Theorie der Geldpolitik 1 Seite 59

tatias wrote:

[COLOR=black]L= E ( 0,5 ((Pi -Pi*)[/COLOR][COLOR=black]^2+ b(y-y*)[/COLOR][COLOR=black]^2 ))[/COLOR]
[COLOR=black]L= E ( 0,5 ((Pi -Pi*)[/COLOR][COLOR=black]^2+ b(cPi -CPi+ Epsilon-y*)[/COLOR][COLOR=black]^2 ))[/COLOR]
[COLOR=black]L= E ( 0,5 ((Pi -Pi*)[/COLOR][COLOR=black]^2+ b(cPi -CPi+ Epsilon-y*)[/COLOR][COLOR=black]^2 ))[/COLOR]
[COLOR=black]dL/ dP = E ( 0,5 (2(Pi -Pi*)[/COLOR][COLOR=black]+ 2cb(cPi -CPi[/COLOR][COLOR=black]^e[/COLOR][COLOR=black]+ Epsilon-y*)[/COLOR][COLOR=black])[/COLOR]
[COLOR=black]0= Pi -Pi*[/COLOR][COLOR=black]+ cb(cPi -CPi[/COLOR][COLOR=black]^[/COLOR][COLOR=black]e+ Epsilon-y*)[/COLOR]
[COLOR=black]0= Pi -Pi*[/COLOR][COLOR=black]+ c[/COLOR][COLOR=black]^2[/COLOR][COLOR=black]bPi -C[/COLOR][COLOR=black]^2[/COLOR][COLOR=black]Pi[/COLOR][COLOR=black]^e[/COLOR][COLOR=black]+cb Epsilon-cby*[/COLOR]
[COLOR=black]Pi [/COLOR][COLOR=black]+ c[/COLOR][COLOR=black]^2[/COLOR][COLOR=black]bPi=Pi*[/COLOR][COLOR=black]+[/COLOR][COLOR=black]C[/COLOR][COLOR=black]^2b[/COLOR][COLOR=black]Pi[/COLOR][COLOR=black]^e[/COLOR][COLOR=black]-cb Epsilon+cby*[/COLOR]
[COLOR=black]Pi [/COLOR][COLOR=black]+ (1+c[/COLOR][COLOR=black]^2[/COLOR][COLOR=black]b)=Pi*[/COLOR][COLOR=black]+[/COLOR][COLOR=black]C[/COLOR][COLOR=black]^2b[/COLOR][COLOR=black]Pi[/COLOR][COLOR=black]^e[/COLOR][COLOR=black]-cb Epsilon+cby*[/COLOR]

[COLOR=black]E(Pi) [/COLOR][COLOR=black]+ (1+c[/COLOR][COLOR=black]^2[/COLOR][COLOR=black]b)=E(Pi*)[/COLOR][COLOR=black]+[/COLOR][COLOR=black]C[/COLOR][COLOR=black]^2b E([/COLOR][COLOR=black]Pi[/COLOR][COLOR=black]^e)[/COLOR][COLOR=black]-cb E(Epsilon)+cb E (y*)[/COLOR]

[COLOR=black]Pi[/COLOR][COLOR=black]^e[/COLOR][COLOR=black]+ (1+c[/COLOR][COLOR=black]^2[/COLOR][COLOR=black]b)=Pi[/COLOR][COLOR=black]^e[/COLOR][COLOR=black]+[/COLOR][COLOR=black]C[/COLOR][COLOR=black]^2b[/COLOR][COLOR=black]Pi[/COLOR][COLOR=black]^e[/COLOR][COLOR=black]-0+cby*[/COLOR]
[COLOR=black]Pi[/COLOR][COLOR=black]^e[/COLOR][COLOR=black]+c[/COLOR][COLOR=black]^2[/COLOR][COLOR=black]bPi[/COLOR][COLOR=black]^e=Pi[/COLOR][COLOR=black]^e[/COLOR][COLOR=black]+[/COLOR][COLOR=black]C[/COLOR][COLOR=black]^2b[/COLOR][COLOR=black]Pi[/COLOR][COLOR=black]^e[/COLOR][COLOR=black]-0+cby*[/COLOR]

[COLOR=black]und wenn ich jetzt auf den anderen Siete multipliziere: -Pi[/COLOR][COLOR=black]^e-[/COLOR][COLOR=black]C[/COLOR][COLOR=black]^2b[/COLOR][COLOR=black]Pi[/COLOR][COLOR=black]^e[/COLOR]

[COLOR=black]dann habe ich : 0= cby*[/COLOR]
[COLOR=black]ich suche aber Pi[/COLOR][COLOR=black]^e[/COLOR]
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L= E ( 0,5 ((Pi -Pi*)^2+ b(y-y*)^2 ))
L= E ( 0,5 ((Pi -Pi*)^2+ b(cPi –Cpi[COLOR=red]^e[/COLOR]+ Epsilon-y*)^2 ))
L= E ( 0,5 ((Pi -Pi*)^2+ b(cPi –Cpi[COLOR=red]^e[/COLOR]+ Epsilon-y*)^2 ))
dL/ dP[COLOR=red]i[/COLOR] = E ( 0,5 (2(Pi -Pi*)+ 2cb(cPi -CPi^e+ Epsilon-y*))
0= Pi -Pi*+ cb(cPi -cPi^e+ Epsilon-y*)
0= Pi -Pi*+ c^2bPi -C^2[COLOR=red]b[/COLOR]Pi^e+cb Epsilon-cby*
Pi [COLOR=red]* [/COLOR]c^2bPi=Pi*+C^2bPi^e-cb Epsilon+cby*
Pi [COLOR=red]*[/COLOR] (1+c^2b)=Pi*+C^2bPi^e-cb Epsilon+cby*

E(Pi)[COLOR=red] *[/COLOR][/COLOR] (1+c^2b)=E(Pi*)+C^2b E(Pi^e)-cb E(Epsilon)+cb E (y*)

Pi^e* (1+c^2b)= 0+C^2bPi^e-0+cby*
Pi^e+c^2bPi^e=[COLOR=red]0[/COLOR]+C^2bPi^e-0+cby*

[COLOR=red]-> [/COLOR][/COLOR][COLOR=red]piê + 2b²piê –2b²piê = bcy*[/COLOR][/COLOR]
[COLOR=red]piê=bcy*[/COLOR][/COLOR]
[/COLOR]
[COLOR=#ff0000]Dein Erwartungswert über pi* war einfach nur falsch?[/COLOR][/COLOR]

Vielen Dank!
Hatte den gleichen Fehler in der Einsendearbeit!