i *1 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. III 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. - 21. 22. () 23. *1

i *1 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. III 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. - 21. 22. () 23. *1

ii 24. 25. 1. 2. 3. 4. R. 5. 6. 7. 8. 9. 10. L A TEX pdf (http://opencourse.doshisha.ac.jp) *2 2015 9 27 *2

iii i 1 1 1.1.................................... 1 1.1.1............................... 1 1.1.2................................... 2 1.1.3.................................. 3 1.1.4.................................. 3 1.1.5......................... 4 1.1.6............................. 4 1.1.7.............................. 5 1.2................................ 5 1.2.1.................................. 5 1.2.2............................... 5 1.2.3................... 6 1.3............................... 7 1.4................................ 8 1.4.1................................. 8 1.4.2................................. 9 1.5................................ 9 1.5.1.................................. 9 1.5.2............................... 9 1.5.3................... 11 1.6............................... 11 1.7.................................... 12 1.7.1............................... 12 1.7.2........................... 13 1.8...................... 13

iv 1.9........................... 15 1.9.1........................... 15 1.9.2........................... 17 1.10............................... 19 1.10.1............ 19 1.10.2........................ 20 1.10.3.................. 23 2 25 2.1............................... 25 2.1.1 -............. 26 2.1.1.1...................... 26 2.1.1.2................. 28 2.1.1.3..................... 31 2.1.2............................... 32 2.1.3.............................. 33 2.1.4........................... 36 2.1.5.............................. 37 2.1.6............................... 38 2.2................................... 38 2.2.1....................... 38 2.2.2...................... 40 2.3............................... 42 2.3.1............................ 42 2.3.2............................ 43 2.3.3........................... 44 2.4............................... 44 2.4.1 -................ 44 2.4.2......................... 45 2.4.3............................. 46 2.5.............................. 47 2.6................................. 51 2.6.1....................... 51 2.6.2...................... 53 2.7.......................... 55 2.7.1............................... 55 2.7.2.................. 58

v 2.7.3.... 61 2.8........................... 63 2.8.1 - -......... 63 2.8.2....... 65 2.8.3.............................. 70 2.8.4... 71 2.8.5................... 73 2.8.6......................... 75 2.9.................................... 77 2.10.............................. 80 2.10.1............................. 80 2.10.2.... 85 2.11 -................ 88 2.11.1.............................. 88 2.11.2 -................ 90 3 92 3.1................................... 92 3.1.1.................................. 92 3.1.2............................ 92 3.1.3............................... 93 3.1.4........................ 93 3.1.5............................ 94 3.1.6.................................. 94 3.1.7.................... 94 3.1.8............................ 95 3.1.9....................... 95 3.2......................... 96 3.2.1............................... 96 3.2.2.............................. 96 3.2.3............................ 96 3.2.4........................... 97 3.3................................... 97 3.3.1............................. 97 3.3.2............................... 98 3.3.3........................... 99 3.3.4...................... 100

vi 3.3.5......................... 101 3.3.6......................... 102 3.3.7....................... 103 3.4.............................. 104 3.5............................ 108 3.5.1...................... 108 3.5.2.............................. 109 3.5.3............................... 112 3.5.4........................... 112 3.6........................... 114 3.6.1............................... 114 3.6.2.............................. 114 3.6.3.............................. 115 3.7.............................. 116 3.7.1.................. 116 3.7.2.................. 118 3.8........................... 121 3.9................................ 125 3.9.1............................... 126 3.9.2........................ 126 3.9.3....................... 129 3.9.4........................... 129 3.9.5............................... 130 3.10........................... 131 3.10.1.............................. 131 3.10.2.............................. 132 3.11........................... 133 3.11.1 -.................. 133 3.11.2-3............. 134 3.11.3 -........ 136 3.11.4...................... 137 3.12........................... 138 3.13............................... 139 3.13.1 -.............. 139 3.13.2....... 139 3.13.3 -......... 140

vii 3.14....................... 142 3.15.................................... 142 3.15.1 1............................ 142 3.15.2 2............................ 143 3.15.3 3............................ 143 3.16................................. 144 3.17....................... 146 3.18..................................... 149 3.18.1.............................. 149 3.18.2........................... 150 3.18.3............................ 151 3.18.4 (Groves mechanism)............. 152 3.19................................. 155 3.20 -................. 156 3.21.................... 159 3.21.1................... 159 3.21.2.................... 162 3.21.3...................... 163 3.21.4........................ 164 3.21.5............ 165 3.21.6.................. 168 3.21.7........................... 170 3.21.8 CES............................. 170 4 172 4.1........................... 172 4.2....................... 173 4.2.1............. 173 4.2.2............................. 175 4.2.3............................... 178 4.2.4...................... 183 4.3.................... 185 4.3.1............ 185 4.3.2......................... 187 4.3.3................... 190 4.3.4........... 190 4.3.5...................... 191

viii 4.4................................ 196 4.4.1............................. 196 4.4.2......................... 198 4.4.3........................ 198 4.5.......... 200 4.5.1.... 200 4.5.2............................. 200 4.5.3........................ 201 4.5.4 (Tit for tat strategy)................. 201 4.5.5............. 203 4.5.6............. 204 4.6................. 206 4.7............................... 211 4.8................... 213 4.8.1........................... 213 4.8.2......................... 215 4.8.3 (reasonable)............. 219 4.8.4......... 220 4.9.............................. 229 4.9.1................... 229 4.9.2 Separating Pooling........ 230 4.9.3................ 232 4.10............................... 233 4.10.1.................................. 233 4.10.2 (nucleous)............................. 236 4.10.3............................ 240 4.10.4................. 244 4.11................................ 246 4.12.................... 251 4.13............................ 253 256 272 5 321 5.1.......................... 321

5.2...................... 322 5.3..................... 323 5.3.1........................... 323 5.3.2....................... 325 5.3.3........................... 326 5.4.................... 327 5.5........... 332 5.5.1 2...... 332 5.5.2........ 334 5.6.................... 343 5.7................................... 345 5.7.1............................ 345 5.7.2.................. 349 355

1 1 1.1 1.1.1 (producer)

2 1 (firm) (consumer) (household) 1.1.2 (good) (service) 3 *1 DVD, Brue-ray CD CD CD (CD DVD ) *1 1 3 1

1.1 3 1.1.3 *2 1.1.4 *3 *2 *3

4 1 1.1.5 *4 1.1.6 *4

1.2 5 1.1.7 *5 *6 ( ) 1.2 1.2.1 (demand) 1 1 1 1 1 1 1.2.2 1.1 *5 3 *6

6 1 p 0 D x 0 1.1 (demand curve) D D D.p/I p ; D *7 1.1 p 0 x 0 x 0 p 0 1.2.3 1. 2. *7 D p

1.3 7 2 1899 *8 1.3 (price elasticity of demand) D ( ) 10 20 2 5 15 3 100 150 150 100 " " D p x dx dx dpx D = x dp x x X p x x dx dp x p x *8 2

8 1 *9 1.4 1.4.1 A B A B A B (substitutes) p A p B AB x A x B AB " AB D p B x A dx A dp B D dxa x A dpb = p B > 0 " BA D p A x B dx B dp A D dxb dpa = > 0 x B p A B A A B (cross elasticity) * 10 *9 *10

1.5 9 1.4.2 A B A B A B (complements) " AB D p B x A dx A dp B D dxa x A dpb = p B < 0 " BA D p A x B dx B dp A D dxb dpa = < 0 x B p A 1.5 1.5.1 (supply) 1.5.2 1.2

10 1 S p 1 x 1 1.2 1.2 (supply curve) S D S.p/I p ; S * 11 p 1 x 1 x 1 p 1 1 * 12 p 1 *11 S p *12 1 2 1kg2kg 1

1.6 11 1.5.3 1 3 1. 2. 1.6 D ( ) 10 20 2 5 15 3 100 200 200 100 D p x x dx dp x D dx = x dpx p x X p x x x 1 2 1 2

12 1 1.7 1.7.1 1.3 1.3 E p x 1. 2. 3. 4K

1.8 13 S p E D x 1.3 1.7.2 x p p D 100 4x p D 2x C 16 * 13 x D 14; p D 44 1.8 *13

14 1 3 3 3 1 300 2 200 3 100 (reservation price) * 14 300 3 200 300 2 100 200 1 100 0 350 1 240 2 120 3 350 0 240 350 1 120 240 2 120 3 4 200 240 2 1.4 200 240 2 1000 2000 10cm 1000 10cm 1 0.1mm *14

1.9 15 350 300 240 200 120 100 1 2 3 1.4 1.9 1.9.1 1.5 1. 2. 3. 4.

16 1 S p 0 E 0 p E D 2 D 1 1.5 * 15 1.5 * 16

1.9 17 S 2 S 1 E 0 p 0 p E D 1.6 1.9.2 1.6 1. 2. * 17 1.6 *15 *16 *17

18 1 * 18 1 t p p 0 x x 0 p 0 t < p < p 0 x > x 0 t p 0 p t p 0 C p p0 p tp 0 Cp " " " D x 0 x x p 0 p p ; D x 0 x x p 0 tp p " D p 0 p p p 0 tp p D p0 p t p 0 C p *18

1.10 19 S p 1 p E p 2 D 1.7 1.10 1.10.1

20 1 (excess demand) (excess supply) * 19 * 20 1.7 p p p 1 p p 2 1.7 1.8 p 1 p 2 p 1 p 2 1.10.2 1.9 x 1 p D p S *19 *20

1.10 21 p 1 p p 2 E S D 1.8 S p D E p S D x 1 x x 2 1.9 p S p D * 21 *21

22 1 E D S x 1 x x 2 1.10 1.9 x 1 x 2 1.9 1.10

1.10 23 S p 1 p 3 E p 2 D 1.11 1.10.3

24 1 1.11 1.11 p D 36 x p D 2x p x p 0 x 1 D 1 2 p 0 p 1 D 36 x 1 D 36 1 2 p 0 p 2 D 36 1 2 p 1p 3 D 36 1 2 p 2 p n D 36 1 2 p n1 p n 24 D 1 2.p n1 24/ p n 24 1 ˇˇ 2 1ˇ < 1 p n 24 0 p n 24 x D 12 (partial equilibrium analysis) (general equilibrium analysis) 2 3 2

25 2 2.1 (utility)

26 2 2.1.1-2.1.1.1 1 2 1 2 3 4 1 100 2 3 2.1 xy u b.x/u d.y/ u.x; y/ u.x; y/ D u b.x/ C u d.y/ u.x; y/ 2 3 2 3 u b.x/ 2 u d.y/ 3 *1 2 97 (marginal utility) 2 197 1 100 1 2 2 1 2 3 944 91 1 *2 *1 2.1.6 u b.x/ u d.y/ u b.x/ 2 u d.y/ 3 6 u b.x/ 2 u d.y/ 3 *2 1 5 6 1 5 6 1

2.1 27 1 100 1 100 2 97 2 197 3 94 3 291 4 91 4 382 5 88 5 470 6 85 6 555 7 82 7 637 8 79 8 716 9 76 9 792 10 73 10 865 11 70 11 935 12 67 12 1002 13 64 13 1066 14 61 14 1127 2.1 1 1 8 9 100 200 1 1 1 100 2.2 1 49 120 2.1 2.2 (preference) A

28 2 1 49 1 49 2 47 2 96 3 45 3 141 4 43 4 184 5 41 5 225 6 39 6 264 7 37 7 301 8 35 8 336 9 33 9 369 10 31 10 400 11 29 11 429 12 27 12 456 13 25 13 481 14 23 14 504 2.2 2.1.1.2 A 1 3000 1 200 1 100 x y 200x C 100y D 3000 3000 8 13 2.3 8 2.1 8 79 200 14 2.2 14 23 100 11 8

2.1 29 8 14 1220 0.395 0.23 9 12 1248 0.38 0.27 10 10 1265 0.365 0.31 11 8 1271 0.35 0.35 12 6 1266 0.335 0.39 13 4 1240 0.32 0.43 2.3 D D D

30 2 B 2.1 2.2 2.4 1 50 1 50 2 48 2 98 3 46 3 144 4 44 4 188 5 42 5 230 6 40 6 270 7 36 7 306 8 32 8 338 9 28 9 366 10 24 10 390 11 20 11 410 12 16 12 426 13 12 13 438 14 8 14 446 2.4 B B A 200x C 100y D 3000 x y A 8 13 B 2.5 8 14 1162 0.395 0.08 9 12 1218 0.38 0.16 10 10 1255 0.365 0.24 11 8 1273 0.35 0.32 12 6 1272 0.335 0.4 13 4 1254 0.32 0.44 2.5 B

2.1 31 A 11 8 11 8 6 12 11 8 2.1.1.3 A 3000 3300 200x C 100y D 3300 10 13 2.6 12 9 3000 2.3 1 (superior good) (normal good) 10 13 1346 0.365 0.25 11 11 1364 0.35 0.29 12 9 1371 0.335 0.33 13 7 1367 0.32 0.37 14 5 1352 0.305 0.41 2.6 B 3000 3300 10 14 2.7 13 7 3000 2.5 2 8 7 (inferior good) B

32 2 10 13 1303 0.365 0.12 11 11 1345 0.35 0.2 12 9 1368 0.335 0.28 13 7 1372 0.32 0.36 14 5 1357 0.305 0.42 2.7 B 2.1.2 XY X 2 Y 1 (2,1).X; Y / X Y (2,1) 2 1 *3 (2,2) (1,1) (2,2) (3,2) (2,2) (3,2) (3,2) (2,3) (4,4) (3,5) (3,2) (2,3) (2,3) (3,2) (3,2) (2,3) (indifferent) (3,2) (2,3) 2 *4.4; 2/.2; 3/.2; 3/.1; 5/.4; 2/.1; 5/.4; 2/.2; 3/.2; 3/.1; 5/.4; 2/.1; 5/ *3 20g 100g *4 (completeness)

2.1 33 2 4 2 2 3 2 3 1 5 4 2 1 5.4; 2/.2; 3/.4; 2/.2; 3/.2; 3/.1; 5/ 1. (4,2) 2. (2,3) 3. (1,5).4; 2/.2; 3/.2; 3/.1; 5/.1; 5/.4; 2/ 2 *5 2.1.3 2 X Y.X; Y / X Y.X; Y / 2 (indifference curve) 2.1 2 XY (3,2) (2,3) (3,2) (2,3) YY (2,10) (3,2) (2,3) (2,10) (3,2) (3,2) (2,3) (3,2) *5 3.1; 3; 2/

34 2 A B C U 2 U 1 2.1 X X (0.1,3) (3,2) (2,3) (0.1,3) (3,2) (3,2) A C U 2 1. 2.1 B A X Y A B A A X B Y A C A C A 2. 2.1 A A A

2.1 35 U 1 U 2 A A 0 C B U 2 U 1 2.2 3. 2 2.2 A C C B A B A 0 B A A 0 A 0 A X Y A X-Y

36 2 A C B 2.3 2.1.4 2.1 2.3 (convex) 2 2.3 A B C A B A B C 2 2 1 1 1 2 1

2.1 37 A X B Y C 2.4 2.1.5 (marginal rate of substitution) 2.4 X X Y A BB C X A C X Y A C Y 2 A C Y X (2.1) C A C A X Y A X X B A B Y Y A C AC 2 X X Y Y (2.1) AC X 1 Y C A A A A X X X Y X

38 2 X Y 2.1.6 (utility function) XY 2 x; y U D u.x; y/ X Y 1 X Y u.x; y/ D NU ; NU xy D a; a U D xy U D 3xy U D x 2 y 2 2.2 2.2.1 1 1 100 X 200 Y

2.2 39 M N N 0 2.5 100x C 200y D 10000 X Y x; y 1 mx Y p x ; p y p x x C p y y D m 2.5 MN N.m=p x ; 0/ (100,0)M.0; m=p y / (0,50) M Y N X p x =p y X Y X Y X 1 Y X p x MN 0 X X

40 2 M A E C U 3 U 2 B U1 N 2.6 2.2.2 MN 2.6 AB A A B A B A B B A E E E C *6 *6 1

2.3 41 X Y *7 X Y D (2.2) 2 > 2.6 A X X X Y A E < 2.6 B X X Y B E D

42 2 M 3 M 2 M 1 A B C U 1 U 2 U 3 N 1 N 2 N 3 2.7 2.3 2.3.1 2.7 M 1 N 1 M 2 N 2 M 3 N 3 ABC *7 u.x; y/ D xy @u @u dx C @x @y dy D 0 @u @x @u @y @u dy dx D @x @u @y dy dx

2.3 43 M 3 M 2 M 1 A B C U 1 U 2 U 3 N 1 N 2 N 3 2.8 U 1 U 2 U 3 ABC X Y X Y 2.3.2 2.8 M 1 N 1 M 2 N 2 X Y M 2 N 2 M 3 N 3 X Y Y

44 2 2.3.3 D 10 20 2 5 15 3 *8 1 1 2.4 2.4.1-2.9 2 Y X X Y M 1 N 1 M 1 N 2 M 1 N 3 M 1 A! B! C ABC U 1 U 2 U 3 U 1 U 2 U 2 U 3 X A B Y B C Y X C! B! A X 1 Y *8

2.4 45 M 1 A B C U 1 U 2 U 3 N 1 N 2 N 3 2.9 2.4.2 2 2.10 X M 1 N 1 M 1 N 2 A B X Y M 0 1 N0 1 M 1N 2 U 1 A 0 X X Y 2 1. A A 0 X Y

46 2 M 1 M 0 1 A B A 0 U 1 U 2 N 1 N 0 1 N 2 2.10 2. A 0 B X 2.10 2.8? X Y X Y 2.9 2.4.3 2.8

2.5 47 ( X ( Y?? 2.8 X M 1 B U 2 A U 1 N 1 N 2 2.11 2.11 X M 1 N 1 M 1 N 2 A B B A B X A X 2.5

48 2 M E O A N(24,0) 2.12 XY 1 1 x w (wage) l (leisure) x D w.24 l/ (2.3) x 1 24 l 1 1 x C l D 24 (2.4) w 1 1 w 1 1 24 1 24

2.5 49 M 0 M E F O A N(24,0) 2.13-1 1 1 w 1 x C wl D 24w 1 w w w (2.3) 2.12 MN OA AN 24 24 24 N 2.13 E F

50 2 M 00 M 0 M F G E O 2.14 N(24,0) - F 1. 1 (2.4) 1 2. X 2.14 E F

2.6 51 S 2.15 F G (backward bending) 2.15 2.6 1 2.6.1 2

52 2 m 1 m 2 c 1 c 2 XY 2 m 2 c 2 m 2 D m 1 c 1 C r.m 1 c 1 / (2.5) r *9 m 1 c 1 r.m 1 c 1 / (2.5) (2.5) r.m 1 c 1 / 1 C r.1 C r/c 1 C c 2 D.1 C r/m 1 C m 2 c 1 C 1 1 C r c 2 D m 1 C 1 1 C r m 2 (2.6) * 10 2 (2.6) (2.6) u.c 1 / C 1 1 C ı u.c 2/ *9 10 0.15 0.05 *10 r 10000 10000 1Cr 10000 10000 10000 1Cr 1Cr 10000

2.6 53 u./ ı ı > 0 * 11 XY 2 ı (2.6) (2.6) 1=.1 C r/.1 C r/ 2.16 U 1 MN E U 2 E U 1 E MN U 2 MN E 2.6.2 m 2 D 0 2.17 M 1 N 1 M 2 N 1 *11 1 1 1 (1+ )

54 2 M E U 1 U2 N 2.16 E E 0 XY 2 E A A E 0 2.17 3

2.7 55 M 2 M 0 1 E 0 M 1 A E U 1 U 2 N 0 1 N 1 2.17 * 12 2.7 2.7.1 (exchange economy) A B XY A X Nx A Y Ny A B X Nx B Y Ny B (initial endowment) A XY x A y A B x B y B A x A Nx A X A X x A Nx A < 0 Nx A x A X A Y Ny A y A *12

56 2 M Ny A y A A C E Nx A 2.18 x A A N Ny A y A < 0 y A Ny A A Y X Y X X p x Y p y A p x.x A Nx A / D p y. Ny A y A / (2.7) X Y (2.7) x A Nx A Ny A y A D p y p x (2.8) Y 1 X X Y X Y (2.7) p x x A C p y y A D p x Nx A C p y Ny A (2.9) A X Y X Y (2.9) (2.7)(2.8) X - Y. Nx A ; Ny A / p x =p y A A x A y A 2.18

2.7 57 M 0 y B Ny B E 0 D B x B 2.19 Nx B B N 0 MN A A X Y E X Y ACE CE A X AC Y A X Y A E A Y X A E X Y B p x x B C p y y B D p x Nx B C p y Ny B (2.10) B A X Y 2.19 B B XY E 0 E 0 DB DB X E 0 D Y A X B X A Y B Y CE D DBAC D E 0 D XY * 13 *13 2.18 ACE 2.19 E 0 DB A B AEC D E 0 BD CE D DB AC D E 0 D AC D E 0 D

58 2 1 A X B X X X Y B X A X X X Y X X Y A X Y M M A A A 2.20 M 0 N 0 X E E 0 X X Y A X X * 14 Y Y A M 0 N 0 E X Y M 0 N 0 MN Y E 0 E X Y Y 2.7.2 A X B X A Y B Y 2.21 2.18 2.19 2.19 180 E 0 2.18 E CE D DB CE D DB X AC D E 0 D Y n n 1 1 *14 A M 0 N 0 E X X

2.7 59 M 0 M A E E 0 N 0 N 2.20 - A E O OCOB A XY E O 0 O 0 FO 0 D B XY OC+O 0 F X OB+O 0 D Y A O A O 0 B E A B MN MN ENR AMQ ENR 2.18 MN AMQ 2.19 MN 2.21 A O B O 0 E A MN AB * 15 E A E B O 0 E B *15 (Edgeworth box)

60 2 F O 0 M Q A B E D O C R N 2.21 A E E (Pareto efficient) (Pareto optimal) 2 2 2.22 (contract curve) E E 0

2.7 61 O 0 M A 0 A E 0 E O N 2.22 1. 2. 2.22 2.22 E E 0 E 0 A E B 2.7.3 AB X Y xa x B y A y B

62 2 x A x B y A y B 2 u A.x A ; y A / > u A.x A ; y A /; u B.x B ; y B / = u A.x B ; y B / u A.x A ; y A / = u A.x A ; y A /; u B.x B ; y B / > u B.x B ; y B / A B u A u B AB x A y A A p x p y X Y p x x A C p y y A > p x Nx A C p y Ny A p x x B C p y y B = p x Nx B C p y Ny B B Nx A Ny A Nx B Ny B 2 p x.x A C x B / C p y.y A C y B / > p x. Nx A C Nx B / C p y. Ny A C Ny B / (2.11) x A x B y A y B x A C x B D Nx A C Nx B y A C y B D Ny A C Ny B (2.11) p x. Nx A C Nx B / C p y. Ny A C Ny B / > p x. Nx A C Nx B / C p y. Ny A C Ny B / 3 * 16 AB 0 < < 1 U D u A.x A ; y A / C.1 /u B.x B ; y B / *16

2.8 63 x A C x B D Nx A C Nx B ; y A C y B D Ny A C Ny B U D u A.x A ; y A / C.1 /u B. Nx A C Nx B x A ; Ny A C Ny B y A / x A y A 0 @u A @x A.1 / @u B @x B D 0 @u A @y A.1 / @u B @y B D 0 @u A @x A @u B @x B D @u A @y A @u B @y B D 1 @u A @x A @u A @y A D A B @u B @x B @u B @y B * 17 2.8 2.8.1 - - (2.12) (2.13) z D x 2 C y 2 (2.12) x C 2y D 5 (2.13) (2.12) (2.13) L D x 2 C y 2 C.x C 2y 5/ (2.14) *17

64 2 (2.14) (2.12) (2.13) x C 2y 5 D 0 (2.14) x y 2x C D 0 2y C 2 D 0 2 x D 1 y D (2.13) 2 D 2 x D 1 y D 2 (2.12) 5 xy x C 2y D 5 x C 2y D 5 (2.13) (2.12) xy z D f.x; y/ g.x; y/ D 0 f.x; y/ x y g.x; y/ D 0 x y y x * 18 g.x; y/ D 0 x y g x C g y dy dx D 0 g x g y g xy x g y g dy dx x g.x; y/ D 0 y g y dy dx x y g g.x; y/ 0 g 0 dy dx D g x g y x *18 g.x; y/ D 0 1 x g.x; y/ D 0 y 1

2.8 65 f.x; y/ f x C f y dy dx f x f y f xy x f dy y f f y x y dx dy f f f x C f y dx D 0 g x f x f y D 0 g y f x g x D f y g y L D f.x; y/ C g.x; y/ f x C g x D 0 f y C g y D 0 D f y g y f x g x 2.8.2 2 XY u D u.x; y/ p x x C p y y D m (2.15) xy X Y p x p y m L D u.x; y/ C.p x x C p y y m/ (2.16)

66 2 (2.16) xy u x C p x D 0 (2.17) u y C p y D 0 (2.18) u x u y u xy (2.17) (2.18) u x p x D u y p y D (2.19) u x u y D p x p y (2.20) (MRSmarginal rate of substitution) X Y c u.x; y/ D c xy u x dx C u y dy D 0 MRS D dy dx D u x u y (2.21) (2.20) (2.21) D (2.22) (2.19) u x p x X 1 X u y p y 1 Y 1 * 19 u D x 2 y (2.23) (2.23) (2.15) L D x 2 y C.p x x C p y y m/ xy *19 1

2.8 67 2xy C p x D 0 (2.24) x 2 C p y D 0 (2.25) p x x D 2p y y (2.15) x D 2m 3p x y D m 3p y 2/3 X 1/3 Y * 20 2m 2 m v D D 4m3 3p x 3p y 27px 2p y v (indirect utility function) p x p y m @v D 8m3 @p x 27px 3p y @v D @p y @v @m D 4m3 27p 2 x p2 y 4m2 9p 2 x p y @v @p x @v @p y @v = @m = @v @m D D 2m 3p x D x m 3p y D y p x x C p y y D m x y xy y x D p x p y u @u @u D 2xy @x @y D x2 u D.2xy p x p y x 2 /x D x.2y p x p y x/x *20

68 2 x <.>/ 2m 3p x y >.</ m 3p y 2y >.</ p x p y x x <.>/ 2m 3p x u >.</0 x x u x u x D 2m 3p x u u D x yˇ p x x C p y y D m x 1 yˇ C p x D 0; ˇx yˇ1 C p y D 0 x D m. C ˇ/p x ; y D ˇm. C ˇ/p y x y f.x; y/ f * 21 f.x; y/ f x y f x xy y f x f x D 0 x y y x f y xy x f y f y D 0 x y x x f x D 0 f y D 0 x y g.x; y/ D 0 2x C y D 6 g.x; y/ D 2x C y 6 g.x; y/ D 0 x y x *21 1 1

2.8 69 f x x f x x (f ) x f x y f y y f x x C f y y x y g.x; y/ D 0 f xy g g x x C g y y g.x; y/ D 0 g 0 g x x C g y y D 0 y D g x g y x f x x C f y y f x g x f y x g y g.x; y/ D 0 f * 22 f x f y D g x g y L D f.x; y/g.x; y/ xy f x g x D 0; f y g y D 0 D f x g x f x f y D g x g y g.x; y/ f.x; y/ g.x; y/ D 0 1 f.x; y/ 1 g.x; y/ f.x; y/ 1 1 1 3 g.x; y/ f.x; y/ 1 *22

70 2 2.8.3 u D x 2 y Nu x 2 y D Nu m D p x x C p y y xy L D p x x C p y y C.x 2 y Nu/ p x C 2xy D 0 p y C x 2 D 0 p x C @u @x D 0 p y C @u @y D 0 p x x D 2p y y * 23 x 2 y D Nu s 2p x D 3 y Nu p x s p y D 2 3 x Nu 4py 2 (compensated demand function) q Qx D 3 2py Nu p x r Qy D 3 px 2 Nu 4p * 24 y 2 *23 @u = @u D p x @x @y p y D *24 (Hicks)

2.8 71 p x x D 2p y y m D p x x C p y y x D 2m 3p x y D m Nu m 3p y 1 2.8.4 u D x 2 y p y p x x D 2m 3p x y D @x D 2m @p x 3px 2 @y @p x D 0 m Qx D 3 q 2py Nu p x @x @m D 2 3p x @y @m D 1 3p y r Qy D 3 px 2 Nu 4py 2 s @ Qx D 1 2p 3 y Nu @p x 3 px 4 @ Qy D 2 s 3 Nu @p x 3 4p x py 2 D 1 3 Nu p x m s 2 Nu 3 p x p 2 y m 3p y s s s s @m @ Qx @ Qy 2p D Qx C p x C p y D 3 y Nu 1 2p 3 y Nu C 1 2p 3 y Nu 2p D 3 y Nu @p x @p x @p x p x 3 p x 3 p x p x m m D p x Qx C p y Qy D 3 q 2p 2 x p y Nu C 3 r p 2 x p y Nu 4 D 3 q 3 2px 2 2p y Nu

72 2 p x p y Nu (expenditure function) m.p x ; p y ; Nu/ @x @p x s @x 2p D 3 y Nu @p x px 4 @ Qx D @x C @x @p x @p x @m @m @p x 1 p x X 2 X @x D @ Qx @x @p x @p x @m @m @p x 1 X 2 p x X @y D @ Qy @y @p x @p x @m @y @p x D 0 m p x p y @m @p x s @m 2p D 3 y Nu D Qx @p x p x s @m p D 3 x 2 Nu D Qy @p y 4py 2 * 25 * 26 *25 *26

2.8 73 2.8.5 1. (i) (ii) (iii) (iv) (quasi-convex function) p m v.p; m/.p ; m / f.p; m/jv.p; w/ 5 v.p ; m /g.p ; m / v.p; m/ 2.p; m/.p 0 ; m 0 /. p C.1 /p 0 ; m C.1 /m 0 / 0 5 5 1 y. p C.1 /p 0 /y D py C.1 /p 0 y 5 m C.1 /m 0 py 5 mp 0 y 5 m 0 py y.p; m/.p 0 ; m 0 / y v.p; m/v.p 0 ; m 0 / y v.p ; m /

74 2. p C.1 /p 0 ; m C.1 /m 0 / (quasi-convex function function) XY u.x; y/.x ; y / f.x; y/ju.x; y/ = u.x ; y /g.x ; y / u.x; y/ 2. (i) (ii) (iii) (iv) (concave function) Nu p e.p; Nu/ Nu p xp 0 x 0 p C.1 /p 0 y 0 5 5 1y Nu p y e.p; Nu/ p 0 e. pc.1 /p 0 ; Nu/ D. pc.1 /p 0 /y D pyc.1 /p 0 y = e.p; Nu/C.1 /e.p 0 ; Nu/ py e. p C.1 /p 0 ; Nu/ = e.p; Nu/ C.1 /e.p 0 ; Nu/

2.8 75 1 2.8.6 u D x 2.y C 2/ p x x D 2p y.y C 2/ p x x C p y y D m 2x.y C 2/ p x D 0; x 2 p y D 0 x D 2m C 4p y ; y D m 4p y D m 4 3p x 3p y 3p y 3 ; y < 0 y D 0 y 0 m 4p y v D 4.m C 2p y/ 3 27p 2 x p y p x x D 2p y.y C 2/ s s 2p Qx D 3 y Nu p ; Qy D 3 x 2 Nu 2 p x 4py 2 Qy < 0 Qy D 0 Qy 0 Nu 32p2 y px 2 m D 4p y Nu q r r p m D 3 2px 2p y Nu C 3 2 x p y Nu p 2p y D 3 3 2 x p y Nu 2p y 4 4 m e Nu Nu v v D.m C 2p y/ 3 27p 2 x p y

76 2 m p x X @x D 2m C 4p y ; @p x 3px 2 s @ Qx D 1 2p 3 y Nu @p x 3p x p x p x s @x D 1 2p 3 y Nu @p x p x p x s @x @m D Qx @x @m D 2 2p 3 y Nu @m @p x @m @p x 3p x s s s 1 2p 3 y Nu 2 2p 3 y Nu D 1 2p 3 y Nu 3p x p x 3p x p x p x p x p x x D @v @p x @v @m D 2.mC2p y / 3 3pxp 3 y.mc2p y / 2 p 2 xp y D 2m C 4p y 3p x y D @v @p y @v @m D 4.mC2p y / 3 27p 2 xp 2 y 8.mC2p y/ 2 9p 2 xp y 4.mC2p y / 2 9p 2 xp y D m 3p y 4 3 y mc2p y 3p y D y C 2 2.mC2p y/ 3p x D x u D x 2.y C 2/ Qx Qy xy

2.9 77 Nu u u x 2 D 3 s! 2 s 2p y u 4p D 3 y 2u2 p x px 2 y C 2 D 3 s p 2 x u 4p 2 y u D x 2.y C 2/ 2.9 1. (i) u D p x C y (ii) u D x 2 C y 2 (iii) u D 3x C y (iv) u D min.x; y/x; y (i) L D p x C y C.p x x C p y y m/ xy 1 2 p p x x p y 1 2 p x C p x D 0; 1 C p y D 0 D 0 X x D p2 y 4p 2 x Y y D m p y p y 4p x m y y D 0

78 2 (ii) y D m p y p xx p y m u D x 2 C p 2 xx p y p y x x 0 5 x 5 m m 2x 2 p x x D 0 u D p y D m m p x u D p x p x > p y x D 0; y D m p y p x < p y x D m p x ; y D 0 p x D p y (iii) u x u y D 2 px p y 2 y D m p y ; x D 02 x D m p y ; x D 0 2 2x C y D m xy (iv) x D y m x D y D p x C p y 2. X, Y 2 A, B2 u A D x 2 y; u B D xy A.6; 2/B.2; 8/ X Y XY p x p y A L D x 2 y C.p x x C p y y 6p x 2p y / xy 2xy C p x D 0; x 2 C p y D 0 p x x C p y y D 6p x C 2p y x D 2.6p x C 2p y / ; y D 6p x C 2p y 3p x 3p y B x D 2p x C 8p y ; y D 2p x C 8p y 2p x 2p y

2.9 79 A x 6 D 2.2p y 3p x / 3p x ; y 2 D 2.3p x 2p y / 3p y B x 2 D 8p y 2p x ; y 8 D 2p x 8p y 2p x 2p y 0 X Y 32p y 18p x 6p x D 0 p x p y D 16 19 A.x; y/ D. 9 4 ; 38 /B 9.x; y/ D. 13 4 ; 52 9 / 3. c 1, c 2 m 1, m 2 r u D c 1 c 2 c 1 C c 2 1 C r D m 1 C m 2 1 C r c 1 D 1 2.m 1 C m 2 1 C r /; c 2 D 1 2 Œ.1 C r/m 1 C m 2 c 1 m 1 c 1 m 1 m 1 m 2 1 C r m 1 D m 2 1Cr c 1 D m 1 m 1 < m 2 1Cr c 1 m 1 c 1 c 2 @u @c 1 D c 2 @u @c 2 D c 1 c 2 c1 c 2 c1 1 C r c 1 c 1 m 1 c 2 m 2 m 1 < m 2 1Cr c 1 < c 2 1Cr c 2 c1 > 1 C r c 1 D m 1 c 2 D m 2 c 1 m 1 c 1 D m 1 c 2 D m 2 c 1 D 0 c 1 D m 1 c 1 D 0 c 1 D m 1

80 2 M E U 1 N 2.23 c 1 D m 1 c 1 D m 1 2.23 2.10 2.10.1 1 1 1 6 1/6

2.10 81 2 4 36 4 3 1 32 23 1 1/12 (expected value) 2 2 C 3 2 C 4 3 C 5 4 C 6 5 C 7 6 C 8 5 C 9 4 C 10 3 C 11 2 C 12 36 D 7 1 2 2000 1 2 0 800 1000 2000 0 900 800 1000 1000 1200 2 800 500 1. 3 L 1 L 2 L 3 L 3 L 1 L 2 L 3 L 1 L 2 1 L 3 2 L 1 : 1 2 2000 1 2 0 L 2 : 1 2 1500 1 300 2 2 p W 1 p.0 5 p 5 1/ pl 1 C.1 p/l 2 : 1 2 p 2000 1.1 p/ 1500 2

82 2 1 2.1 p/ 300 1 2 p 0 p L 1 L 2 2. L 1 L 2 L 3 1 1 L 1 L 2 L 3 2.10.1 (). L: p x 1 p y L u.x/u.y/ xy u.l/ D pu.x/ C.1 p/u.y/ u u 0 D au C ba.> 0/b u 0.L/ D pu 0.x/ C.1 p/u 0.y/ D pau.x/ C pb C.1 p/au.y/ C.1 p/b D au.l/ C b 2 L 1 L 2 u.l 1 / = u.l 2 / u 0.L 1 / = u 0.L 2 / u u 0. x > y hl 1 r x h1 r x l x r x.0 < r x < 1/ x D h r x D 1x D l r x D 0 r y h1 r y l y r y xy u.x/ D r x

2.10 83 u.y/ D r y u.h/ D 1u.l/ D 0 ab u.x/ D ar x C bu.y/ D ar y C b xy 2 L pr x C.1 p/r y h p.1 r x / C.1 p/.1 r y / l L pr x C.1 p/r y pu.x/ C.1 p/u.y/ xy u.x/ D ar x C bu.y/ D ar y C b L aœpr x C.1 p/r y C b D p.ar x C b/ C.1 p/.ar y C b/ pu.x/ C.1 p/u.y/ (expected utility) L E.L/ E Expected value E1 x 2 1 2 u 1.x/ D 6800x x 2 u 2.x/ D 8200x 2x 2 L 1 E 1.L 1 / D 1 2.6800200020002 C0/ D 4800000E 2.L 1 / D 1 2.8200 2000 2 20002 C 0/ D 4200000 1 800 2 600 2 ab u 1 u 0 1 D a.6800x x2 / C b u 2 u u 0 D au C b u 0 D u 2 u 0 D u 3 u 0 D aucb u 0 D u 2 u 0 D u 3 u u 0 - (von Neumann-Morgenstern)

84 2 * 27 u.x/ D 300 C 140x x 2 x x D 30 100 1 3000 x D 0 30 1 10 E.u/ D 3600 9 10 C 300 1 10 D 3270 y u.30 y/ D 300 C 140.30 y/.30 y/ 2 D 3600 80y y 2 3600 80y y 2 D 3270 y 2 C 80y 330 D 0 y D 40 C p 1930 3:9 3 3 3.9 *27

2.10 85 1. 1 A 1000 B10% 2500 89% 1000 1% 2. 2 A11% 1000 89% B10% 2500 90% 1 A 2 B 1000 2500 u 1 u 2 0 01 u 1 > 0:1u 2 C 0:89u 1 0:11u 1 > 0:1u 2 2 0:11u 1 < 0:1u 2 1 10% 2500 1% A 2 1000 2500 1 B 2500 B 2.10.2 1 2 1 2 * 28 *28 3 4

86 2 2 3 2 3 - x 1 x D 100x D 0 2 y D 50 3 1. u D x a > 0b u D ax C b EŒu.x/ D 100C0 2 D 50 EŒu.y/ D 50 (risk neutral) 2. u D x 2 u D ax 2 C b EŒu.x/ D 1002 C0 2 2 D 5000 EŒu.y/ D 50 2 D 2500 (risk loving) 3. u D p x u D a p x C b p EŒu.x/ D 100C0 D 5 2 EŒu.y/ D p 50 D 5 p 2 7:1 (risk averse)

2.10 87 u u 2 C B A u 1 x 1 Nx x 2 x 2.24 2.24 (concave) (convex) (linear) Nx D x 1Cx 2 2 x 1 x 2 3 Nx B Nu D u 1Cu 2 2 A Nu C Nu 1 2 x 1x 2 Nu Nx

88 2 2 x 3 u 1 D 20x x 2 ; u 2 D 20x; u 3 D 20x C x 2 4 x D 0 x D 4 1 2 y x D 4 y u 1 2.25 20.4 y/.4 y/ 2 D 32 y 2 C 12y 32 D 0 y D 6 C 2 p 17 2:25 u 2 2 u 3 1.83 20.4 y/ C.4 y/ 2 D 48 y 2 28y C 48 D 0 y D 14 2 p 37 1:83 u 1 u 2 u 3 2.11-2.11.1 2 AB A

2.11-89 200 B 100 240 120 200 240 100 120 1 2 1 2 120 C 1 240 D 180 2 120 180 200 180 120 (adverse selection) 1 1

90 2 3 2 (moral hazard) 2.11.2-1 2 30 0 30 1. 1 1 10 u 1.x/ D 300 C 140x x 2 2. 2 1 5 u 2.x/ D 600 C 160x 2x 2 x D 0 x D 30 2 1 3270 2 3600 4 5 C 600 1 5 D 3000 3000 y 600 C 160.30 y/ 2.30 y/ 2 D 3600 40y 2y 2 D 3000 y 10 2 10 1 1 3.9 2 1 2 3 20 4.5 3.9 1 1 2 1. 1 30 6 6

2.11-91 2. 2 10 1 23 1 1. 1 1 3084 2 3519 9 10 C 1479 1 3315 > 3270 10 2 2. 2 1 3288(>3000) 2 3558 4 5 C 1878 1 5 3222 1 2 1 2 (screening) * 29 1 2 2 45 *29 (screening)

92 3 CES 3.1 3.1.1 (production) 3.1.2 (labor)

3.1 93 (capital) *1 2 (input) (output) 3.1.3 3.1.4 1 1 *1

94 3 3.1.5 1 1 1 1 1 3.1.6 3.1.7

3.1 95 3.1.8 D *2 3.1.9 2 1. - 2. *2

96 3 3.2 3.2.1 x D f.l; K/ LK x L K x *3 LKx 3.2.2 (marginal product) 1 *4 1 1 1 3.2.3 *3 x L K *4 1

3.3 97 3.2.4 (economies of scale) 3.3 3.3.1 3.1 I 1 I 2

98 3 A C B I 2 (x=150) I 1 (x=100) 3.1 100 150 I 1 AB 100 A B C A B AB 100 3.3.2 2 1 wr L K c c D wl C rk

3.3 99 M N 3.2 c 3.2 MN 2 w=r 3.3.3 3.3 100

100 3 M 0 M A E E 0 B I 2 (x=150) I 1 (x=100) N 0 N 3.3 AB 100 A I 1 A B AB 100 x=100 E E E x=150 E 0 70 3.3.4 3.4 M 0 N 0 MN E E 0

3.3 101 M 0 M E 0 E I 1 (x=100) N 0 N 3.4 *5 3.3.5 C D C.x/; x 3.5 *5

102 3 c 0 3.5 3.3.6 (variable cost) (fixed cost) *6 3.5 c 0 *6

3.3 103 3.3.7 K x C.x/ D K C x2 K x C.x/ K C K x C K 1 x2 K 2 D 0 K D x C L.x/ C L.x/ D 2x x D 16 K D 16 C.16/ D 32 K D 8 K D 32 C.16/ D 40 K *7 (envelope curve) 3.6 C.x/ D K C x2 8K *7

104 3 3.6 x D 0 x D 181 3.4 average costac 1 D C.x/ AC D x 1 average variable costavc 1

3.4 105 MC c 0 AC 3.7 (marginal costmc ) D C MC D x x C 1,2,3, 1 *8 *9 MC D dc.x/ dx.d C 0.x// 3.7 AC MC c 0 *8 1 *9

106 3 3.1 1,2,3, 500 7 650 7 93 1150 7 164 6 7 7 650 6 580 70 * 10 1 150 2 3 120100 2 1 2 3 2 3 * 11 10 30 30 11 30 30 *10 6 7 7 *11

3.4 107 0 500 0 500 1 500 150 650 150 650 150 2 500 270 770 130 385 120 3 500 370 870 123 290 100 4 500 450 950 113 238 80 5 500 520 1020 104 204 70 6 500 580 1080 97 180 60 7 500 650 1150 93 164 70 8 500 730 1230 91 154 80 9 500 830 1330 92 148 100 10 500 950 1450 95 145 120 11 500 1100 1600 100 145.5 150 12 500 1280 1780 107 148 180 13 500 1490 1990 115 153 210 14 500 1730 2230 124 159 240 15 500 2000 2500 133 167 270 3.1 1 C.x/ C.x/ x x d dx C.x/ x D C 0.x/x C.x/ x 2 C 0.x/x C.x/ D 0

108 3 C 0.x/ D C.x/ x C.x/ 3.1 8 10 3.7 3.5 3.5.1 1. 1 2. 3. 4. (price taker)

3.5 109 140 140 200 200 0 0 500 0 500 1 140 510 200 450 2 280 490 400 370 3 420 450 600 270 4 560 390 800 150 5 700 320 1000 20 6 840 240 1200 120 7 980 170 1400 250 8 1120 110 1600 370 9 1260 70 1800 470 10 1400 50 2000 550 11 1540 60 2200 600 12 1680 100 2400 620 13 1820 170 2600 610 14 1960 270 2800 570 15 2100 400 3000 500 3.2 3.5.2 D D. / D. / 3.1 140 200 3.2 200 12 620

110 3 12 12 180 13 210 1 1 200 12 250 14 1270 14 140 10 50 140 10 145 500 90 8 510 90 8 1 91 1. 1 2. 3. 3.1 3.8 200 1 12 12 * 12 200 12 1 *12

3.5 111 200 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 3.8 12 12 13 200 3.8 3.9 MC * 13 AVC * 14 1 *13 1 1 *14 3.1 3.8

112 3 MC p AVC B 3.9 x - 3.9 p x 3.5.3 3.9 3.5.4 C.x/ D 3x 2 C 200 (3.1)

3.5 113 x 200 60 D 60x 3x 2 200 x D 3.x 10/ 2 C 100 x D 10 100 aa 1 x D 10 x D 10 a x D 10 MC.10/ D 3.10/2 C 200 Œ3.10 a/ 2 C 200 D a D 60 3a 60a 3a2 a 10 a x D 10 C a x D 10 x D 10 C a MC.10 C a/ D 3.10 C a/2 C 200 Œ3.10/ 2 C 200 D a D 60 C 3a 60a C 3a2 a a > 0 x D 10 60 a x D 10 C a x D 10 a MC.10/ D 60 * 15 x D 10 C.x/ C 0.x/x x Z x 0 Œp C 0.x/dx f D p x C.x/ f R x 0 Œp C 0.x/dx 3.9 *15

114 3 3.6 3.6.1 1. 2. 3. 3.6.2

3.6 115 MC 200 AC p E x 3.10 3.6.3

116 3 1 D D (3.2) 3.10 E x p E x 3.7 3.7.1 2 2 (2.2) XY 2 X * 16 X D X.D X Y / D X Y (3.3) X D X Y (3.4) *16 X X Y Y

3.7 117 * 17 (3.4) X > X Y (3.5) Y 1 X Y 1 Y X X Y X (3.4) X 1 X X X 1 Y X 1 Y 1 X 1 Y 1 * 18 Y 1 X Y Y X (3.6) X (3.5) (3.6) 1 (3.5) Y 1 X X Y X * 19 X Y (3.5) (3.5) *17 X (marginal rate of transformation) X Y Y X 1 Y X Y *18 1 1 1 (marginal) *19 3.8 3.9

118 3 X < X Y (3.7) X Y (3.7) (3.4) X Y 3.7.2 2.7.3 XY 2 2 A B 2 1 22 LK 2 p x p y wr NL A KN A NL B KN B L 1 K 1 L 2 K 2 X 1 Y 1 X 2 Y 2 x A y A x B y B L 1 K 1 L 2 K 2 X 1 Y 1 X 2 Y 2 x A y A x B y B L 1 K 1 L 2 K 2 AB u.x A ; y A / > u.x A ; y A /; u.x B; y B / = u.x B ; y B / u.x A ; y A / = u.x A ; y A /; u.x B; y B / > u.x B ; y B / 1 D p xx 1 C p yy 1 wl 1 rk 1 ; 1 D p x X 1 C p y Y 1 wl 1 rk 1 2 D p xx2 C p yy2 wl 2 rk 2 ; 2 D p x X 2 C p y Y 2 wl 2 rk 2 1 C 2 D p x.x1 C X 2 / C p y.y1 C Y 2 / w.l 1 C L 2 / r.k 1 C K 2 / 1 C 2 D p x.x 1 C X 2 / C p y.y 1 C Y 2 / w.l 1 C L 2 / r.k 1 C K 2 / X1 C X 2 D x A C x B ; Y 1 C Y 2 D y A C y B

3.7 119 X 1 C X 2 D x A C x B ; Y 1 C Y 2 D y A C y B L 1 C L 2 D NL A C NL B ; K 1 C K 2 D N K A C N K B L 1 C L 2 D NL A C NL B ; K 1 C K 2 D N K A C N K B 1 C 2 D p x.x A C x B / C p y.y A C y B / w. NL A C NL B / r. N K A C N K B / 1 C 2 D p x.x A C x B / C p y.y A C y B / w. NL A C NL B / r. N K A C N K B / (3.8) 1 = 1; 2 = 2 (3.9) 1 C 2 = 1 C 2 x A y A A p x x A C p y y A > w NL A C r N K A C 1 2. 1 C 2 / p x x B C p y y B = w NL B C r N K B C 1 2. 1 C 2 / B (3.9) 2 p x x A C p y y A > w NL A C r N K A C 1 2. 1 C 2 / p x x B C p y y B = w NL B C r N K B C 1 2. 1 C 2 / p x.x A C x B / C p y.y A C y B / > w. NL A C NL B / C r. N K A C N K A / C 1 C 2 (3.8) p x.x A C x B / C p y.y A C y B / > p x.x A C x B / C p y.y A C y B /

120 3 XY XY x A C x B y A C y B XY L x L y x A C x B D f.l x /; y A C y B D g.l y / NL L x C L y D NL x B D f.l x / x A ; y B D g. NL L x / y A U D u A.x A ; y A / C.1 /u B.f.L x / x A ; g. NL L x / y A / x A y A L x 0 @u A @x A.1 / @u B @x B D 0 @u A @y A.1 / @u B @y B D 0 @u B @x B f 0 @u B @y B g 0 D 0 2.7.3 2 @u A @x A @u A @y A D @u A @x A @u B @y B @u B @x B @u B @y B D g0 f 0 f 0 g 0 XY 1 D X Y

3.8 121 A S p 0 p H C I E p 1 L G B O K J 3.11 D 3.8 3.11 p ACE CBE * 20 1 2 3 2 3 1 1 1 1 1 * 21 *20 A ACCE B CBCE *21

122 3 D 1 A 1 OA K p 0 J p AOJE OJ AOJE COJE X X X X 2 COJE BOJE ABE

3.8 123 1 p p 0 OK AHI HBGI ABGI p IGE p p 1 OK LBG ALGI IGE D px c.x/ f p x c.x/ f p x 0 p c 0.x/ D 0 c 0.x/ p p x Z x 0.p c 0.x//dx D Œpx c.x/ x 0 D px c.x /; c.0/ D 0 x c 0.x/ c.x/ c 0.x/ c.x/

124 3 1 X Y 1 u.x; y/; px C y D m x X p y Y m m px C y D m y D m px u.x; m px/ x x 0 u x pu y D 0 u x u y X Y u x u y D p X Y u y 1 u x D p u.x; y/ D u.x/ C y u 0.x/ D p X Y u y 1 u 0. u x /u.x/ Y 1 X Y 1 Y u 0 u.x/ X Z x 0.u 0.x/ p/dx D Œu.x/ px x 0 D u.x / px ; u.0/ D 0

3.9 125 x u 0.x/ u x.x/ u.x/ u 0.x/ u.x/ X X u.x / px C px c.x / D u.x / c.x / X x u.x /c.x / = X 3.9 (monopoly) 2 1

126 3 3.9.1 1 (marginal revenue) D 3.3 3.1 p D 320 10x p x (3.10) * 22 10 10 2200 9 2070 130 10 10 220 9 230 220 90 130 3.9.2 1 D D *22

3.9 127 0 320 0 500 500 1 310 310 650 310 150 340 2 300 600 770 290 120 170 3 290 870 870 270 100 0 4 280 1120 950 250 80 130 5 270 1350 1020 230 70 330 6 260 1560 1080 210 60 480 7 250 1750 1150 190 70 600 8 240 1920 1230 170 80 690 9 230 2070 1330 150 100 740 10 220 2200 1450 130 120 750 11 210 2310 1600 110 150 710 12 200 2400 1780 90 180 620 13 190 2470 1990 70 210 480 14 180 2520 2230 50 240 290 15 170 2550 2500 30 270 50 3.3 3.3 10 750 10 130 120 1 11 110 150 40 40 1

128 3 MC p m A p B E MR D x m 3.12 - * 23 3.12 MR E x m 3.3 MR E A p m

3.9 129 3.9.3 3.3 12 10 3.12 B p 3.9.4 C.x/ D 4x 2 C 300 (3.11) x 300 p p D 180 2x (3.12) x x D.180 2x/x 4x 2 300 D 6x 2 C 180x 300 x D 6.x 15/ 2 C 1050 x D 15 1050 aa 1 x D 15 x D 15 a x D 15 MC.15/ D 4.15/2 C 300 Œ4.15 a/ 2 C 300 D a D120 4a 120a 4a2 a *23 1 1

130 3 15 a x D 15 C a x D 15 x D 15 C a MC.15 C a/ D 4.15 C a/2 C 300 Œ4.15/ 2 C 300 D a D 120 C 4a 120a C 4a2 a R R D D.180 2x/x x D 15 x D 15 a x D 15 15.180 30/.15 a/.180 30 C 2a/ MR.15/ D D a D 120 C 2a 120a C 2a2 a 15 a x D 15 C a x D 15 x D 15 C a.15 C a/.180 30 2a/ 15.180 30/ MR.15 C a/ D D a D 120 2a 120a 2a2 a a > 0 x D 15 a x D 15 C a x D 15 MC.15/ D 120 4a < 120 C 2a D MR.15/ MC.15 C a/ D 120 C 4a > 120 2a D MR.15 C a/ a MC.15/ D MR.15/ D 120 x D 15 3.9.5 p x 1:1 120 p D 20 C 2x

3.10 131 D 120x.20 C 2x/x D 100x 2x 2 (=) 25 20 C 4x D 120 70 120 (=) 50 3.10 3.10.1 Q A Q A K L A SD (product differentiation)

132 3 MC p E AC A MR D x 3.13 3.10.2 (monopolistic competition) 3.13 A x

3.11 133 E x x 3.11 3.11.1 - (oligopoly) 2 2 (duopoly) A B p D 20 X (3.13) p X A B x y X D x C y AB c.x/ D 2x c.y/ D 2y 2 A A D px 2x D.20 x y/x 2x (3.14) B B D py 2y D.20 x y/y 2y (3.15) A B A( B) B( A) B( A) x( y)

134 3 (3.14) A y A D.20 x y/x 2x D x 2 C.18 y/x D Œx.9 1 2 y/2 C.9 1 2 y/2 A x x D 9 1 2 y (3.16) B y A (3.16) B y D 9 1 2 x (3.17) (3.16) A (3.17) B (reaction function) (3.16)(3.17) x D y D 6 (3.18) (3.13) p D 2012 D 8 AB 36 3.14 RARB AB (3.16) (3.17) (reaction curve) RA RB C 3.11.2-3 3 n i x i X p p D p.x/

3.11 135 RA 9 6 C RB 6 9 3.14 i c.x i / c.0/ i i D p.x/x i c.x i / @ i @x i D p C x i p 0.X/ c 0.x i / D 0 c 0.x i / p 0.X/ x i X p.x/ p D 10 Xc.x i / D x 2 i C 2 10.n C 1/x i 2x i D 0 x i D 10 n C 3 p D 30 nc3 i D 200.n C 3/ 2 2

136 3 200.n C 3/ 2 2 = 0 n D 7 3.11.3-2 AB x A x B p A p B p A D 12 x A kx B p B D 12 x B kx A k 1 < k < 1 k 1 k A A D.12 x A kx B /x A x A D 6 k 2 x B x B D 6 k 2 x A k x A D x B D 12 2 C k p A D p B D 12 2 C k

3.11 137 3.11.4 3 n p i D a b nx j D1;j i x j x i p i x i P n j D1;j i x j i a > 0b.0 < b < 1/ n cf c i D cx i C f c f i D.a b nx j D1;j i x j x i /x i cx i f a Œ.n 1/b C 2x i c D 0 x i D a c.n 1/b C 2 i D a c.n 1/b C 2 2 f D x 2 i f x i D p f AC i AC i D c C f x i x i dac i dx i D f x 2 i

138 3 x i D p f dac i dx i D 1 3.13 3.12 A B B B A A B xy p c.x/ D 2x c.y/ D 2y p D 20 x y B y D 9 1 2 x B A A A D Œ20 x.9 1 2 x/x 2x D 9x 1 2 x2 x D 9 B 4:5 AB 40:520:25 A (leader) B (follower)

3.13 139 3.13 3.13.1 - * 24 AB 2 p D 20 x y AB 8 36 A 7 A A 13 65 B 0 B 6 B 14 56 A 0 A 4 16 32 2 2 0 2 0 2 3.13.2 AB xy p A p B p A p B p p D 1 x y 1 2 x2 1 2 y2 1 2 A p A D 1 3 0 p B > p A B *24

140 3.1 p A /p A 1 2.1 p A/ 2 = 0 p A = 1 3 p A D p B D 1 0 5 p D p A D p B 1p 2 p.1p/2 8 = 0 p = 1 5 p D 3 7.1 p/p 1 2.1 p/2 = 1p 2 p.1p/2 8 p = 3 7 p D p A D p B 1 5 5 p 5 3 7 1 3 0 1 5 1 5 0 3 7 3 7 1 5 < p 5 3 7 3.13.3-2 AB x A x B p A p B p A D 12 x A kx B p B D 12 x B kx A 1 < k < 1 x A D 1 1 k 2 Œ12.1 k/ p A C kp B x B D 1 1 k 2 Œ12.1 k/ p B C kp A

3.13 141 A A D 1 1 k 2 Œ12.1 k/ p A C kp B p A p A D 6.1 k/ C 1 2 kp B p B D 6.1 k/ C 1 2 kp A p A D p B D 12.1 k/ 2 k 0 < k < 1 1 < k < 0 * 25 * 26 69 k p A D 24 2x A x B p B D 24 2x B x A p A D 24 2x A C x B p B D 24 2x B C x A *25 12 12.1 k/ 12k 2 D 2 C k 2 k.2 C k/.2 k/ > 0 *26 k D 1

142 3 3.14 AB X m D.20 X/X 2X (3.19) X D 9 11 81 AB 9 18 2 3.15 3.15.1 1 1 1 1 1000 1 5 2000 1600 1300 1000 800 1 1 4 2000 1600 1300 1000 1900 5 1

3.15 143 3 1900 1500 1200 1600 1000 1 1 1 2 : : : 1 2 3 3.15.2 2 2 20 p D 120 x; p x 1. p D 70x D 50 2500 1.120 70/ 50 D 1250 2 3750 2. 20 x D 100 1.12020/100 D 5000 2 5000 5000 3.15.3 3 3

144 3 2 AB p A p B x A x B p A D 24 x A ; p B D 32 2x B 0 A D.24 x A /x A ; B D.32 2x B /x B 272 p A D 12; p B D 16; x A D 12; x B D 8 2 p x A D 24 p; x B D 32 p 2 x x D 40 3 2 p D.40 3 2 p/p p D 40 800 20 3 3 < 272 3.16 2 A B q A q B p A p B p A D a q A 1 2 q B; p B D a q B 1 2 q A 1 2 c2 A 1 2 c2 B c Ac B c A D c B

3.16 145 A p A q A p A B MR A D a 2q A 1 2 q B; MR B D a 2q B 1 2 q A Nq A Nq B A B q B D Nq B C 1 2.q A Nq A / B A q A D Nq A C 1 2.q B Nq B / p A D a q A 1 2 ΠNq B C 1 2.q A Nq A / D a 5 4 q A 1 2 Nq B C 1 4 Nq A q A D Nq A q B D Nq B 1 5 4 B A MRA 0 D a 5 2 q A 1 2 Nq B C 1 4 Nq A q A D Nq A MR A > MRA 0 MR A MRA 0 a 2 Nq A > c A > a 5 2 Nq A 3.15 C A B c A C

146 3 C c A A B Nq A 3.15 pc0 p c 0 p 1 1 D c 0 " " D 1 " 3.17

3.17 147 X A 100 x c A D x 2 Y 90 y c B D 2y 2 C xy A Y B A A D 100x x 2 50 B B D 90y 2y 2 50y 10 A x 2 xy AB D 100x C 90y x 2 2y 2 xy xy @ @x @ @y D 100 2x y D 0 (3.20) D 90 4y x D 0 (3.21) (3.20) y x y (3.21) x y x x D 310 44:3 7 y D 80 11:4 X Y 7 * 27 *27 (3.20) x D 50 1 2 y y

148 3 A X 1 A 310 7 A D 620 7 x x2 1 100 620 7 D 80 7 B B D 90y 2y 2 310 7 y 80 7 AB xy A D 80x 2x 2 B D 80y y 2 xy A 20 B D 80y y 2 20y B 30 xy A C B D 80x 2x 2 C 80y y 2 xy 80 4x y D 0; 80 2y x D 0 x D 80 240 < 20; y D > 30 7 7 A A D 320 7 x 2x2 C

3.18 149 1 80 320 7 D 240 7 0 Nx 1 240 7 A A D 80x 2x 2 C 240 320. Nx x/ D 7 7 x 2x2 C 240 7 Nx 240 7 Nx 80 7 12800 49 800 240 7 Nx 26400 49 240 7 Nx D 26400 49 Nx D 110 A 7 240 7 30 7 D 7200 240 49 7 80 7 D 19200 49 26400 A 80 49 7 32000 A 49 A 32000 49 3 3.18 3.18.1 (private good) (public good) * 28 1 *28

150 3 (free ride) 3.18.2 x i 1 y 1 1 u i.x i ; y/ 2 m i 1 p n nx.m i x i / D py id1 m i x i P n id1 iu i.x i ; y/ ( P n id1 i D 1) i L D nx nx iu i.x i ; y/ C..m i x i / py/ id1 id1

3.18 151 x i y i nx id1 nx id1 @u i i D 0 @x i @u i i @y p D 0 i D @ui @y 1= @u i @x i = @ui D p (3.22) @x i 1 1 (Samuelson) y D 1 p nx.m i x i / id1 nx iu i.x i ; 1 p id1 nx.m j x j // (3.23) ( P n id1 i D 1) j D1 3.18.3 1 1 t i y i x i D m i pt i y i pm i t i max u i.x i ; y i /y i D m i x i pt i @u i @x i D 1 pt i @u i @y i (3.24)

152 3 y i t i @u i @u i @y i @x i (3.24) y i (Lindahl equilibrium) y (3.24) @ui @y i @ui = @x i D pt i P n id1 t i D 1 nx @ui id1 @y i = @ui D p @x i (3.22) * 29 3.18.4 (Groves mechanism) 2 AB * 30 v A v B c 1. r i.i D A; B / r i D v i 2. r A C r B = c r A C r B < c *29 *30

3.18 153 3. c A c r B B c r A 2 v A C v B c v i B r B A r A A 1. v A C r B c > r A C r B c = 0 r A < v A v A r A A v A C r B c A A 2. v A C r B c = 0 > r A C r B c r A < v A v A A v A C r B c v A r A 0 v A 3. 0 > v A C r B c > r A C r B c r A < v A v A r A 0 4. r A C r B c > v A C r B c = 0 r A > v A v A r A A v A C r B c 5. r A C r B c = 0 > v A C r B c r A > v A v A v A r A 0 > v A C r B c v A 0 6. 0 > r A C r B c > v A C r B c r A > v A v A r A 0 v A B c 2 A c v B B c v A 2c.v A C v B / v A C v B > c 2c.v A C v B / < c

154 3 2 A r A 1. r B 5 c 2 (i) r A C r B = 0 v A C r B c (ii) r A C r B < 0 0 2 v A 2. r B > c 2 (i) r A C r B = 0 v A c 2 c r B C.r B c 2 / D c 2 (ii) r A C r B < 0 c 2 r B < 0 A v A C r B c v A C r B c = 0 v A v A v A v A C r B c < 0 v A v A v A C v B = c v B > c 2 v A < c 2 A c v B C v B c 2 D c 2 B c v A 3 2 c v A v A < c 2 c v A = c 2 v B = c 2 A B c c 2 c 2

3.19 155 A B A A * 31 3.19 AB xy A D 80x 2x 2 B D 80y y 2 xy A 20 B 30 x D 80 7 < 20; y D 240 32000 > 30 A 653 B 57600 1176 7 49 49 2 1. B A A B A 0 B B D 80y y 2 40 1600 A 0 A B *31 A B

156 3 B 1600 A A D 80x 2x 2 1600 C 80y y 2 xy A B.1600 80y C y 2 C xy/ A D 80x 2x 2 C 80y y 2 xy 1600 A 1600 x D 80 7 ; y D 240 B 1600 7 A 229 2. A B B A x D 20 y D 30 A 800 B 900 B A 800 B B D 80y y 2 xy 800 C 80x 2x 2 B A.800 80x C 2x 2 / B D 80x 2x 2 C 80y y 2 xy 800 B 800 x D 80 7 ; y D 240 7 A 1029 B 800 AB Ronald Coase 2 3.20-80% 20%

3.20-157 1. w * 32 (i) 5000 w w 200200 (ii) 2000 w w 200 (iii) 2000 w w (iv) 0 500500 w 200 < w w 500 w D 500 2000 500 D 1500 2. w b (i) 5000 w b w C b 200200 (ii) 2000 w w 200 (iii) 2000 w w (iv) 0 500500 E 1 E 1 D 0:8.w b 200/ C 0:2.w 200/ D w 0:8b 200 w C 0:8b 200 w b 250 *32 (payoff)

158 3 w C 0:8b 200 500 b 1:25w C 875 E 2 E 2 D 0:8.5000 w b/ C 0:2.2000 w/ D 4400 w 0:8b b D 1:25w C 875 E 2 D 3700 b D 1:25w C 875 b 250 w b 3700.w; b/ D.0; 875/.w; b/ D.500; 250/ b D 1:25w C 875 3700 b 200 b w C 700.w; b/ D.500; 200/.w; b/ D.0; 700/ 3700

3.21 159 3.21 3.21.1 x D f.l; K/ (3.25) x LK c D wl C rk (3.26) w r x (3.25) (3.26) L K L D wl C rk C Œ.f.L; K/ x (3.27) (3.27) LK w C f L D 0 (3.28) r C f K D 0 (3.29) f L f K f LK * 33 (3.28)(3.29) w D r D (3.30) f L f K f L f K D w r (3.31) (3.31) *33 f L D @f @L ; f K D @f @K

160 3 x rw x c.r; w; x/ D rk.r; w; x/ C wl.r; w; x/ K.r; w; x/l.r; w; x/ rwx x r @c @r D K C r @K @r C w @L @r f.l; K/ D x x r (3.31) @f @K @K @r C @f @L @L @r D 0 r @K @r C w @L @r D 0 (3.32) @c @r D K @c @w D L (3.30) f L w 1 f K r 1 1 1 c D rk C wl LK @c @r D K r L K (3.32)

3.21 161 1 (3.26) x D L 1 3 K 2 3 (3.33) L D wl C rk C.L 1 3 K 2 3 x/ LK w C 1 3 L 2 3 K 2 3 D 0 (3.34) r C 2 3 L 1 3 K 1 3 D 0 (3.35) (3.34)(3.35) K D 2w r L (3.36) rk D 2wL (3.37) (3.36)(3.37) (3.33) 2 (3.36)(3.37) (3.33) L D r 2 3 x (3.38) 2w 1 2w 3 K D x (3.39) r (3.38) w r (3.39) r w L 1 3 K 2 3 D x L K LK @x @x K C @K @L L D 0 K L D @x @x = @L @K D 1 L 3 2 K 2 3 2 L 1 3 K 1 3 D 1 K 2 L c c D rk C wl D 1 K 2 L r C w L

162 3 L <.>/ r 2w 2 3 x K >.</ 1 2w 3 x K L >.</ 2w L <.>/ 2 r 3 x c <.>/0 L r 2w L c L c L D r 2w 2 3 x c r 3.21.2 3 T t * 34 x D f.l; K; T / c D wl C rk C tt x L D wl C rk C tt C.x f.l; K; T // LKT w C f L D 0; r C f K D 0; t C f T D 0 f T f L w D f K r D f T t (3.40) wrt L.w; r; t/; K.w; r; t/; T.w; r; t/ c.w; r; t/ D wl.w; r; t/ C rk.w; r; t/ C tt.w; r; t/ w @c @w D L C w @L @w C r @K @w C t @T @w (3.41) *34 Land L rent r T t

3.21 163 x D f.l; K; T / x w (3.40) (3.41) @L f L @w C f @K K @w C f @T T @w D 0 w @L @w C r @K @w C t @T @w D 0 @c @w D L @c @r D K @c @t D T 3 3.21.3 C.x/ x D px C.x/ (3.42) p x x (3.42) x p C 0.x/ D 0 C 0.x/ C.x/,

164 3 2 D px.x 2 C 10/ (3.43) x 2 10 (3.43) x p 2x D 0 x D 1 2 p p C 0.x/ x D 0 x.x / Z x.x / D.p C 0.x//dx 0 3.9 3.21.4 X C.X/ p D p.x/ D p.x/x C.X/ X d dx D p C p0.x/x C 0.X/ D 0 (3.44) p 0.X/ MR MR D p C p 0.X/X (3.45) 1 p 2 p 0.X/X (3.44)(3.45)

3.21 165 (3.45) MR D p 1 C p0.x/x p D p 1 1 " (3.46) " p dx dp " D p 0.X/X D = X p dpdx (3.44) " p 1 1 D C 0.X/ (3.47) " p X X p p m Z x.x / D.p m C 0.X//dX 0 3.12 p m 3.21.5 D pf.l; K/ wl rk p L K LK @ @L D pf L w D 0 @ @K D pf K r D 0 L.p; w; r/k.p; w; r/ x.p; w:r/ D f.l.p; w; r/; K.p; w; r// pf L D wpf K D r L.p; w; r/k.p; w; r/.p; w; r/ D pf.l.p; w; r/; K.p; w; r// wl.p; w; r/ rk.p; w; r/

166 3.p; w; r/ pwr @ @p D f.l; K/ C pf LL p C pf K K p wl p rk p @ @w D pf LL w C pf K K w wl w L rk w @ @r D pf LL r C pf K K r wl r rk r K L p K p L w K w L r K r 3 pf L D wpf K D r @ @p @ @w D L; D f.l; K/ D x @ @r D K D px wl rk xlk @ @p D x p xlk pf L D wpf K D r x p x D L 1 2 K 2 5 D pl 1 2 K 2 5 wl rk LK 0 1 2 pl 1 2 2 2 K 5 D w; 5 pl 1 3 2 K 5 D r L 1 2 D 2w p K 2 5 L 1 2 D p 2w K 2 5 p 2 5w K 1 5 D r K 1 5 D p2 5rw K D p10 5 5 r 5 w 5

3.21 167 L 1 2 D p 2w L D wl D p 4 5 2 r 2 w 2 p 10 2 2 5 4 r 4 w 6 x D L 1 2 K 2 5 D p 9 2 5 4 r 4 w 5 p10 rk D p10 2 2 5 4 r 4 w 5 5 5 r 4 w 5 wl D 5 1 4 rk D 2 rk D px wl rk D wr p 10 2 5 4 r 4 w 5 p 10 2 2 5 4 r 4 w 5 p10 5 5 r 4 w 5 D p 10 20 5 4 r 4 w 5 2 5 @ @p D p 9 2 5 4 r 4 w D x 5 @ @w D p 10 4 5 4 r 4 w D L 6 @ @r D p10 5 5 r 5 w D K 5 r w px wl rk C.L 1 2 K 2 5 x/ LK 0 w C 1 2 L 1 2 2 2 K 5 D 0; r C 5 L 1 3 2 K 5 D 0 x x px wl C rk wl D 5 5r rk L D 4 4w K L 1 2 K 2 5 D xx 1 5r 2 K 10 9 D x 4w K D 5 4w 9 10 x 9 5r

168 3 r w L D 4 5r 9 10 x 9 4w r w 5 4 r 4 w 5 c D wl C rk D D 1 2 2 8 1 9 2 5 4 r 4 w 5 1 9 x 10 9 C 2 5 wr x 10 9 C 2 10 r 4 w 5 5 5 1 9 x 10 9 2 5 4 r 4 w 5 1 9 x 10 9 D 9 10 4 @c 5r @w D 9 10 x 9 D L 4w @c @r D 5 4w 9 10 x 9 D K 5r 2 5 4 r 4 w 5 1 9 x 10 9 c x dc dx D 2 5 4 r 4 w 5 1 9 x 1 9 x D p 9 2 5 4 r 4 w 5 ( 1 2 C 2 5 ) 1 1 3.21.6 x LK x D f.l; K/ a f.al; ak/ f.al; ak/ D af.l; K/ D ax

3.21 169 * 35 a f L L C f K K D x pf L D wpf K D r wl C rk D px x D AL K 1 A 0 < < 1 p D pal K 1 wl rk LK pal 1 K 1 w D 0.1 /pal K r D 0 L K wl D pal K 1 D px rk D.1 /pal K 1 D.1 /px wl C rk D px ( wl px ) ( rk px ) 1 *35 a a a 0

170 3 3.21.7 x D f.l; K/ x D dk @f dl D @L x D L Kˇ dk L 1 Kˇ dl D K D ˇL Kˇ1 ˇL L C ˇ 1 1 LK 2 x 2 2 @f @K 3.21.8 CES CES 2 CES x D f.l; K/ D. L C ˇK / 1 ; C ˇ D 1; 0 < < 1; 0 < ˇ < 1 x LK ˇ < 1LK 2 x 0 x 0 D..2L/ C ˇ.2K/ / 1 D Œ2 1. L C ˇK / 1 D 2x f L f K f L D. L C ˇK / 1 L 1 D x 1 L 1 f K D ˇ. L C ˇK / 1 K 1 D ˇx 1 K 1

3.21 171 f L D f K ˇ L 1 K ( w r ) L ˇ K D f L f K 1 1 L K f L fk d L K d D 1 1 1 ˇ 1 1. 1 1/ D 1 D 1 L K D d L K d L K D d L K L K! d = D 1 1 (elasticity of substitution) ( w r ) CES (constant elasticity of substitution) 0 f L D x L f K D ˇ x K x D f.l; K/ D L Kˇ ; C ˇ D 1 CES! 0! 1

172 4 Separating Pooling 4.1 1994 (player) 1 2 AB A B

4.2 173 5, 5 1, 7 7, 1 2, 2 4.1 1 B A 2 (strategy) *1 (equilibrium) 2 2 3 4.2 4.2.1 1 AB A B A A 4.1 A B *1

174 4 (payoff) *2 *3 (non-cooperative game) 2 (static game) 4.1 (normal form game) *4 (best response) 4.1 (1). A (i) B! 5 7 (ii) B! 1 2 (2). B (i) A! 5 7 (ii) A! 1 2 *2 - *3 2 *4 (strategic form game)

4.2 175 4.2.2 1 (Nash equilibrium) 1 A B B A A B 4.1 (2,2) 2 (5,5) (dominant strategy) (prisoner s dilemma) 4.1 4.2 4.1 7 2 AB 0 6 6 5

176 4-2, -2-6, 0 0, -6-5, -5 4.2 X Y X 8, 6 4, 4 Y 3, 3 6, 8 4.3 2 2 1 2 A B X Y 2 A X B Y 4.3 A B (1). A (i) B X! X X 8Y 3 (ii) B Y! Y X 4Y 6 (2). B (i) A X! X

4.2 177 5, 3 1, 1 0, 0 3, 5 4.4 X 6Y 4 (ii) A Y! Y X 3Y 8 2 (1). 1 A B X A X B X B X A X (2). 2 A B Y A Y B Y B Y A Y 2 X A Y B 4.3 4.4 4.3 3 2 2 1 1

178 4 X Y X 5, 5 8, 2 Y 8, 2 5, 5 4.5 3 4.2.3 3 A B A B B A XY 4.5 A B (1). A (i) B X! Y X 5Y 8 (ii) B Y! X X 8Y 5 (2). B (i) A X! X X 5Y 2 (ii) A Y! Y X 2Y 5 A B (mixed strategy)

4.2 179 3 A 1/3 X 2/3 Y 1 4 X5 6 Y (pure strategy) X 1 0 4.5 A p X 1 p Y B q X 1 q Y A A B B * 5 A D5pq C 8.1 p/q C 8p.1 q/ C 5.1 p/.1 q/ D5 C.3 6q/p C 3q (4.1) B D5pq C 2.1 p/q C 2p.1 q/ C 5.1 p/.1 q/ D5 C.6p 3/q 3p (4.2) A (4.1) p B (4.2) q (4.1) 3 6q p D 1 3 6q > 0 p D 03 6q < 0 A *5 2 1 1200 1 2 300 1 1 36 1200 C 1 300 D 50 18 2 1 36 1 18

180 4 3 6q D 0 q D 1=2 (4.2) 6p 3 q D 16p 3 > 0 q D 06p 3 < 0 B 6p 3 D 0 p D 1=2 3 3 A B 1/2 X Y A 6.5 B 3.5 q D 1=2 B 1/2 X Y (4.1) 3 6q A X Xp D 1 Yp D 0 p D 1=2 p D 1=2 A 1/2 X Y (4.2) 6p 3 B X q D 1=2 p D 1=2q D 1=2 *6 1/2 B A 1/2 X X Y A B 1/2 X X Y 1/2 2 2 2 A 5/7 X 2/7 Y B 2/7 X 5/7 Y *6 2 2 3 3 3 2 2

4.2 181 3 A p X 1 p Y B q X 1 q Y A A B B A D 8pq C 3.1 p/q C 4p.1 q/ C 6.1 p/.1 q/ D 6 C.7q 2/p 3q (4.3) B D 6pq C 3.1 p/q C 4p.1 q/ C 8.1 p/.1 q/ D 8 C.7p 5/q 4p (4.4) (1). A (i) 2 < q 5 1 p D 1 7 (ii) 0 5 q < 2 p D 0 7 (iii) q D 2 p 7 (2). B (i) 5 < p 5 1 q D 1 7 (ii) 0 5 p < 5 q D 0 7 (iii) p D 5 q 7 (1). p D 1, q D 1 A XB X (2). p D 0, q D 0 A YB Y (3). p D 5 7, q D 2 7 A 5/7 X 2/7 Y B 2/7 X 5/7 Y B A 5/7 X X Y A B 2/7 X X Y 5/7 2/7 (John Nash) 2 *7 *7 2

182 4 G C P G 0, 0 1,-1-1, 1 C -1, 1 0, 0 1, -1 P 1,-1-1, 1 0, 0 4.6 AB 3 G, C, P 4.6 1 1 0 G, C, P p A, q A, 1 p A q A G, C, P p B, q B, 1 p B q B A Dp A Œ0p B C q B.1 p B q B / C q A Œp B C 0q B C.1 p B q B / C.1 p A q A /Œp B q B C 0.1 p B q B / Dp A.3q B 1/ C q A.1 3p B / C p B q B 3q B 1 D 0 1 3p B D 0 p B D q B D 1 3 p A D q A D 1 3 1 3

4.2 183 4.2.4 B X Y A X 4, 4 0, 6 Y 6, 0 2, 2 B XY A Y A B Y AB Y X X Y X X A X B X Y A Y 6, 0 2, 2 B X Y Y Y B X Y A X 4, 4 0, 6 Y 6, 2 2, 0 A X Y B A B A X B X Y A Y 6, 2 2, 0 B Y X Y (Y,X) B

184 4 A X A X B Y 3 2 B X Y A X 4, 4 0, 4 Y 4, 2 2, 0 2 (X,X) (Y,X) AB X Y A X Y Y X A X Y B Y X A X B X Y A Y 4, 2 2, 0 B Y X (Y,X) 1 3 B X Y Z A X 4, 4 0, 4 3, 6 Y 4, 2 2, 0 3, 3 Z 2, 2 1, 1 1, 0 (X,Z) (Y,Z) 2 A Z Y B A Z A Z

4.3 185 B X Y Z A X 4, 4 0, 4 3, 6 Y 4, 2 2, 0 3, 3 B XY Z (X,Z)(Y,Z) 2 A X Y (X,Z) B Y X B X Z A X 4, 4 3, 6 Y 4, 2 3, 3 Z 2, 2 1, 0 A X Y Z 2 4.3 1 (dynamic game) 4.3.1 2

186 4 X (8,6) X B 1 Y (4,4) A Y X (3,3) B 2 Y (6,8) 4.1 4 4 2 A B X Y A B 4 4.1 (game tree) (extensive form game) *8 A A B 1 B 2 B A B 1 A B 2 X Y A B A X Y 2 B A A X Y *9 B (1). XX A X Y X *8 *9 A B B

4.3 187 XX XY YX YY X 8,6 8,6 4,4 4,4 Y 3,3 6,8 3,3 6,8 4.7 4 (2). XY A X X A Y Y (3). YX A X Y A Y X (4). YY A X Y Y XY YX B A 4 4.7 4.3.2 4.7 4 (1). A (i) B XX! X X 8Y 3 (ii) B XY! X X 8Y 6 (iii) B YX! X X 4Y 3 (iv) B YY! Y X 4Y 6 (2). B (i) A X! XX XY

188 4 XX 6XY 6YX 4YY 4 (ii) A Y! XY YY XX 3XY 8YX 3YY 8 3 (1). 1 A X B XX A X B XX XY B XX A X (2). 2 A X B XY A X B XY XX B XY A X (3). 3 A Y B YY A Y B YY XY B YY A Y 3 3 3 B 4.1 B 1 B 2 Y A Y B 1 B X Y YY A Y X Y A X B 1 B Y X B 1 B X A X 8 Y 6 A X 3 B A X Y A A X B Y X Y (incredible threat)

4.3 189 1 B 1 B X A Y B 2 B X B 2 B Y 4 2 (subgame) (subgame) 4 B 1 B 2 2 1 2 1 B 2 2 B 1 2 2 A B B B 1 X B 2 Y 1 2 4 3 1 B 2 B 3 B 1 B 2 1 2 (subgame perfect equilibrium) 4 2 (Reinhert Selten)

190 4 4.3.3 4 A B 1 B 2 B 1 B 2 B B 1 B X 6Y 4 X 1 B 2 Y Y 2 B A A X Y X B X A 8Y B Y A 6 A A X A A X B 1 B 2 B XY (backward induction) * 10 4.3.4 D r D 2r D R 2R D D R 2 R > D > r > D 2 *10 R.