# Values of A,K,N,a in Cobb-Douglas function expressing GDP

In many basic macroeconomics textbooks a Cobb-Douglas production function with constant returns to scale is used to express the output of the economy as a function of labor and capital: $$Y=AK^aN^{1-a}$$.

Question: Given that a is normally assumed to be between 0.3 and 0.5, that the current output of the US economy is around 22T\$/year, and that $$N$$ (number of worked hours in a year) could be around 0.3TH/year, is there any kind of consensus on what are the values of $$K$$ and $$A$$ (at least the current values for the US economy)? If I assume $$a=0.5$$, $$A=5.4$$ and $$K=54$$, then $$Y=A\sqrt{KN}=21.7$$, is that an OK choice? I am puzzled to why I can't seem to find actual values for these parameters. If a book or a paper says that the GDP is expressed with this function, shouldn't it also at least give a realistic example with a range and units for the involved parameters? Maybe I am just looking in the wrong places? Any thought? Thank you in advance • I'm not an expert in this area, but as far as I understand,$Y$,$K$, and$N$are data,$a$is estimated from the data, and$A$is the residuals. For example, your model is$\ln Y = \ln A + a\ln K + b\ln N$[if you impose the restriction that$b=1-a$, the model becomes$\ln (Y/N) = \ln A + a\ln (K/N)$], where$\ln A = \mu + \varepsilon$. You can just calculate$A$as$Y/(K^a N^{1-a})$from$Y, K, N$and$a\$. – chan1142 Mar 21 at 4:25