Production Function
Categories: Econ
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.
Related or Semi-related Video
Econ: What are Production Functions?2 Views
And finance Allah Shmoop what Our production functions well Grandma's
air The source of all A lot of useful wisdom
They say stuff like happiness isn't found It's created and
good manners don't cost nothing And there hasn't been any
good music since the the Elvis died Okay well maybe
not Everything they say is golden But here's another good
one You get out of something what you put into
it Yeah well that one actually works for economics to
it's the basic sentiment behind the production functions The production
function is a process that economists used to show how
much stuff you can make for every potential combination of
input It's essentially a mathematical equation based on data gathered
through the production process And it allows companies to graph
what production would look like given different inputs You know
they consider different questions Like what if we use more
workers Or what if we bought Mohr equipment You know
some big fancy factory with robots What if we replaced
the dehydrated milk in our baby formula with pot ash
All right well these are the kinds questions of production
function answers and well then businesses can allocate their resource
is in the most efficient way possible Well they find
the point on the graph where they get the most
out of what they're putting in and that's what they
shoot for McDonald's is slowly replacing human workers with robots
Well how do they know if it's a good investment
Well they asked the production function or at least look
at it a fry flipping robot Kaswell ten thousand dollars
at volume It costs another two thousand dollars a year
in maintenance and appreciation per year and that fry flipping
baht can cover one friar And there are five fryers
at the restaurant so it takes five bots to replace
one worker or about fifty grand to replace that one
worker Wealthy company does some trials and finds that a
fry flipping robots can do the job two times faster
than one person In actuality or reality that person cost
twenty dollars an hour after salary of fifteen bucks and
then taxes and all the everything's company has to pay
pension health care all that stuff So over the course
of a year a fulltime fried flipper cost McDonald's forty
thousand dollars well to replace the employees the company needs
five bots costing a total of fifty grand It'll cost
another ten thousand dollars total in the maintenance and appreciation
But the Frye body is twice as fast as the
worker meaning McDonald's Khun turnover twice a cz many fries
So you'd need to workers to match the output of
the fry bots Well the bots cost say sixty thousand
dollars in Year one And yes we're making up a
lot of numbers The workers costal eighty thousand those two
workers But the company is already in the black They've
made twenty thousand dollars in savings by replacing those low
skilled workers with robots Well the production function can have
many variables in practice The production function depends on the
product being produced Different products require different levels of inputs
and the relationships between the inputs are different That cab
all of relationships includes things like land and labor and
capital in raw materials and time However many of these
dropout is being irrelevant or they get combined and kind
of fade away Key idea here is that the simple
version of all of this has two variables to variable
inputs There's labor that's usually represented by a big fancy
capital L And then there's capital that's usually represented by
you Hey there And this combo gives you the quantity
of output like in the equation And this gets a
queue right Belle Plus Que is cute that's in its
simplest form and that's the production function And that's what
it looks like The amount of labour and the amount
of capital gives you the amount of output The production
function can help measure the marginal productivity of one factor
of production It can also help figure out the least
expensive and most efficient way to make a product like
Say you're going to make pies with Grandma You're going
to need to spend a little capital on ingredients and
you know pie tins Well that's the capital That's the
big K You've also got labor That's you And grandmama
That's the big Al there for labor Enough for losers
Sorry Grandma Alright now onto your production function right there
Well you could decide whether getting some more money for
ingredients will help you bake more pies Or if you
call your cousins to help with the baking and Ad
Tio El there Or you could do both Now we
just need to talk to Grandma about her musical taste 00:04:17.677 --> [endTime] Yeah