Productivity= Outputs/Inputs
The Production Function
Economists often use a production function to describe the relationship between the quantity of inputs used in production and the quantity of output from production.
The Production Function:
Y = A F(L, K, H, N)
Y = quantity of output
A = available production technology
L = quantity of labor
K = quantity of physical capital
H = quantity of human capital
N = quantity of natural resources
F( ) is a function that shows how the inputs are combined.
A production function has constant returns to scale if, for any positive number x,
xY = A F(xL, xK, xH, xN)
That is, a doubling of all inputs causes the amount of output to double as well.
Production functions with constant returns to scale have an interesting implication. Setting x = 1/L,
Y/ L = A F(1, K/ L, H/ L, N/ L)
Where:
Y/L = output per worker
K/L = physical capital per worker
H/L = human capital per worker
N/L = natural resources per worker
The preceding equation says that productivity (Y/L) depends on physical capital per worker (K/L), human capital per worker (H/L), and natural resources per worker (N/L), as well as the state of technology, (A).
