Quiz 4

Q:  Find the returns to scale and the rate of technical substitution is f(L,K)=L^1/3K^1/2.

A:  For the returns to scale we need to compare 2*f(1,1) to f(2,2).
    f(1,1)=1^1/31^1/2=1.  f(2,2)=2^1/32^1/2=2^1/3+1/2=2^5/6<2.  
    Since 2*f(1,1) > f(2,2) the production function exhibits decreasing returns to scale.  

    The RTS=MP_L/MP_K={(1/3)L^-2/3K^1/2 }/ {(1/2)L^1/3K^1/2}=2K/3L.