The Cobb Douglas production function exhibits “constant returns to scale”.
Can someone help to explain what that means? Thanks!
Constant return to scale means, for a function of multiple variables (such as the Cobb-Douglas production function), that :
f( a*x ; a*y)= a*f(x,y)
(if all input are multiplied by the same figure, the result of the function is multiplied by the same figure
In the case of Cobb Douglas production function:
Cobb-Douglas Production Function : Y(K,L)=T*K^(alpha)*L^(beta)
(Y=Production, T= total productivity factor, K=Kapital, L= Labor)
Constant return to scale => Y(a*K,a*L)=a*Y(K,L)
This condition imply that alpha+beta=1
That is what you need to remember , if you see constant return to scale , beta=1-alpha , and the function can be written:
Y(K,L)=T*K^(alpha)*L^(1-alpha)
If you are interested in the Production growth :
DY/Y= DT/T + alpha*DK/K + (1-Alpha)DL/L