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

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.

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!

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 ?

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.

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!

## 40 thoughts on “Golden Rule Level of Capital & Savings Rate – Solow Model”

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

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

Voice is not properly heard

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

what software do you use? thanks for everything

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.

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

Thank you it is really really helpful

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_ginto 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

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

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.

thank you

Nice

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

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

hey these lectures are very helpful for me. good job

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!

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

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, What software are you using to create your graphs?

What's the name of the software?

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)

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

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

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

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

thanks, from geottingen germany, 😛

Good Job!, Münster, Germany

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

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 ?

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

Thanks from Karlsruhe, Germany

Thank you, from Germany (RUB BOCHUM)

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

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

Awesome, very helpful!!

your videos are awesome thanks so much for doing them!

Thankkkkkkkkkkkk you!!!!!!!

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.

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!