The Per-Worker Production Function
We have shown that the per-worker production function is a single-variable function for , which we can obtain from the intersection of the original production function and the plane, plotted in red.
Because the number of workers does not matter to the relationship between and , we denote all quantities in per-worker terms. We refer to these in lowercase letters, so and designate output and capital per worker respectively.
We can now re-write the per-worker production function as:
We recall that for a Cobb-Douglas production function, and hence:
Hence, we have derived the per-worker production function as . Let's see how this function changes shape as we vary .