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CES-függvény

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CES-függvény


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A konstans helyettesítési rugalmasságú függvények vagy CES-függvények (angol constant elasticity of substitution) olyan, a mikroökonómiai fogyasztás- és termeléselméletben, valamint a makroökonómiában is alkalmazott n-változós függvények, amelyek általános képlete így fest:


CES(x1,x2,...,xn)=α(β1x1ρ+β2x2ρ+...+βnxnρ)1ρ,displaystyle CES(x_1,x_2,...,x_n)=alpha (beta _1x_1^rho +beta _2x_2^rho +...+beta _nx_n^rho )^frac 1rho ,displaystyle CES(x_1,x_2,...,x_n)=alpha (beta _1x_1^rho +beta _2x_2^rho +...+beta _nx_n^rho )^frac 1rho ,

ahol a görög betűk valós konstansokat jelölnek.


Belátható, hogy a CES-függvény helyettesítési rugalmassága σ=11−ρdisplaystyle sigma =frac 11-rho displaystyle sigma =frac 11-rho .


A CES-függvényt 1961-ben alkották meg az úgynevezett stanfordi kör tagjai, Kenneth Arrow, Chenery, Minhas és Robert Merton Solow.



Speciális CES-függvények[szerkesztés]



  • Cobb-Douglas-függvény: ρ→0displaystyle rho rightarrow 0displaystyle rho rightarrow 0, ezért σ=1displaystyle sigma =1,displaystyle sigma =1,.

  • Tökéletes helyettesítés: ρ=1displaystyle rho =1,displaystyle rho =1,, ezért σ→∞displaystyle sigma rightarrow infty displaystyle sigma rightarrow infty .

  • Tökéletes kiegészítés (fogyasztáselmélet) vagy rögzített arányú tényezőfelhasználás (termeléselmélet): ρ→−∞displaystyle rho rightarrow -infty displaystyle rho rightarrow -infty , ezért σ→0displaystyle sigma rightarrow 0displaystyle sigma rightarrow 0.



A lap eredeti címe: „https://hu.wikipedia.org/w/index.php?title=CES-függvény&oldid=13143641”





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