User:Ericandude/sandbox

Mathematical setup

 * $$ y=Y/L ,k=K/L, c=C/L \,$$

Since: Y=K^a(EL)^1-a Prove the a=capital share of income (rK)/Y and r=MPK at max. profit and MPK= dY/dK = aK^a-1(EL)^1-a dY/dK=a(K/EL)^1-a = ak^1-a therefore r=ak^1-a and since (rK)/Y then (ak^1-aK)/Y (aK^a-1K)/(EL)^a-1