Mikro攌onomik - Vorlesung 5

Mikro攌onomik - Vorlesung 5 - !"" #...

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(' ? $ ,( ) ): # ) () 1 " D < F * & ) 4 # $ ,( ? ( "( ? '0↑) # M↓ 2 6( , S 0 M ↑↓3+ ( 8* & $ # + ( MS M6 0+) dx dp G da db " # " )# # 0 "* 0' .L # ##" M 8 0 ( 8" # /) # 7# G4 # 0 ' ; ( ( 8 # # & 0 € Stck. € 1000Stck. 1 8, C5 4' , # 8 8% T O ; ! F # )# # # 8* : # 6 0 *' S .0 * 2( 2 4 ) 1 -D /8 * ) # C+ ' 1 -D 7 ∆a a = relative ("prozentuale") Veränderung von a ∆b relative ("prozentuale") Veränderung von b b " ? # +' " ( 8 " *6 # " 6 , #+ & (* ∆a ∆b ∆a b ∆a b : = ⋅ = ⋅ ab a ∆b ∆b a && ( H 6 ∆→ + & " (# )" # " + ) ' * 2( 10 # 0 ( * # # 9 2( + H " S6 #+ 0 ' ηab := ( G" ## 6 9 8 * " *) # *) da b ⋅ 6η db a da < 0, a,b>0 db & " )# (* ) H 8 , ( H # ) ∆a ) # 8 < # ηab < 0 . =< 2 ( #6 ( ) ∆b + ( # + 8 da ,* db ( ; 6 '8 H C * 8 2( # ) =– 1 8, C5 4' , # 8 8% b R S P T 0 = Q PT PR a ## #") '$ 8 # " * '1 ( : S EJ ( #S E # # 2 ) ηab = – SP OS · . SR OQ " # (' 'E J S 6 #'E S J +) ηab = – OS SP OS · =– . SR SR SP $ ) 6 ; ?0 5 = + #' OS PT =– ) SR PR PT PR 0 () EL – ab = – 1 8, C5 4' , # 8 8% B # * ' 2( Abs tan d von P zur Abszisse Abs tan d von P zur Ordinate ( 8 * < 1 $ 4 " ' 8 ; L+ <)" # " # G" 2( 6 *" (" * & ηab ) 0 , # ) ( * 0 ## + ' # 2( 2( - ' " ;L 6 b R S P T Q = PT PR a ## 7* ( ." *# ' /2 ( & : 0 #( * 2( )# (2( L * # " # * 8 # 1 8, C5 4' , # 8 8% R $ $ " " (* " & # # % & 8 # 6 F 2( " +$ ( ) ' M6 S 0+ < #0 & 0 )( ) ? " * 8 # ' 7" 8 # * $ F : # # ) # $ U $ * ## (* V ' =& 8 # E # D 2( (* p x (p) = a - bp a b R xp >1 a 2b xp =1 <1 xp a 2 a x ## 8 # & 0S 2 ', 4' * 0 ( $ 2( ⇔0S ( M6 S 0+ 5 # : 3 < #0' → MS , " MS →# 0S * ηxp ηxp = dx p ⋅ dp x 1 8, C5 4' , # 8 8% 4 , dx = −b dp # xp = # " #" E D ) " , , P ( Q, (MS 2 0 # * ( G = ( −1) # " " , (" ) -+ " " 2 ,( # '., )" * 8 ? * ( * 8* ? 7 # $ ( 5 # 0 ( 0 S ' ηxp = 0 ' ηxp → ∞ bzw. # −b ⋅ p a − b ⋅p " ηxp = ∞ " 6 , : * " " $ " + ( 6 ) " ηab S 4 # 0 # ) ) F 1" : * =$ + #( M ) * 2 8 ,( ( 3/ " & ( , # " ηxp ) * ( 6 S ) :0 ,( )" # * *# , ? S - S' E = p ⋅ x(p) $ : ' dE dx = p⋅ +x dp dp " M5 M' = p dx ⋅ ⋅x+ x x dp ηxp 1 8, C5 4' , # 8 8% 44 ( M #' = x ⋅ (1 + ηxp ) #" dE = x ⋅ 1 − ηxp dp ( ) 4 ( & ( , 8 <)" * * 8 ? < & " 6 " * , ## * ? -D , =$ + # <) " 4) ( # " (0 # 64+ 50 & ## 0 # * < *( ? # S4 4 ηxp = ( −1) # " ηab * ) 6 " + - $ ηxp = ( −1) # " ηab S 43 * ' * 3, ' ηxp = −b ⋅ p ! =( −1) a − b ⋅p ⇔ −bp = −a + bp ⇔ 2bp = a ⇔p= D) ? 3 F * & a 2b 4# 0 7* 7* # 0 * 0S 5 #3 x L * 46 ## 4+ '1 # * / a ba a =a− =. / 2b 2b 2 7* # $ 0 ( & 7* 1 8, C5 4' , # 8 8% 4 ' #" ηxp > 1: S & $ $ ( $ $ # * ( ( 6 6 M5 M+ ) @ # ) " * =$ + # F $ )" ( * # ( ) ) 6 05 ) 0+ 7* # # ) ηxp < 1: S #" & ' $ " * 7* $ " * * 2 6 S 0 " # $ 2 8 ' (5 )# ( ,( 5 0+ ( $ 6ηxp > 1+ ) $ 6ηxp < 1 + 2 # M # * & # . 6 / ## . #+ /$ p p xp a) ## '0 * x b) ( * : = xp =0 x 1 8, C5 4' , # 8 8% 4K ## + dp =0 dx bzw. 1 dx = ∞, also dp ( ηxp → ∞ bzw., vereinfachend, ηxp = ∞ $ " 2' # # 0( 0* ) ? ( , #" # D # 1 * "# = : 2' # 0 ( # ( 1 : 0 *( )" " ( #( 8 ( ( (7 # " ) " ) 0 (# ) && * 9* #0 M) 8# 8# 0* ? #6 (+ ' # * ) 1" " ) ( ) $ ## #+ dp =∞ dx 2 & # * G" M * +# " F " " # 7 ( -( #" #0 F ) * () G 0 #* M" ) : " # ( "* 2( F * < ) # 2( 6 ## : M ' # $ 0 ( bzw. dx = 0, also dp $ ηxp = 0 P G" #+ 0 L ( Q F $ : ' ( # ( )" * # # 6 ## * " ) # 1 " * * 8 # 8 ( ( , #" # ) ( $ D ' ( $ ( 6 &F 0+ $ #G F #" ? *( , #" ## 8 (# *D " * 7 ) " (* * 8 * 1 8, C5 4' , # 8 8% 4A 79 ; $ ( -) L * 0 O 0 # * ) # ( 2 G W0 ( (@ * #* $ ( 4R 6 & +( $ ( 0 (6 # F- ( 6 # 9 'G 6 ' 0 # +& 0 4RB O $ # ( U ## #+ 0 V ,( $ 0 D ) 8# + "( " 6& -5 + # ( 2 H + H ; # # * " ( F & G 2( # * " 6 2( ## K+ ( * b R S P T Q = PT PR a ## K' * da SP = db SR SP OS ⋅ SR SP ηab = 1 8, C5 4' , # 8 8% 4% = OS PT = SR PR 6 ) # + F 6 + ) 4< ) A F 6 4RRR+ ) TK < (5 # ; ...
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This note was uploaded on 11/04/2009 for the course VWL VWL taught by Professor Ka during the Spring '06 term at Uni Münster.

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