Physical Capital and Diminishing Returns

Do you recall our question about Germany and Japan from our previous video?
How did they achieve record economic growth following World War II?
Today's video will help answer that question. We'll be digging into the K variable of our simplified Solow model: physical capital.
To help with our discussion, we’ll be exploring two specific concepts. The first is the iron logic of diminishing returns which states that, for each new input of capital, there is less and less output produced. Your first input of capital will likely be the most productive, because you’ll allocate this first unit to the most important, value-adding tasks.
The second concept we’ll cover is the marginal product of capital. This concept describes the output created by each new unit of invested capital.
Can you already see how these two forces of capital help answer our question about Germany and Japan?
For these two war-torn countries, the first few units of invested capital had a lot of bang for their buck. The first roads between destroyed cities, the first new steel mills, the first new businesses-these helped boost their growth rate tremendously.
Even more so, remember that Germany and Japan were growing from a low economic base after the war. It's easy to grow a lot when the base is small. But all else being equal, you'd rather have a larger base, and grow slower.
Capital has some more nuances worth thinking about, which we'll show in the next video. So get to watching, and in our next macroeconomics video, we'll show you yet another problem surrounding physical capital.
Related video: Puzzle of Growth: bit.ly/1T5yq18
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[@andymonarrez1639]

I'm an economics major and I am upset at myself for not finding this channel earlier. Very helpful!

[@gopalmanemi3423]

Me too Man

[@Yasha-uh9vj]

Probably because you were too busy with ATHLEAN-X channel

[@OscarChristi]

me too :(

[@mugshot1087]

@@Yasha-uh9vj underrated comment even two years later

[@Yasha-uh9vj]

@@mugshot1087 bro I don’t remember writing that fr 😂😂

[@skillhood5459]

Your lectures and hosting is simply phenomenal. Please continue to increase our marginal utility!

[@kubagasienica99]

Skillhood wrong. Just utility. Marginal means the derivative of utility. Seeing your comment I suppose u want to say that the videos increase your utility and not increasing the rate of increase in our utility. Stay safe ;)

[@servantofthelord8147]

Woah. I did not understand this nearly as much as I thought I did. Thank you for clearly explaining this concept and the motivation behind it. Wow. I am genuinely impressed.

[@kennethkau2332]

The most concise solow model explanation I've ever seen.

[@kaolonly]

great video...llovedd itt!!!!! thanks a ton

[@nosakharegideon4005]

I have almost hated macro Economics, but i am loving this topic now.

[@MidNightStudiosFilms]

AMAZING...PLEASE KEEP IT COMING!

[@albertknecht7160]

love your videos!

[@user-mu7ri4wz1s]

thx for this series!!! it's really helpful!! easy understanding for someone without any economics background like me. my macroeconomics classroom just shifted here lol

[@econchoi]

Very useful for newbie establishing ideas. Nice work!!

[@marcelbachmann1383]

Great videos!

[@beboysub]

Thank You ❤

[@alparslankorkmaz2964]

Nicely explained

[@TheLinorox]

hi! This video is currently the third in the growth model playlist, but it should be the second. ;)

[@MarginalRevolutionUniversity]

+Marcio Lino de Almeida Thank you for telling us, we goofed! I fixed it. Best, Roman

[@happyfrogkhmel]

That is just amazing! Thank you from Germany)

[@shoto6329]

thank u for this. u make the economics more interesting

[@feynstein1004]

I didn't know that the law of diminishing returns was accurately modeled by the square root function. I always assumed it'd be an exponential decay function.

[@stephenmason7549]

Very helpful.

[@PunmasterSTP]

Physical capital? More like "Precisely the best overall." Your videos are phenomenal!

[@sonder2075]

Thanks!!

[@SarevokRegor]

Question, is the model required by empirical observation or reasoning to have the form Output = K^a * L^(1-a) (apart from the constant returns to scale requirement)? Because your tractor example looks like it would take the form of Output = (1-x^k)*L, where L is total labour, k is capital per labourer, and x is some number between 0 and 1?

[@natejweidner]

THank you!!

[@user-ww9iw3hi9v]

Amazing 🎉

[@007MrEmir]

Thanks.

[@amoghpatki5596]

good effects on THE IRON LOGIC...

[@omerozbakkal2346]

Abi harikasınız Hayranınızım.

[@walterdennisclark]

Krugman is attracted to the effect of war on the resetting of the "diminishing returns" curve. I'm pretty sure he is aware of the cost of war, but his claim is that if we pretend there is a war on, we can have our cake and eat it too. A refuting of that would be very interesting.

[@hungdaoxuan601]

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[@user-kj2fj8qr9l]

Why the Square root function specifically though? Is there a differential equation it satisfies? Or is it just a simple function for education purposes and in reality there's no real general function? For tractors I would have thought the productivity would converge to some value representing what it would be like if the farmer always had a tractor on hand, like 1-p^n where n is the number of trackers and p is the probability that a given tractor breaks down.

[@tiendoan1333]

The formula is deduced through empirical observation so yes it is a representation of reality. However, it is important to understand the equation's assumption so you know when it does and doesn't work

[@aakashbagaria1429]

great video but mentioning of catch up effect would have been easier in case of japan nd germany.

[@michaelnguyen7406]

But how do you measure something that is as heterogeneous as capital???

[@rosinagallo9223]

ma dei sottotitoli in italiano non si possono avere? GRAZIEEEEE

[@ExcelTutorials1]

thx

[@RonVillejoConsulting]

Is diminishing returns inevitable, i.e. as physical assets increase? I know this episode focuses only on K, but what if the farmer hired an employee to operate each new tractor he buys; what would the curve of returns look like?

[@drustevenson]

They said they were going to hold Labor constant for this video to illustrate K. Hiring more workers means increasing labor as you increase K. In some situations, it is hard to find enough new workers, or at least workers with the skills you need. If you can't find more workers, adding more equipment or facilities will be a waste, as they will sit unused.

[@XINJILU]

His theory has been established. No matter how many people you ask to operate the equipment, the lifespan of nature says that if it can prosper, it will decline. It is just how to maximize benefits through process management.

[@XINJILU]

Hello, I have also been studying management profit maximization recently, or we can discuss it together.

[@madmasontv7254]

Haha the first tractor helps him to grow most weed :D But seriously, very good and helpful videos, even to study for university in Germany!

[@PunmasterSTP]

Hey I came across your comment, and I was just curious how the rest of your studies went.

[@madmasontv7254]

It went very well, currently writing my master‘s thesis

[@PunmasterSTP]

@@madmasontv7254 I'm really glad to hear it! By the way, what's your thesis about?

[@madmasontv7254]

@@PunmasterSTP Applied machine learning

[@PunmasterSTP]

@@madmasontv7254 That sounds really cool, and I've read up on it a tiny bit from a hobbyist perspective. If I wanted to tinker around with ML, what might you recommend as a good place to start? As far as programming languages, would you recommend Python, R, Java and/or something else?

[@marianid98]

why is y = √ K and not y = F(K) as shown in the beginning?

[@IonSterpan]

Y= F(K) means that Y, the output, depends on K without specifying how it depends. it just says it is a function of K. Y = square root of K is an attempt to give a concrete mathematical expression to that function. An attempt to specify how it depends. K to the second power, or any other mathematical operation applied to K, would still be a function. But we work with square root of K to express mathematically that K has diminishing returns in terms of output.

[@sunset2.00]

Farmer capacity to sell his ever growing products is important

[@nmikloiche]

Let’s use this idea of tractors - let’s say before I bought my first tractor I could work 5 acres of my farm a day. My first tractor allowed me to work 20 acres a day, 4 times what I could do by hand. When I bought my 2nd tractor, I bought the best one available, and it lets me work 100 acres a day. Since my 2nd tractor has the benefit of technological advancement it allows me to complete 5 times what I could with tractor. In this example, how is tractor 2 a diminished return? This question.may have nothing to do with diminishing return, but it’s bugging me -. Does the idea of diminished return require the prior capital to continue to be used, and if so used at some particular level. Let me try this with an example. If I add a 2nd tractor, it would be most beneficial if I could have both tractor 1 and 2 in service at the same time versus using tractor 2 as my primary and 1 as my spare. Now, having both in service would require I have the need for such production, so let’s assume I do. It also means I would re-train an existing worker (assuming I had one) or hiring a worker to operate the additional tractor. So does diminished return care if I use both tractors simultaneously vs primary and spare?

[@alexandertubbs5995]

because in economics all other factors are held equally so you may only have 75 max, 1st tractor allowes you to do 25 acres a day second boosts you to 50 and third to 75, the increases are infinite, 100% and 50% thus the returns form each unit are small percentage wise, plus other factors that limit you, one farmer so you can only do 30 arces a day max etc.

[@tomsv7]

At 1:18 I think you said one farmer can produce more output with two tractors than one.. it is not possible as you only have one farmer.

[@pku2death]

farmers have workerssssssssssssssssssssssss

[@PrinceKumar-hh6yn]

Iron law of diminishing returns 🎭

[@Nathaneal51]

at 2:01, why would the 2nd tractor be less productive than the first 1? especially if its the same tractor and it's doing the same job. i understand the law of diminishing returns but this is a terrible explanation of it

[@besseralsdu1372]

I know it's late lol, but basically you can rather compare it to: No tractor = you do everything by hand, only one little field. One tractor= big boost, you can grow 10 fields. So the boost is immense. And then the second tractor may increase by 10 to but from 1 field to 10 fields is a way bigger boost than from 10 to 20 fields. There might be a better metaphor but you can see it like that

[@jonaharmbruster8342]

pls include me in your next video and pls am only 9

[@mattgunter9674]

"Iron law" of diminishing returns is complete BS. Capital Units don't have to be redundant, they can be completely unrelated or they can have synergies. Structure matter! Imagine if each tractor was autonomous and came with ability to create seeds and fertilzer and land....then the production function would be linear. I can also imagine scenarios where the curve bends upward. Let's not fool ourselves with so called "iron laws".🤣