0
|
1 |
|
|
2 |
654 164 217 211 236 212 217 164 236
|
|
3 |
|
|
4 |
THE 659 211 727 233 728 211 659 233
|
|
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
|
|
8 |
|
|
9 |
SEPTEMBER 1557 217 1766 239 1768 217 1557 239
|
|
10 |
1980 1781 220 1846 239 1847 220 1781 239
|
|
11 |
|
|
12 |
dispersion 161 307 340 344 341 307 160 343
|
|
13 |
and 356 307 418 336 419 307 356 336
|
|
14 |
models 434 307 557 336 558 307 434 336
|
|
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
|
|
19 |
- 938 317 959 337 960 317 938 337
|
|
20 |
|
|
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
|
|
28 |
- 938 366 959 386 960 366 938 386
|
|
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
|
|
38 |
|
|
39 |
Wilde-Schwartz 160 445 439 474 440 445 160 474
|
|
40 |
model, 458 445 576 474 577 445 458 474
|
|
41 |
have 597 446 675 475 676 446 597 475
|
|
42 |
equilibria 695 446 864 484 865 446 694 483
|
|
43 |
with 883 446 957 475 959 446 883 475
|
|
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
|
|
51 |
|
|
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
|
|
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
|
|
91 |
density, 380 768 512 806 513 768 379 806
|
|
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
|
|
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 |
|