Question

Normalize the cobb douglas production function Y = F (K,L) = K^1/2L^1/2 in terms of output per unit of labor. Note that this function does not have technology change. Your answer should be in terms of y = f(k) =

Answer is y = (K/L)^1/2 = k^1/2

^{Please show step by step how to do this including the derivate and exponent laws you use}

Answer 1

Answer - The production function is given, Y = F(K,L) = K^1/2 L^1/2. Here 'Y' is output and K and L are capital and labor respectively. If we want to find output per unit of labor then we have divide production function by 'L'. Amount of labor units are represented by 'L'.

Output per unit of labor(y) = Y/L ('y' represents output per unit of labor)   

Then,

Y/L = (K^1/2 L^1/2) / L

y = K^1/2 L ^{1/2 - 1}

y = K^1/2 L^-1/2

y = (K/L)^1/2

This is output per unit of labor production function.