Production Function

As your boss tries to optimize her workforce and capital equipment, she's probably thinking about a production function, whether she realizes it or not. Besides sounding like a kid’s song about where babies come from, the production function helps capitalists measure inputs (labor, equipment costs, etc.) and outputs (what they’re selling).

Lots of useful info can be gleaned from a production function. Besides the totalities on inputs and outputs, it also looks at averages, and something called the “marginal product,” which helps capitalists see changes in the output with tweaks to the inputs. It also helps capitalists determine things like efficiency, and helps them see how much growth there is thanks to advancing technology.

Yet...production functions aren’t considered a universal truth. The production function comes from neoclassical economics, which many economists see as unrealistic (it assumes people are...rational). Still, it can be a useful tool for business owners trying to squeeze all the profit they can out of their machine that they “own.”

The production function is essentially a mathematical equation based on data gathered through the production process, it allows companies to graph what production would look like given different inputs. What if we used more workers? What if we bought more equipment? What if we replaced the dehydrated milk in our baby formula with potash?

When the production function answers these questions, businesses can allocate their resources in the most efficient way possible. They find the point on the graph where they get the most out of what they're putting in.

McDonald’s is thinking about putting a bunch of fry-flipping robots into its restaurants. A fry-flipping robot costs $10,000. It costs another $2,000 in maintenance and depreciation per year. The fry-flipping bot can cover one fryer. There are five fryers at the restaurant, so it takes five bots to replace one worker.

The company does some trials and finds that a fry-flipping robot can do the job two times faster than a person. The person costs $20 an hour after salary, taxes, and all the other stuff that goes into employing someone. So run the numbers: $20 an hour equates to about $40,000 over the course a year, taking into account vacation days and days the worker just flaked and didn’t show up.

To replace the employee, the company needs five bots. Each bot costs $10,000, meaning McDonald’s would need to spend a total of $50,000 up front. It will cost another $2,000 each in maintenance and depreciation. Five bots means $10,000 a year total But the fry-bot is twice as fast as the worker. Meaning that McDonald’s can turn over twice as many fries. So you’d need two workers to match the output of the fry-bots.

The bots cost $60,000 in year one. The initial $50,000 plus the $10,000 in annual maintenance cost. The workers cost $80,000. Already in the black. The production function can have many variables. In practice, it depends on the product being produced. Different products require different levels of inputs, and the relationships between the inputs are different. It can include land, labor, capital, raw materials, and time. However, many of these often drop out as irrelevant, or can be combined.

The simplest version has two variables. There's labor. That's usually represented by an L. And there's capital. That's represented by a K. This gives you the quantity of output. In the equation, this gets a Q. So, in its simplest form, the production function goes L plus K equals Q. The amount of Labor and the amount of Capital give you the amount of output.

The production function can help measure the marginal productivity of one factor or production. It can also help figure out the least expensive and most efficient way to make a product.

Say you’re going to make pies with Grandma. You’re going to need to spend a little capital on ingredients and pie tins. That’s the capital.

You’ve also got labor. That’s you and Grandma, or “L” for labor. Now, with your production function, you can decide whether getting some more money for ingredients will get you more pies. Or calling your cousins to help with baking. Or both.

Now we just need to talk to Grandma about her taste in music.