610 862 660 891 661 862 610 891 |
|
114 cumulative 681 862 876 891 877 862 681 891 |
|
115 dis 895 862 935 891 936 862 895 891 |
|
116 - 936 871 956 891 957 871 936 891 |
|
117 |
|
118 tribution 160 905 314 935 315 905 160 935 |
|
119 function 348 905 493 935 494 905 348 935 |
|
120 for 526 905 576 935 577 905 526 935 |
|
121 f(p); 602 909 695 944 696 909 601 944 |
|
122 thus 735 907 805 936 806 907 735 936 |
|
123 f(p)= 833 907 950 944 951 907 832 944 |
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124 |
|
125 F‚( 160 951 210 981 211 951 160 981 |
|
126 p) 218 962 257 989 258 962 217 989 |
|
127 almost 275 951 390 981 392 951 275 981 |
|
128 everywhere. 408 951 615 989 616 951 407 989 |
|
129 |
|
130 We 201 998 257 1027 258 998 201 1027 |
|
131 can 275 1007 334 1027 335 1007 275 1027 |
|
132 now 351 1007 422 1027 424 1007 351 1027 |
|
133 construct 440 998 602 1027 603 998 440 1027 |
|
134 the 620 998 672 1027 673 998 620 1027 |
|
135 expected 689 999 843 1037 844 999 688 1037 |
|
136 profit 861 999 956 1037 957 999 859 1037 |
|
137 |
|
138 function 160 1042 305 1072 307 1042 160 1072 |
|
139 for 328 1042 376 1072 377 1042 328 1072 |
|
140 a 396 1052 413 1072 414 1052 396 1072 |
|
141 representative 434 1042 680 1080 681 1042 433 1080 |
|
142 store. 701 1044 793 1073 794 1044 701 1073 |
|
143 When 816 1044 918 1073 920 1044 816 1073 |
|
144 a 940 1053 956 1073 957 1053 940 1073 |
|
145 |
|
146 store 161 1088 244 1118 245 1088 161 1118 |
|
147 charges 262 1088 392 1126 393 1088 261 1126 |
|
148 price 409 1088 493 1126 494 1088 408 1126 |
|
149 p, 504 1099 538 1126 539 1099 503 1126 |
|
150 exactly 557 1088 681 1126 682 1088 556 1126 |
|
151 two 700 1090 761 1119 762 1090 700 1119 |
|
152 events 779 1090 889 1119 890 1090 779 1119 |
|
153 are 907 1099 959 1119 960 1099 907 1119 |
|
154 |
|
155 relevant. 160 1135 309 1164 310 1135 160 1164 |
|
156 It 338 1135 364 1164 366 1135 338 1164 |
|
157 may 389 1144 461 1172 462 1144 388 1172 |
|
158 be 488 1135 526 1164 527 1135 488 1164 |
|
159 that 555 1135 621 1164 622 1135 555 1164 |
|
160 p 641 1146 661 1174 662 1146 640 1174 |
|
161 is 688 1136 713 1165 714 1136 688 1165 |
|
162 the 741 1136 792 1165 793 1136 741 1165 |
|
163 smallest 819 1136 959 1165 960 1136 819 1165 |
|
164 |
|
165 price 160 1181 245 1218 246 1181 159 1218 |
|
166 being 261 1181 356 1218 357 1181 259 1218 |
|
167 charged, 370 1181 517 1218 518 1181 369 1218 |
|
168 in 535 1181 565 1210 566 1181 535 1210 |
|
169 which 581 1181 683 1210 685 1181 581 1210 |
|
170 case, 701 1191 781 1211 783 1191 701 1211 |
|
171 the 799 1182 851 1211 852 1182 799 1211 |
|
172 given 866 1182 959 1220 960 1182 865 1220 |
|
173 |
|
174 store 161 1225 244 1255 245 1225 161 1255 |
|
175 gets 274 1225 338 1263 340 1225 272 1263 |
|
176 all 369 1225 407 1255 408 1225 369 1255 |
|
177 of 438 1225 470 1255 471 1225 438 1255 |
|
178 the 500 1225 551 1255 552 1225 500 1255 |
|
179 informed 582 1225 741 1255 742 1225 582 1255 |
|
180 customers. 772 1227 957 1256 959 1227 772 1256 |
|
181 |
|
182 This 160 1273 236 1302 237 1273 160 1302 |
|
183 event 266 1273 357 1302 359 1273 266 1302 |
|
184 happens 387 1273 531 1311 532 1273 386 1311 |
|
185 only 561 1273 635 1311 636 1273 559 1311 |
|
186 if 666 1274 688 1303 689 1274 666 1303 |
|
187 all 718 1274 757 1303 758 1274 718 1303 |
|
188 the 787 1274 839 1303 840 1274 787 1303 |
|
189 other 870 1274 960 1303 961 1274 870 1303 |
|
190 |
|
191 stores 160 1316 258 1346 259 1316 160 1346 |
|
192 charge 278 1316 393 1354 394 1316 277 1354 |
|
193 prices 412 1316 511 1354 512 1316 411 1354 |
|
194 higher 531 1316 641 1354 642 1316 530 1354 |
|
195 than 660 1318 738 1347 739 1318 660 1347 |
|
196 p, 752 1328 784 1355 785 1328 751 1355 |
|
197 an 805 1327 845 1347 846 1327 805 1347 |
|
198 event 865 1318 957 1347 959 1318 865 1347 |
|
199 |
|
200 which 160 1362 263 1392 264 1362 160 1392 |
|
201 has 281 1362 337 1392 338 1362 281 1392 |
|
202 probability 356 1362 550 1400 551 1362 355 1400 |
|
203 (1 568 1372 595 1392 596 1372 568 1392 |
|
204 …F(p)) 610 1366 735 1401 737 1366 609 1401 |
|
205 ? 737 1374 755 1393 757 1374 737 1393 |
|
206 ? 757 1374 775 1393 777 1374 757 1393 |
|
207 ‚. 777 1374 816 1393 817 1374 777 1393 |
|
208 On 837 1364 888 1393 889 1364 837 1393 |
|
209 the 907 1364 957 1393 959 1364 907 1393 |
|
210 |
|
211 other 160 1410 250 1439 251 1410 160 1439 |
|
212 hand, 268 1410 364 1439 366 1410 268 1439 |
|
213 there 386 1410 470 1439 471 1410 386 1439 |
|
214 may 488 1419 562 1448 563 1419 487 1448 |
|
215 be 579 1410 620 1439 621 1410 579 1439 |
|
216 some 638 1420 726 1440 727 1420 638 1440 |
|
217 store 746 1413 830 1440 831 1413 746 1440 |
|
218 with 848 1411 921 1440 922 1411 848 1440 |
|
219 a 940 1420 959 1440 960 1420 940 1440 |
|
220 |
|
221 lower 161 1453 256 1483 257 1453 161 1483 |
|
222 price, 274 1453 367 1491 368 1453 272 1491 |
|
223 in 386 1453 416 1483 418 1453 386 1483 |
|
224 which 434 1453 537 1483 538 1453 434 1483 |
|
225 case 556 1463 628 1483 629 1463 556 1483 |
|
226 the 647 1455 698 1484 699 1455 647 1484 |
|
227 store 716 1455 798 1484 799 1455 716 1484 |
|
228 in 818 1455 850 1484 851 1455 818 1484 |
|
229 ques 868 1464 936 1492 937 1464 866 1492 |
|
230 - 937 1464 957 1484 959 1464 937 1484 |
|
231 |
|
232 tion 162 1500 229 1529 230 1500 162 1529 |
|
233 only 252 1500 328 1537 329 1500 251 1537 |
|
234 gets 351 1500 416 1537 418 1500 350 1537 |
|
235 its 440 1500 478 1529 479 1500 440 1529 |
|
236 share 503 1500 592 1529 594 1500 503 1529 |
|
237 of 617 1501 650 1530 651 1501 617 1530 |
|
238 the 675 1501 727 1530 728 1501 675 1530 |
|
239 uninformed 753 1501 959 1530 960 1501 753 1530 |
|
240 |
|
241 customers. 161 1546 347 1575 348 1546 161 1575 |
|
242 This 370 1546 444 1575 445 1546 370 1575 |
|
243 event 466 1546 558 1575 559 1546 466 1575 |
|
244 happens 579 1546 725 1583 726 1546 578 1583 |
|
245 with 748 1547 822 1576 823 1547 748 1576 |
|
246 proba 844 1547 937 1585 938 1547 843 1585 |
|
247 - 938 1556 959 1576 960 1556 938 1576 |
|
248 |
|
249 bility 162 1593 251 1631 252 1593 161 1631 |
|
250 1 285 1602 294 1622 295 1602 285 1622 |
|
251 … 308 1602 331 1622 333 1602 308 1622 |
|
252 (1 342 1602 369 1622 370 1602 342 1622 |
|
253 … 383 1602 407 1622 408 1602 383 1622 |
|
254 F( 418 1600 455 1622 457 1600 418 1622 |
|
255 p 465 1603 485 1631 486 1603 464 1631 |
|
256 ))fl 493 1600 535 1622 536 1600 493 1622 |
|
257 - 544 1603 558 1622 559 1603 544 1622 |
|
258 I 571 1600 576 1622 577 1600 571 1622 |
|
259 (By 620 1594 677 1632 679 1594 618 1632 |
|
260 Proposition 709 1594 911 1632 912 1594 708 1632 |
|
261 3 942 1603 957 1624 959 1603 942 1624 |
|
262 |
|
263 we 161 1646 206 1666 207 1646 161 1666 |
|
264 can 229 1646 288 1666 289 1646 229 1666 |
|
265 neglect 309 1637 431 1674 432 1637 308 1674 |
|
266 the 453 1637 503 1666 504 1637 453 1666 |
|
267 probability 525 1637 720 1674 721 1637 524 1674 |
|
268 of 742 1638 774 1667 775 1638 742 1667 |
|
269 any 796 1647 857 1675 858 1647 794 1675 |
|
270 ties.) 879 1638 959 1667 960 1638 879 1667 |
|
271 |
|
272 Hence 164 1683 272 1712 274 1683 164 1712 |
|
273 the 297 1683 348 1712 349 1683 297 1712 |
|
274 expected 372 1683 523 1720 524 1683 370 1720 |
|
275 profit 546 1683 643 1720 644 1683 545 1720 |
|
276 of 667 1684 700 1713 701 1684 667 1713 |
|
277 a 724 1693 740 1713 741 1693 724 1713 |
|
278 representa 764 1684 937 1722 938 1684 762 1722 |
|
279 - 938 1693 959 1713 960 1693 938 1713 |
|
280 |
|
281 tive 161 1730 222 1759 223 1730 161 1759 |
|
282 store 240 1730 322 1759 323 1730 240 1759 |
|
283 is 341 1730 364 1759 366 1730 341 1759 |
|
284 |
|
285 f 178 1846 253 1868 255 1846 178 1868 |
|
286 ? 255 1855 269 1868 270 1855 255 1868 |
|
287 ( 270 1855 284 1868 285 1855 270 1868 |
|
288 ? 285 1855 300 1868 301 1855 285 1868 |
|
289 s(p)(l 301 1846 387 1877 388 1846 300 1877 |
|
290 ? 438 1855 388 1867 388 1854 438 1868 |
|
291 (p))fl 438 1846 574 1877 575 1846 437 1877 |
|
292 ? 575 1855 589 1868 590 1855 575 1868 |
|
293 |
|
294 p 196 1886 210 1908 211 1886 194 1908 |
|
295 |
|
296 1 424 1979 432 1999 433 1979 424 1999 |
|
297 … 446 1979 468 1999 470 1979 446 1999 |
|
298 (1 481 1979 510 1999 511 1979 481 1999 |
|
299 …F(p)) 525 1970 661 2007 662 1970 524 2007 |
|
300 ? 662 1979 682 1999 683 1979 662 1999 |
|
301 ? 683 1979 703 1999 705 1979 683 1999 |
|
302 1 705 1979 725 1999 726 1979 705 1999 |
|
303 j 738 1979 746 2007 747 1979 737 2007 |
|
304 JJ(o) 760 1970 863 1999 864 1970 760 1999 |
|
305 dp 876 1971 911 2009 912 1971 875 2009 |
|
306 |
|
307 where 162 2070 265 2100 266 2070 162 2100 |
|
308 r 322 2079 433 2100 434 2079 322 2100 |
|
309 ? 434 2079 454 2100 455 2079 434 2100 |
|
310 (p)=p(U+I)…c(U+i) 455 2070 803 2108 804 2070 454 2108 |
|
311 |
|
312 ? 316 2173 405 2192 406 2173 316 2192 |
|
313 ? 406 2173 425 2192 426 2173 406 2192 |
|
314 (p)=pU 426 2164 544 2200 545 2164 425 2200 |
|
315 ? 545 2173 564 2192 565 2173 545 2192 |
|
316 c(U) 565 2164 643 2192 644 2164 565 2192 |
|
317 |
|
318 The 203 2261 269 2291 270 2261 203 2291 |
|
319 maximization 289 2261 530 2291 531 2261 289 2291 |
|
320 problem 550 2261 695 2299 696 2261 549 2299 |
|
321 of 716 2262 751 2292 752 2262 716 2292 |
|
322 the 772 2262 823 2292 824 2262 772 2292 |
|
323 firm 844 2262 915 2292 916 2262 844 2292 |
|
324 is 936 2262 960 2292 961 2262 936 2292 |
|
325 |
|
326 to 162 2306 194 2336 196 2306 162 2336 |
|
327 choose 212 2306 330 2336 331 2306 212 2336 |
|
328 the 350 2306 400 2336 401 2306 350 2336 |
|
329 density 418 2306 543 2344 544 2306 416 2344 |
|
330 function 563 2306 708 2336 709 2306 563 2336 |
|
331 f(p) 721 2307 803 2345 804 2307 720 2345 |
|
332 so 823 2317 857 2337 858 2317 823 2337 |
|
333 as 876 2317 908 2337 909 2317 876 2337 |
|
334 to 927 2307 960 2337 961 2307 927 2337 |
|
335 |
|
336 maximize 162 2351 328 2381 329 2351 162 2381 |
|
337 expected 361 2351 512 2389 513 2351 360 2389 |
|
338 profits 544 2351 657 2389 659 2351 543 2389 |
|
339 subject 689 2352 812 2390 813 2352 688 2390 |
|
340 to 845 2352 876 2382 877 2352 845 2382 |
|
341 the 908 2352 960 2382 961 2352 908 2382 |
|
342 |
|
343 constraints: 164 2398 367 2428 368 2398 164 2428 |
|
344 |
|
345 f(p)>=0; 327 2506 493 2538 494 2506 325 2538 |
|
346 frj(p)dp=l 545 2506 790 2538 791 2506 544 2538 |
|
347 |
|
348 p 564 2554 578 2577 579 2554 563 2577 |
|
349 |
|
350 expected 1047 312 1200 350 1201 312 1046 349 |
|
351 profit; 1224 312 1332 350 1333 312 1223 349 |
|
352 for 1361 312 1410 342 1411 312 1361 342 |
|
353 if 1433 312 1457 342 1458 312 1433 342 |
|
354 some 1481 322 1568 342 1569 322 1481 342 |
|
355 price 1592 314 1679 351 1680 314 1590 350 |
|
356 yields 1703 314 1803 351 1804 314 1701 350 |
|
357 a 1828 323 1846 343 1846 323 1828 343 |
|
358 |
|
359 greater 1047 357 1168 395 1169 357 1046 394 |
|
360 profit 1183 357 1280 395 1281 357 1182 394 |
|
361 than 1298 357 1372 387 1373 357 1298 387 |
|
362 some 1388 367 1477 387 1478 367 1388 387 |
|
363 other 1494 359 1582 388 1583 359 1494 388 |
|
364 price 1599 359 1684 396 1685 359 1598 395 |
|
365 it 1701 359 1722 388 1723 359 1701 388 |
|
366 would 1738 359 1844 388 1846 359 1738 388 |
|
367 |
|
368 pay 1046 413 1107 441 1109 413 1045 440 |
|
369 to 1135 403 1165 433 1166 403 1135 433 |
|
370 increase 1192 403 1333 433 1334 403 1192 433 |
|
371 the 1360 403 1411 433 1412 403 1360 433 |
|
372 frequency 1438 403 1614 441 1615 403 1437 440 |
|
373 with 1640 405 1714 434 1716 405 1640 434 |
|
374 which 1740 405 1844 434 1846 405 1740 434 |
|
375 |
|
376 the 1047 450 1097 479 1098 450 1047 479 |
|
377 more 1111 459 1197 479 1198 459 1111 479 |
|
378 profitable 1211 450 1383 487 1384 450 1210 486 |
|
379 price 1396 450 1481 487 1482 450 1394 486 |
|
380 were 1494 460 1574 480 1575 460 1494 480 |
|
381 charged. 1587 451 1737 488 1738 451 1586 487 |
|
382 Since 1753 451 1843 480 1844 451 1753 480 |
|
383 |
|
384 we 1045 504 1090 524 1091 504 1045 524 |
|
385 require 1107 494 1228 532 1229 494 1106 531 |
|
386 zero 1243 504 1314 524 1315 504 1243 524 |
|
387 profits 1331 494 1444 532 1445 494 1329 531 |
|
388 due 1461 494 1521 524 1522 494 1461 524 |
|
389 to 1538 496 1569 525 1570 496 1538 525 |
|
390 free 1586 496 1651 525 1652 496 1586 525 |
|
391 entry, 1667 496 1765 533 1766 496 1666 532 |
|
392 this 1783 496 1842 525 1843 496 1783 525 |
|
393 |
|
394 common 1046 550 1198 570 1200 550 1046 570 |
|
395 level 1218 540 1295 570 1296 540 1218 570 |
|
396 of 1315 540 1350 570 1351 540 1315 570 |
|
397 profit 1368 540 1466 578 1468 540 1367 577 |
|
398 must 1487 542 1569 571 1570 542 1487 571 |
|
399 be 1590 542 1629 571 1631 542 1590 571 |
|
400 zero. 1650 551 1727 571 1729 551 1650 571 |
|
401 6 1729 551 1749 571 1750 551 1729 571 |
|
402 This 1768 542 1842 571 1843 542 1768 571 |
|
403 |
|
404 argument 1046 587 1211 624 1212 587 1045 624 |
|
405 yields 1227 587 1325 624 1326 587 1225 624 |
|
406 |
|
407 PROPOSITION 1047 677 1333 707 1334 677 1047 707 |
|
408 4: 1354 687 1384 707 1385 687 1354 707 |
|
409 if 1413 685 1445 707 1446 685 1413 707 |
|
410 f(p) 1450 680 1531 715 1533 680 1449 715 |
|
411 >0, 1543 689 1607 708 1608 689 1543 708 |
|
412 then 1627 681 1694 708 1696 681 1627 708 |
|
413 |
|
414 r 1316 786 1322 806 1322 786 1316 806 |
|
415 ? 1322 786 1342 806 1344 786 1322 806 |
|
416 (p)(l 1344 777 1445 814 1446 777 1342 814 |
|
417 …F(p)) 1459 777 1603 814 1605 777 1458 814 |
|
418 ? 1605 786 1625 806 1626 786 1605 806 |
|
419 ? 1626 786 1646 806 1647 786 1626 806 |
|
420 |
|
421 1(1 1334 891 1422 911 1423 891 1334 911 |
|
422 F(p)) 1471 882 1574 920 1575 882 1470 920 |
|
423 ? 1575 891 1595 911 1596 891 1575 911 |
|
424 ? 1596 891 1616 911 1618 891 1596 911 |
|
425 ‚j 1618 891 1658 920 1659 891 1616 920 |
|
426 =0 1673 891 1727 911 1729 891 1673 911 |
|
427 |
|
428 (Of 1087 999 1143 1028 1144 999 1087 1028 |
|
429 course, 1162 1008 1283 1028 1285 1008 1162 1028 |
|
430 Proposition 1306 999 1508 1037 1509 999 1305 1037 |
|
431 4 1527 1009 1546 1029 1547 1009 1527 1029 |
|
432 also 1566 1000 1633 1029 1634 1000 1566 1029 |
|
433 follows 1653 1000 1777 1029 1778 1000 1653 1029 |
|
434 di 1797 1000 1821 1029 1822 1000 1797 1029 |
|
435 - 1822 1009 1842 1029 1843 1009 1822 1029 |
|
436 |
|
437 rectly 1045 1044 1140 1081 1142 1044 1044 1081 |
|
438 from 1170 1044 1253 1073 1254 1044 1170 1073 |
|
439 the 1282 1044 1332 1073 1333 1044 1282 1073 |
|
440 application 1360 1044 1559 1081 1560 1044 1359 1081 |
|
441 of 1587 1045 1620 1074 1621 1045 1587 1074 |
|
442 the 1650 1045 1700 1074 1701 1045 1650 1074 |
|
443 Kuhn 1731 1045 1821 1074 1822 1045 1731 1074 |
|
444 - 1822 1054 1842 1074 1843 1054 1822 1074 |
|
445 |
|
446 Tucker 1045 1090 1170 1119 1171 1090 1045 1119 |
|
447 theorem 1192 1090 1333 1119 1334 1090 1192 1119 |
|
448 to 1357 1090 1387 1119 1388 1090 1357 1119 |
|
449 the 1411 1090 1462 1119 1463 1090 1411 1119 |
|
450 specified 1485 1091 1639 1129 1640 1091 1484 1129 |
|
451 maximiza 1661 1091 1822 1120 1823 1091 1661 1120 |
|
452 - 1823 1100 1843 1120 1844 1100 1823 1120 |
|
453 |
|
454 tion 1046 1137 1112 1166 1113 1137 1046 1166 |
|
455 problem.) 1142 1137 1311 1175 1312 1137 1140 1175 |
|
456 Rearranging 1341 1137 1561 1175 1562 1137 1340 1175 |
|
457 this 1590 1138 1651 1168 1652 1138 1590 1168 |
|
458 equation, 1680 1138 1843 1176 1844 1138 1679 1176 |
|
459 |
|
460 we 1046 1191 1091 1211 1092 1191 1046 1211 |
|
461 have 1126 1182 1205 1211 1207 1182 1126 1211 |
|
462 a 1242 1191 1260 1211 1260 1191 1242 1211 |
|
463 formula 1294 1182 1431 1211 1432 1182 1294 1211 |
|
464 for 1468 1182 1516 1211 1517 1182 1468 1211 |
|
465 the 1553 1183 1603 1212 1605 1183 1553 1212 |
|
466 equilibrium 1640 1183 1843 1221 1844 1183 1639 1221 |
|
467 |
|
468 cumulative 1046 1230 1238 1260 1240 1230 1046 1260 |
|
469 distribution 1256 1230 1462 1260 1463 1230 1256 1260 |
|
470 function: 1481 1230 1639 1260 1640 1230 1481 1260 |
|
471 |
|
472 l 1158 1371 1295 1400 1296 1371 1158 1400 |
|
473 ? 1296 1380 1316 1400 1318 1380 1296 1400 |
|
474 F(P)=( 1318 1371 1440 1400 1442 1371 1318 1400 |
|
475 ? 1442 1380 1462 1400 1463 1380 1442 1400 |
|
476 ($¼1s(p) 1463 1380 1626 1409 1627 1380 1462 1409 |
|
477 )nlt 1644 1372 1724 1401 1725 1372 1644 1401 |
|
478 |
|
479 Note 1046 1502 1131 1531 1132 1502 1046 1531 |
|
480 that 1149 1502 1215 1531 1216 1502 1149 1531 |
|
481 the 1233 1502 1281 1531 1282 1502 1233 1531 |
|
482 denominator 1298 1502 1525 1531 1527 1502 1298 1531 |
|
483 of 1541 1503 1574 1533 1575 1503 1541 1533 |
|
484 this 1592 1503 1651 1533 1652 1503 1592 1533 |
|
485 fraction 1667 1503 1803 1533 1804 1503 1667 1533 |
|
486 is 1821 1503 1843 1533 1844 1503 1821 1533 |
|
487 |
|
488 negative 1046 1547 1190 1585 1191 1547 1045 1585 |
|
489 for 1209 1547 1259 1576 1260 1547 1209 1576 |
|
490 any 1276 1556 1337 1585 1338 1556 1275 1585 |
|
491 p 1348 1557 1371 1585 1372 1557 1347 1585 |
|
492 between 1390 1547 1534 1576 1535 1547 1390 1576 |
|
493 p 1546 1559 1564 1586 1566 1559 1544 1586 |
|
494 * 1566 1557 1586 1577 1587 1557 1566 1577 |
|
495 and 1608 1548 1671 1577 1672 1548 1608 1577 |
|
496 r. 1688 1559 1712 1577 1713 1559 1688 1577 |
|
497 Hence 1733 1548 1843 1577 1844 1548 1733 1577 |
|
498 |
|
499 the 1047 1595 1097 1625 1098 1595 1047 1625 |
|
500 numerator 1130 1595 1314 1625 1315 1595 1130 1625 |
|
501 must 1346 1595 1430 1625 1431 1595 1346 1625 |
|
502 be 1462 1595 1500 1625 1501 1595 1462 1625 |
|
503 negative 1531 1596 1678 1634 1679 1596 1530 1634 |
|
504 so 1711 1606 1745 1626 1746 1606 1711 1626 |
|
505 that 1777 1596 1843 1626 1844 1596 1777 1626 |
|
506 |
|
507 profits 1046 1639 1157 1677 1158 1639 1045 1677 |
|
508 in 1179 1639 1209 1668 1210 1639 1179 1668 |
|
509 the 1233 1639 1282 1668 1283 1639 1233 1668 |
|
510 event 1303 1639 1397 1668 1398 1639 1303 1668 |
|
511 of 1418 1639 1451 1668 1452 1639 1418 1668 |
|
512 failure 1471 1639 1582 1668 1583 1639 1471 1668 |
|
513 are 1605 1650 1657 1670 1658 1650 1605 1670 |
|
514 definitely 1679 1640 1843 1678 1844 1640 1678 1678 |
|
515 |
|
516 negative. 1046 1685 1200 1723 1201 1685 1045 1723 |
|
517 The 1223 1685 1288 1714 1289 1685 1223 1714 |
|
518 construction 1309 1685 1529 1714 1530 1685 1309 1714 |
|
519 of 1550 1686 1585 1716 1586 1686 1550 1716 |
|
520 (1 1606 1696 1633 1716 1634 1696 1606 1716 |
|
521 …F(p)) 1648 1688 1779 1724 1781 1688 1647 1724 |
|
522 ? 1781 1697 1800 1716 1800 1697 1781 1716 |
|
523 |
|
524 is 1045 1730 1067 1759 1068 1730 1045 1759 |
|
525 illustrated 1091 1730 1267 1759 1268 1730 1091 1759 |
|
526 in 1290 1730 1319 1759 1320 1730 1290 1759 |
|
527 Figure 1345 1730 1457 1768 1458 1730 1344 1768 |
|
528 1. 1487 1740 1508 1761 1509 1740 1487 1761 |
|
529 At 1533 1731 1574 1761 1575 1731 1533 1761 |
|
530 each 1598 1731 1677 1761 1678 1731 1598 1761 |
|
531 p 1694 1742 1716 1769 1717 1742 1693 1769 |
|
532 where 1739 1731 1842 1761 1843 1731 1739 1761 |
|
533 |
|
534 f(p)>O 1038 1778 1184 1814 1185 1778 1037 1814 |
|
535 we 1207 1785 1251 1805 1253 1785 1207 1805 |
|
536 can 1275 1785 1332 1805 1333 1785 1275 1805 |
|
537 construct 1357 1776 1521 1805 1522 1776 1357 1805 |
|
538 rf(P) 1543 1779 1640 1807 1641 1779 1543 1807 |
|
539 and 1664 1777 1727 1807 1729 1777 1664 1807 |
|
540 ? 1751 1787 1729 1805 1729 1785 1751 1807 |
|
541 s(P) 1751 1777 1842 1807 1843 1777 1751 1807 |
|
542 |
|
543 as 1045 1833 1078 1853 1079 1833 1045 1853 |
|
544 illustrated 1107 1823 1280 1853 1281 1823 1107 1853 |
|
545 and 1308 1823 1372 1853 1373 1823 1308 1853 |
|
546 take 1401 1823 1472 1853 1474 1823 1401 1853 |
|
547 the 1503 1824 1554 1854 1555 1824 1503 1854 |
|
548 relevant 1582 1824 1724 1854 1725 1824 1582 1854 |
|
549 ratio. 1753 1824 1841 1854 1842 1824 1753 1854 |
|
550 |
|
551 Proposition 1046 1868 1247 1906 1248 1868 1045 1906 |
|
552 4 1264 1877 1283 1898 1283 1877 1264 1898 |
|
553 gives 1299 1868 1384 1906 1385 1868 1298 1906 |
|
554 us 1401 1877 1437 1898 1438 1877 1401 1898 |
|
555 an 1455 1877 1495 1898 1496 1877 1455 1898 |
|
556 explicit 1512 1869 1640 1907 1641 1869 1511 1907 |
|
557 expression 1658 1869 1842 1907 1843 1869 1657 1907 |
|
558 |
|
559 for 1045 1914 1093 1944 1094 1914 1045 1944 |
|
560 the 1116 1914 1166 1944 1168 1914 1116 1944 |
|
561 equilibrium 1189 1914 1391 1952 1392 1914 1188 1952 |
|
562 distribution 1414 1914 1619 1944 1620 1914 1414 1944 |
|
563 function 1641 1915 1789 1945 1790 1915 1641 1945 |
|
564 at 1812 1915 1842 1945 1843 1915 1812 1945 |
|
565 |
|
566 those 1046 1960 1136 1990 1137 1960 1046 1990 |
|
567 values 1152 1960 1260 1990 1261 1960 1152 1990 |
|
568 of 1277 1960 1309 1990 1311 1960 1277 1990 |
|
569 p 1321 1971 1341 1998 1342 1971 1320 1998 |
|
570 where 1359 1960 1463 1990 1464 1960 1359 1990 |
|
571 f( 1474 1967 1505 1990 1507 1967 1474 1990 |
|
572 p)> 1514 1972 1590 1999 1592 1972 1512 1999 |
|
573 0. 1602 1972 1629 1991 1631 1972 1602 1991 |
|
574 If 1648 1961 1675 1991 1677 1961 1648 1991 |
|
575 this 1693 1961 1752 1991 1753 1961 1693 1991 |
|
576 is 1770 1961 1794 1991 1795 1961 1770 1991 |
|
577 to 1811 1961 1843 1991 1844 1961 1811 1991 |
|
578 |
|
579 be 1046 2006 1084 2036 1085 2006 1046 2036 |
|
580 a 1107 2016 1125 2036 1126 2016 1107 2036 |
|
581 legitimate 1149 2006 1318 2044 1319 2006 1148 2044 |
|
582 candidate 1341 2006 1512 2036 1514 2006 1341 2036 |
|
583 for 1536 2007 1586 2037 1587 2007 1536 2037 |
|
584 a 1609 2017 1628 2037 1628 2017 1609 2037 |
|
585 cumulative 1651 2007 1843 2037 1844 2007 1651 2037 |
|
586 |
|
587 distribution 1046 2053 1248 2083 1249 2053 1046 2083 |
|
588 function, 1279 2053 1435 2083 1436 2053 1279 2083 |
|
589 it 1465 2053 1487 2083 1488 2053 1465 2083 |
|
590 should 1516 2055 1632 2084 1633 2055 1516 2084 |
|
591 be 1661 2055 1699 2084 1700 2055 1661 2084 |
|
592 an 1729 2064 1769 2084 1770 2064 1729 2084 |
|
593 in 1800 2055 1822 2084 1823 2055 1800 2084 |
|
594 - 1823 2064 1843 2084 1844 2064 1823 2084 |
|
595 |
|
596 creasing 1045 2097 1188 2135 1189 2097 1044 2135 |
|
597 function 1204 2097 1348 2127 1350 2097 1204 2127 |
|
598 of 1366 2097 1399 2127 1400 2097 1366 2127 |
|
599 p. 1410 2108 1440 2135 1442 2108 1409 2135 |
|
600 This 1458 2097 1533 2127 1534 2097 1458 2127 |
|
601 is 1550 2098 1573 2128 1574 2098 1550 2128 |
|
602 easy 1590 2108 1664 2136 1665 2108 1589 2136 |
|
603 to 1681 2098 1712 2128 1713 2098 1681 2128 |
|
604 verify: 1729 2098 1838 2136 1840 2098 1727 2136 |
|
605 |
|
606 PROPOSITION 1046 2188 1339 2218 1340 2188 1046 2218 |
|
607 5: 1368 2198 1397 2218 1398 2198 1368 2218 |
|
608 ƒj(p)/( 1427 2199 1595 2226 1596 2199 1426 2226 |
|
609 ? 1596 2200 1615 2219 1615 2200 1596 2219 |
|
610 (p) 1615 2200 1674 2227 1675 2200 1614 2227 |
|
611 … 1692 2199 1717 2219 1718 2199 1692 2219 |
|
612 ? 1733 2199 1718 2218 1718 2198 1733 2219 |
|
613 s(P)) 1733 2189 1842 2219 1843 2189 1733 2219 |
|
614 |
|
615 is 1044 2238 1067 2265 1068 2238 1044 2265 |
|
616 strictly 1084 2238 1197 2273 1198 2238 1083 2273 |
|
617 decreasing 1216 2238 1393 2273 1394 2238 1215 2273 |
|
618 in 1411 2238 1438 2265 1439 2238 1411 2265 |
|
619 p. 1452 2246 1482 2273 1483 2246 1451 2273 |
|
620 |
|
621 PROOF: 1046 2326 1198 2356 1200 2326 1046 2356 |
|
622 |
|
623 Taking 1085 2371 1208 2409 1209 2371 1084 2409 |
|
624 the 1231 2371 1281 2401 1282 2371 1231 2401 |
|
625 derivative 1305 2371 1476 2401 1477 2371 1305 2401 |
|
626 it 1500 2371 1521 2401 1522 2371 1500 2401 |
|
627 suffices 1544 2372 1674 2402 1675 2372 1544 2402 |
|
628 to 1699 2372 1730 2402 1731 2372 1699 2402 |
|
629 show 1753 2372 1842 2402 1843 2372 1753 2402 |
|
630 |
|
631 that 1045 2417 1111 2447 1112 2417 1045 2447 |
|
632 |
|
633 It 206 2625 231 2655 232 2625 206 2655 |
|
634 is 251 2625 275 2655 276 2625 251 2655 |
|
635 clear 295 2625 377 2655 379 2625 295 2655 |
|
636 that 398 2625 462 2655 464 2625 398 2655 |
|
637 all 483 2625 522 2655 523 2625 483 2655 |
|
638 prices 543 2625 642 2663 643 2625 542 2663 |
|
639 that 663 2626 731 2656 732 2626 663 2656 |
|
640 are 751 2636 801 2656 803 2636 751 2656 |
|
641 charged 823 2626 961 2664 962 2626 822 2664 |
|
642 |
|
643 with 162 2669 237 2698 238 2669 162 2698 |
|
644 positive 264 2669 398 2707 399 2669 263 2707 |
|
645 density 424 2669 548 2707 549 2669 422 2707 |
|
646 must 575 2669 657 2698 659 2669 575 2698 |
|
647 yield 683 2670 768 2708 770 2670 682 2708 |
|
648 the 797 2670 848 2700 849 2670 797 2700 |
|
649 same 875 2679 961 2700 962 2679 875 2700 |
|
650 |
|
651 6 1080 2600 1100 2617 1101 2600 1080 2617 |
|
652 One 1101 2593 1151 2617 1152 2593 1101 2617 |
|
653 can 1175 2600 1222 2617 1223 2600 1175 2617 |
|
654 also 1244 2593 1296 2617 1298 2593 1244 2617 |
|
655 formulate 1319 2593 1456 2617 1457 2593 1319 2617 |
|
656 the 1479 2593 1520 2617 1521 2593 1479 2617 |
|
657 model 1543 2594 1628 2618 1629 2594 1543 2618 |
|
658 with 1651 2594 1711 2618 1712 2594 1651 2618 |
|
659 a 1735 2601 1748 2618 1748 2601 1735 2618 |
|
660 fixed 1770 2594 1837 2618 1838 2594 1770 2618 |
|
661 |
|
662 number 1038 2640 1145 2664 1146 2640 1038 2664 |
|
663 of 1159 2640 1187 2664 1188 2640 1159 2664 |
|
664 firms. 1202 2640 1277 2664 1279 2640 1202 2664 |
|
665 In 1295 2640 1321 2664 1322 2640 1295 2664 |
|
666 this 1338 2640 1384 2664 1385 2640 1338 2664 |
|
667 case, 1399 2648 1464 2664 1465 2648 1399 2664 |
|
668 expected 1481 2642 1602 2671 1603 2642 1479 2671 |
|
669 profits 1618 2642 1709 2671 1710 2642 1616 2671 |
|
670 must 1725 2642 1790 2665 1791 2642 1725 2665 |
|
671 be 1805 2642 1836 2665 1837 2642 1805 2665 |
|
672 |
|
673 equal 1037 2679 1111 2709 1112 2679 1035 2709 |
|
674 to 1126 2679 1151 2703 1152 2679 1126 2703 |
|
675 H 1168 2679 1174 2703 1174 2679 1168 2703 |
|
676 1 1174 2687 1190 2703 1191 2687 1174 2703 |
|
677 (r). 1191 2687 1257 2703 1259 2687 1191 2703 |
|
678 |
|
679 |