Golden Rule Level of Capital & Savings Rate - Solow Model

We find the level of capital that maximizes consumption. We discuss how adjusting the savings rate results in different steady state capital levels, and that there is a particular savings rate, that results in a particular steady state capital level (the golden rule level of capital) that maximizes consumption.
We discuss several ways to see this, can calculate the golden rule level of capital.
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[@victoriakushchak2692]

As an Economics Masters student I have done many of this before but never quite felt I fully understood some of the topics that I just wanted to say a huge thank you for your videos - your explanations are so clear!

[@brookekonnry1376]

studying for exams right now, youre truly a master jedi of econ. I love you

[@jimmyyiu5219]

I listened to my professor for two hours and got nothing in my head. Your video made me clear in 20 minutes. Thanks a lot, really appreciate it.

[@jinghualiu7519]

You are awesome!!! You did a better job than my professor in explaining Solow Model!!!

[@judearnaoot8969]

this is my first time commenting on any youtube video ever. I would like to thank you from the bottom of my heart. you are the reason I am passing my economic growth class. I wish you nothing but the best in life.

[@MFM88832]

That was extremely helpful! I have had two lecturers who couldn't explain this simple concept to me over 2 hours. I always thought it was some complicated stuff. What a waste of time university can be sometimes...

[@economicurtis]

Sounds good to me. In fact I'm pretty sure that's how Blanchard's Macroeconomics text teaches it. You should post a video response. I posted this thing 6 months ago for a class I taught in the Fall, and I still get a ton people looking for help with the golden rule level of savings. Seems like a lot of people would benefit from your help.

[@MusafarKhan]

hey these lectures are very helpful for me. good job

[@economicurtis]

My nation is motivated mostly by the notation Mankiw's intermediate Macro text uses. But I read through Blancard and Jones' texts as well in prep for the videos too.

[@Alicia-vc9qg]

This is an amazing video! You did a really great job of explaining this. Way better than my professor did, haha. Thank you!

[@TheTimponi]

You're amazing... Thank you for going into such detail... It really does help... I hope you're still making videos!!!! (Sri Lanka)

[@MrMimios]

Please explain the final exponent of s. It seems to me that it is (1-3α) /(1-α).Thanks for these great videos.James

[@economicurtis]

You are welcome Aurora!

[@economicurtis]

Hello Hello, I'm pretty sure what I have there is right. Notice that the \delta is in the denominator, ie (1/x = x^(-1) ). Since to simplify things I moved \delta up to the numerator, I need to make \delta's exponent negative. The algebra is what always get's'ya. So let me know if I'm still wrong.

[@RammTeam]

Thanks from Karlsruhe, Germany

[@moisesclaudino6645]

Very good content, now I can understand properly.

[@ST0orz]

This is really useful! thanks so much for your videos!

[@hoooplah]

Really good video thanks. It's the morning of my exam so hopefully it sinks in :)

[@hamismiraji1894]

why You dnt include population growth(n) and technological progress(g) instead you involve only depreciation rate

[@26lekent]

HAMIS MIRAJI this model presumes that n and A(g) are constant. y = Y/n, k= K/n

[@nedunicht7668]

Good Job!, Münster, Germany

[@Chris-cq5cc]

can you simply set the derivative of production function to equal the depreciation rate and get k from that?

[@richardwu344]

hi, thank you for the video but why is your per capita output function yt=kt^a where is your technology term "A"

[@YasirKhan-jt6ev]

Please if possible add a series on Harrod-Domar model.

[@MrSchube]

Thank you, from Germany (RUB BOCHUM)

[@naveedsyed8288]

i am from bochum too... can you help me solve this in more easy way.. coz i really get it hard to understand. i am weak in economics but this subject is compulsory in my major (MADM) . i have no choice

[@johnnypaul5780]

Your videos are awesome. Very detailed and methodical explanations. I was just wondering which main textbook you're using for these videos? (Since different Macro textbooks use different notations and whatnot). Thanks!

[@tehw000000t]

Never thought I'd be listening to an economics lecture by Justin Trudeau

[@armanddesjardins5791]

Hey great videos they are helping a lot. Do you by any chance have printable versions of your notes

[@kevinleong2855]

at 16:43 when you calculate s^((-a/1-a)-2a-1/1-a)=a, shouldn't it calculate to become (1-3a/1-a)? which would make s= a^(1-a/1-3a)

[@joni7kkk]

I saw that too. You made somehow a mistake, it does not simplify to 1-a/1-a

[@TheOnlyJunniZ]

He made a mistake in: we want to max c, wrt s second line, at last: 1/(1-alpha) - (1-alpha)/(1-alpha) = alpha. where he wrote -alpha. In the third last line he again writes -alpha, but it really is alpha. Then it finally does simplify to s^*.

[@chk9580]

Agreed,took me 5 mins to find to mistake.

[@matth78989]

Cheers old chap, from London

[@richardwu344]

for Cg=yt-it Why do you use fkt- delta kt instead of fkt-skt ?? Cuz c=y-it Isn't it=syt??

[@nicholasfreeman4099]

how come delta k represents investment in the first graph?

[@everta.1141]

what software do you use? thanks for everything

[@nbodanac86]

Awesome, very helpful!!

[@NB19273]

your videos are awesome thanks so much for doing them!

[@tomdalman5773]

From this, when is an economy then described as dynamically inefficient?

[@Jeloha]

You are my hero! Thank you, this is so helpful

[@kasperverkammen9099]

I do think you made a mistake in your calculation: When you write out the equation to maximise consumption, the exponent 1/1-alpha becomes for no (apparent) reason alpha/1-alpha. Also, when solving for s, the third line from the end does not make any sense. Can you check whether the calculations are really right ?

[@economicurtis]

ON the first point, note that f(k*_{g}) = (k*_{g})^\alpha

[@economicurtis]

On the second, I think that's just algebra. I feel I actually went a bit overboard showing how the exponent simplifies. You might check out those step by step simplification software packages (e.g. wolframalphapro) for help with that.

[@Me-ji2pn]

Could you also call the break even investment rate the depreciation rate? Hence why it is dk

[@tayebmustafa8606]

Thank you it is really really helpful

[@ryandodd8934]

economicurtis, What software are you using to create your graphs?

[@economicurtis]

Just excel. www.dropbox.com/s/8xasd9khixd5kt2/Solow%20SoVeryLow.xlsx?dl=0

[@ryandodd8934]

Thanks.

[@ryandodd8934]

Thank you, I appreciate your videos, they really do help foster deeper understanding. Do you have any planned for the Romer model?

[@economicurtis]

Sorry Ryan, no. I started notes (based on Jones and Blancard Macroeconomics texts, I really liked those), but never organized it well enough for a video series. I'd encourage checking out those texts if you don't like whichever text you are working with.

[@aurig1103]

Super helpful!!! Thank you so much!

[@priyaangadi1213]

thank you much

[@economicurtis]

Awesome!

[@azmanalaydeross287]

thank you

[@classicjimmy2828]

shouldnt the output be y=Ak sub t to the power of alpha

[@wassihungebreegizaber115]

Your videos are very keep include some lecture notes it up! Besides, it would be so shiny if you

[@gunnarjensen5910]

Nice

[@man4hire]

Many thanks, UoY ~ York uni, england

[@Duinkher]

thanks, from geottingen germany, :P

[@htetthiri5607]

Thankkkkkkkkkkkk you!!!!!!!

[@marken1994]

Thanks a lot! University of Surrey, England.

[@李之琪-t5x]

using math to get to the s_g-* should not be that complex. you already got the k_t-*, then you want to maximize the c_g-*, you don't need to take s_g* into that equation so early. c_g-*=y_t - i_t =f(k_g-*) - δk_g-* do the first derivative of k_g-*, we get: (c_g-*)' = αk_g-*^(α-1) - δ in order to find max(c_g-*), we make (c_g-*)' = 0 αk_g-*^(α-1) = δ k_g-* = (δ/α)^(1/α-1) Finally, we had 1. k_g-* = (δ/α)^(1/α-1) 2. k_t-* = (s/δ)^(1/1-α) in order to get s_g-*, we make 1.=2. we can get s_g-* easly =α

[@economicurtis]

Break a leg.... or good luck!!

[@HemSingh-rt5bp]

Voice is not properly heard

[@Cocoaces]

Great content. But, are you ever going to do 5.1, .2 and the rest!!

[@bigfriki]

This makes no sense... (or probably I'm not getting it). Could it be that the formulas for Savings and GDP from the short and middle run don't apply here? Take the equation for private savings (given public savings = 0): S = I and S = Y - T - C (right?). If T is also 0 (by assumption), we have: S = I = Y - C or put differently: C = Y - S or C = Y - I. So far so good. But if you ask now the simple question "when is C maximised?" wouldn't the simple answer be: C is maximised when S = 0. This of course implies I = 0. In other words, Y = C + I where I is 0 and C increased by the same amount I dropped. WTF??? Somebody please tell me what's wrong with this rationalization.

[@meeraunnikrishnan6120]

Here we are looking at the steady state level of savings such that consumption is maximised, the case where S = O could be a trivial case, since this does not allow for possibilities of sustained high levels of consumption in future years as well ( no savings this year can lead to capital being used up without further additions next year ). Whereas at the steady state we are ensured that we have a sustained level of capital and per capita income next year as well. Now that we are convinced for the need of a steady state we can look at the level of savings that keeps the economy in the Goldilocks zone, not too much such that the standard of living reduces even, not too less causing the economy to produce less capital and prevent itself from reaching a higher level of output. The savings rate that helps us reach this state is the Golden rule level of savings rate.