Aggregate Production Function

Aggregate Production Function Narrative

The aggregate production function is shows how an economy changes inputs into output.

The aggregate production function is how inputs are magically changed into output. This is a metaphorical production function where corn is turned into an egg. Inputs are land, labor, capital, and technology. Output are goods and services.

The production function I’m going to use in this video is the Cobb-Douglas which takes the form: Y = A√KL where Y is GDP, A is technology, K is capital, and L is labor.

I have used a graphing calculator I found on the web to graph the Cobb-Douglas production function. Notice that as more capital is added to a fixed amount of labor, output increases, but at a decreasing rate.

When more and more capital is added to a fixed amount of labor, output increases by smaller and smaller amounts. This is called decreasing returns to scale. Decades of data confirm both the shape of the curve and diminishing returns.

In this picture, I have taken a graph from Timothy Taylor’s free online textbook that shows the shape of the aggregate production function. If you’d like to access this book, pause this video and use the link on the screen.

When the state of technology changes, the production function shifts up as seen here. Many think that the technological change has to be a whizbang awe inspiring innovation like the internet. But many changes involve finding a faster way to the same task with less.

Here, these women fill up the barrels with water and roll them back home instead of carrying the water on their head. This invention saves four trips to the well and is an example of technology.

One last characteristic about the Aggregate Production Function is that is exhibits constant returns to scale. That is, doubling the amount of land, labor, and capital, doubles the output. If you ever need to know if a production function has constant returns, simply sum the exponents. If the sum equals one, then the curve has constant returns. In this example, doubling the inputs and plant size, doubles the output from 3 to 6.

In this video I have given you the basics of the aggregate production function. I look forward to your comments.