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The '''AK model of economic growth''' is an [[endogenous growth model]] used in the theory of [[economic growth]], a subfield of modern [[macroeconomics]]. In the 1980s it became progressively clearer that the standard [[Neoclassical economics|neoclassical]] exogenous growth models were theoretically unsatisfactory as tools to explore long run growth, as these models predicted economies without [[technological change]] and thus they would eventually [[convergence (mathematics)|converge]] to a [[steady state]], with zero per capita growth. A fundamental reason for this is the diminishing [[return of capital]]; the key property of AK endogenous-growth model is the absence of diminishing returns to capital.  In lieu of the diminishing returns of capital implied by the usual [[parameterization]]s of a [[Cobb–Douglas]] production function, the AK model uses a linear model where output is a [[linear function]] of capital.  Its appearance in most textbooks is to introduce [[endogenous growth theory]].


==Origin of the concept==


In [[neoclassical growth model]]s the economy is assumed to reach a steady state in which all macroeconomic variables grow at the same rate and in the absence of technological progress, per capita growth of these macroeconomic  variable will eventually cease. These kind of neoclassical prepositions have the resemblance with the philosophical contents in Ricardo and Malthus. The basic underlying assumption of neoclassical philosophical is that diminishing returns to capital operates in the production process.
It was the end of June. The weather was very hot but the Boss had prepared a full day`�s sales training in the conference room.<br>After a delicious meal, the sales people went back to the afternoon session. The boss did a short resume of the technical elements of the new products shown that morning. He had always been convinced that a mastery of knowing the technical features of a product was the basis of all long term achievement in sales.<br><br>But, in spite of their efforts, they battled to keep their eyes open. And after that he handed it to me. (I said to myself that this was the most tough time slot of the day, and the boss let me get it! How in the world am I going to pull these professionals out of their wish to take a nap?) Here is what I shared: �How many of you had an appointment with a customer, but who left only a couple of minutes before you arrived?<br><br>� Raise your hands please. � Who has had a consultation with a client, who listened to all you had to say extremely politely however when you started to close, he says: �I�m sorry but I've no more budget for this year. I can�t buy now�. All the hands were rais<br>.
How did you feel? Mike answered, � I just did an hour�s drive to go and see him. He could have told me on the phone. I'd have been better off going fishing that afternoon! �. All the others were laughing. I let them share some of their negative experiences concerning the sales they were counting on, but didn�t come to <br><br>.


During mid-1980s a new beginning of growth theory launched by [[Paul Romer]] in 1986,<ref>{{cite journal |title=Increasing Returns and Long-Run Growth |first=Paul M. |last=Romer |journal=[[Journal of Political Economy]] |volume=94 |issue=5 |year=1986 |pages=1002–1037 |jstor=1833190 }}</ref> where he tried to explain the growth process in a different manner. Thus the dissatisfaction out of neoclassical model motivated to construct new growth theories where the key determination of growth theories are endogenous in the model as in these new theories, the long run growth is not determined by exogenous factors setting up endogenous growth theories.
� That is completely frustrating, isn�t it? But the worst part is what we say: �The day is off to a bad start or is finishing like it started�. We begin worrying. �How will reach my objectives for the month? �Frankly, we do not feel sure of ourselves or our products a<br>more.
And each �No� or client who is absent, weakens our drive to continue. And in that case, we do not try as hard to close the next possible sale that comes up. � A) My very best sale ever Who would be interested by a perfect method to withstand all negative events of the day and never mis<br><br>sale?


The simplest version of endogenous model is AK models which assume constant exogenous saving rate and fixed level of technology. The stickiest assumption of this model is that production function does not include diminishing returns to capital. This means that with this strong assumption the model can lead to endogenous growth.
All of a sudden no one was tired any more. Well, according to Behavioral specialists, most people cannot think about two things at the same time. (Except you, of course, Mike.) Laughter. So it is most likely better if we direct our thoughts in the direction that will create the mo<br> sales.
What do you think? We've the tendency to create a series of events based on inadequate data. I did 4 sales demonstrations with out a [http://tinyurl.com/pch83be ugg boots sale] so the day is off to a poor start. Other days, right from the starting of the day, we did 3 demonstrations, three sales! For those days, I do not need to explain how to go <br><br>t it.


==Graphical representation of the model==<!-- This section is linked from [[Social capital]] -->
Smile. But for the days where we're struggling, what should we do? Does this interest you? Yes! � I have a lot of them, so I certainly wish to know! � stated Mike. You know that although I�m a Sales Director, I�m also selling on the field every day. I wouldn�t wish to tell you anything that I haven�t gone thro<br>h myself.
So I�m going to tell you about my best-ever sales day. I�ll always remember the evening of the 16th of January 1988. My oldest boy who was about 11 at the time ran to meet me with  [http://tinyurl.com/pch83be ugg boots sale] the important question for a family who lives from sales. � Daddy, just how much did you<br><br>l today?


� That way he could proudly bring this info to his mother who was cooking in the kitchen. A great day, at that time, was 5000 French francs. � Guess, � I stated to him. He knew that 5000 was good. Five thousand. More! 10000 ! More ! 20000 ? More ! He began<br>etting giddy.
He ran to see his little brother. It is more than 20000! His little brother continued the bidding. 30000. More! 40000? More! My turn, said Nathan. 50000 ? More! Mommy, Mommy, It�s more than 50000 ! Is that true ? She immediately came, carrying our infant. 60000 ? Nat cont<br><br>d : 70000 ?


The AK model production function is a special case of a Cobb–Douglas function with [[constant returns to scale]].
More ! Eighty-thousand ??? More ! He breathed deeply and closed his eyes. 100000 ? A little less than 93000 in three sales. The client that bought 84000 francs from me between 10 and 12 said I would be paid in 14 days� time! At that time, I was in big finan<br>al difficulty.
: <math>Y=AK^aL^{1-a}\,</math>
I completely needed the money to come in so I could pay my bills. (I had about 30% pure profit on those sales!) Following three weeks our accountant said that the money was in and that he could give us a bank check if we needed an  [http://tinyurl.com/pch83be ugg boots] advance in commissions! We asked him if we could come by today away simply because our banker was<br><br>eatening us.


This equation shows a Cobb–Douglas function where ''Y'' represents the total production in an economy. ''A'' represents [[total factor productivity]], ''K'' is capital, ''L'' is labor, and the parameter <math>a</math> measures the [[output elasticity]] of capital. For the special case in which <math>a = 1</math>, the production function becomes linear in capital and does not have the property of decreasing returns to scale in the capital stock, which would prevail for any other value of the capital intensity between 0 and 1.
All right, come. There was an hour�s drive between our company and our bank. Our boys wanted completely to come with us. On the way back there was a MacDonald�s Restaurant. We stopped there to [http://www.bbc.Co.uk/search/?q=celebrate celebrate]. And we digested it very well (the money I mean). The sales persons gave this story a long applause simply because they have<br>ll been there.
They've all had the large unexpected sale that saved an otherwise horrible month. So I continued. Who has already had a great sale like that? All the hands had been raised, even Mike�s. Alright, this really is what I recommend. Write down on this 3 by 5 Bristol card and describe your<br><br>t sale ever.


<math>n</math> = [[population growth rate]]<br>
Take your time. The idea would be to describe your emotional state before the sale, what you felt when you saw it was going to be a mega sale, and detail the emotions that you had when you told  [http://tinyurl.com/pch83be ugg boots usa] your family and friends about it (or even your boss!). There was a �religious� silence as each one savored some of the memorable moments of their profession. Even the boss, sitting at the back of the room <br><br>writing away!
<math> \delta\ </math> = [[depreciation]] <br>
<math>k</math> = capital per worker <br>
<math>y</math> = output/income per worker<br>
<math>L</math> = labor force <br>
<math>s</math> = saving rate


In an alternative form Y=AK, K embodies both physical capital and human capital.
B) OK, tell us your story, and share with us the feelings you felt! Following some time, I asked who wished to share their best-ever sale. Jean-Marc told us how a transport company that he had prospected months before with out success contacted our service and invited him to ask fo<br><br> appointment.


: <math>Y=AK\,</math>
He said to himself that he might do a great day�s sale, perhaps 5-6000 euros. He was far under! The client wanted to restructure all his archives and be able to find all his documents in 2 seconds. It just happened to be that we had a numeric filing system with folders manufactured in polypropylene in different sizes adapted to his profession. In fact, the client bought 40000� worth of this innovative filing  [http://tinyurl.com/pch83be ugg boots usa] system that Jean-Marc so<br><br>hat very day!


In the above equation A is the level of technology which is positive constant and K represents volume of capital.
He told us that the same client, one month later sent a second order of the same quantity for another department! Mohamed told us how he drove by a company for the last 10 years hidden in a curve of the road. He truly sensed that this looked like an inte<br>sting prospect.
Hence, output per capita is:
But there was no way of stopping and he couldn�t see exactly where the entry road was. But one month of December, times were so difficult, and the sales had been so low, that he said he had nothing to lose to spend some time to attempt to find the entrance<br><br>this company.
: <math> \frac{Y}{L}=A.\frac{K}{L} </math>  ''i.e.''  <math> y = Ak </math>


The model implicitly assumes that the average product of capital is equal to marginal product of capital which is equivalent to:
He was warmly welcomed by the potential client and the he purchased every thing Jean-Marc had to sell. � You know, I don�t have time to go to town to get what I need. It doesn�t bother me to pay a bit more, if somebody comes to visit me. But it�s been ten ye<br>s that I�m here.
I've ever seen a single salesman! � My colleague waived ten years of sales because he didn�t follow his intuition! This totally unexpected sale was equivalent to 3 weeks sales in normal times and it permitted him to appreciate Christmas time with his family. I recommended that they would put themselves two-by-two to share their best-ever sa<br><br>ith each other!


<math>A > 0</math>
(It is much better than sharing your latest disaster, isn�t it?) No one saw the time fly. We were all on another planet! Even Mike (for once) had a great sales adventure to tell the others. Conclusion i) An infallible method to resist negative events durin<br><br>ur selling day.


The model again assumes that labor force is growing at a constant rate ‘n’ and there is no depreciation of capital. (δ = 0 )
ii) How never again miss a sale and always be on top of things. iii) Describe your best sale, write it down, and think of your feelings before and after. iv) Even when you feel depressed, you may be only a minute away from your best sale ever. What do yo<br><br>ink about that?
In this case, the basic differential equation of neo-classical growth model would be:


<math> k(t) = s.f(k) - nk </math>
v) Write several of these stories to encourage you throughout difficult moments. Why not describe your best weekly sale? If you do not encourage your self, who will? AA/01/13 Andre Amsing is the writer of the articles on website and if you would want to find out the very best online profit model that [http://search.usa.gov/search?query=John+Chow John Chow] shares in his new e book �The Ultimate Online Profit Model click right here: website top salespersons have the ability to resist negative influences
 
Hence, <math> \frac{k(t)}{k} = s. \frac{f(k)}{k} - n </math>
 
But in the model   <math> \frac{f(k)}{k} = A </math>
 
Thus,  <math> \frac{k(t)}{k} = s. A - n</math>
 
==See also==
* [[Economic growth]]
* [[Human capital]]
* [[Harrod–Domar model]]
 
==References==
{{Reflist}}
 
==Further reading==
*{{cite book |last=Acemoglu |first=Daron |chapter=First-Generation Models of Endogenous Growth |pages=387–407 |title=Introduction to Modern Economic Growth |location=Princeton |publisher=Princeton University Press |year=2009 |isbn=978-0-691-13292-1 }}
*{{cite book |title=Economic Growth |first=Robert J. |last=Barro |first2=Xavier |last2=Sala-i-Martin |edition=Second |location=Cambridge |publisher=MIT Press |year=2004 |isbn=0-262-02553-1 }}
 
{{Macroeconomics}}
 
[[Category:Economic growth]]
[[Category:Economics terminology]]
[[Category:Economics models]]

Revision as of 22:39, 2 March 2014


It was the end of June. The weather was very hot but the Boss had prepared a full day`�s sales training in the conference room.
After a delicious meal, the sales people went back to the afternoon session. The boss did a short resume of the technical elements of the new products shown that morning. He had always been convinced that a mastery of knowing the technical features of a product was the basis of all long term achievement in sales.

But, in spite of their efforts, they battled to keep their eyes open. And after that he handed it to me. (I said to myself that this was the most tough time slot of the day, and the boss let me get it! How in the world am I going to pull these professionals out of their wish to take a nap?) Here is what I shared: �How many of you had an appointment with a customer, but who left only a couple of minutes before you arrived?

� Raise your hands please. � Who has had a consultation with a client, who listened to all you had to say extremely politely however when you started to close, he says: �I�m sorry but I've no more budget for this year. I can�t buy now�. All the hands were rais
. How did you feel? Mike answered, � I just did an hour�s drive to go and see him. He could have told me on the phone. I'd have been better off going fishing that afternoon! �. All the others were laughing. I let them share some of their negative experiences concerning the sales they were counting on, but didn�t come to

.

� That is completely frustrating, isn�t it? But the worst part is what we say: �The day is off to a bad start or is finishing like it started�. We begin worrying. �How will reach my objectives for the month? �Frankly, we do not feel sure of ourselves or our products a
more. And each �No� or client who is absent, weakens our drive to continue. And in that case, we do not try as hard to close the next possible sale that comes up. � A) My very best sale ever Who would be interested by a perfect method to withstand all negative events of the day and never mis

sale?

All of a sudden no one was tired any more. Well, according to Behavioral specialists, most people cannot think about two things at the same time. (Except you, of course, Mike.) Laughter. So it is most likely better if we direct our thoughts in the direction that will create the mo
sales. What do you think? We've the tendency to create a series of events based on inadequate data. I did 4 sales demonstrations with out a ugg boots sale so the day is off to a poor start. Other days, right from the starting of the day, we did 3 demonstrations, three sales! For those days, I do not need to explain how to go

t it.

Smile. But for the days where we're struggling, what should we do? Does this interest you? Yes! � I have a lot of them, so I certainly wish to know! � stated Mike. You know that although I�m a Sales Director, I�m also selling on the field every day. I wouldn�t wish to tell you anything that I haven�t gone thro
h myself. So I�m going to tell you about my best-ever sales day. I�ll always remember the evening of the 16th of January 1988. My oldest boy who was about 11 at the time ran to meet me with ugg boots sale the important question for a family who lives from sales. � Daddy, just how much did you

l today?

� That way he could proudly bring this info to his mother who was cooking in the kitchen. A great day, at that time, was 5000 French francs. � Guess, � I stated to him. He knew that 5000 was good. Five thousand. More! 10000 ! More ! 20000 ? More ! He began
etting giddy. He ran to see his little brother. It is more than 20000! His little brother continued the bidding. 30000. More! 40000? More! My turn, said Nathan. 50000 ? More! Mommy, Mommy, It�s more than 50000 ! Is that true ? She immediately came, carrying our infant. 60000 ? Nat cont

d : 70000 ?

More ! Eighty-thousand ??? More ! He breathed deeply and closed his eyes. 100000 ? A little less than 93000 in three sales. The client that bought 84000 francs from me between 10 and 12 said I would be paid in 14 days� time! At that time, I was in big finan
al difficulty. I completely needed the money to come in so I could pay my bills. (I had about 30% pure profit on those sales!) Following three weeks our accountant said that the money was in and that he could give us a bank check if we needed an ugg boots advance in commissions! We asked him if we could come by today away simply because our banker was

eatening us.

All right, come. There was an hour�s drive between our company and our bank. Our boys wanted completely to come with us. On the way back there was a MacDonald�s Restaurant. We stopped there to celebrate. And we digested it very well (the money I mean). The sales persons gave this story a long applause simply because they have
ll been there. They've all had the large unexpected sale that saved an otherwise horrible month. So I continued. Who has already had a great sale like that? All the hands had been raised, even Mike�s. Alright, this really is what I recommend. Write down on this 3 by 5 Bristol card and describe your

t sale ever.

Take your time. The idea would be to describe your emotional state before the sale, what you felt when you saw it was going to be a mega sale, and detail the emotions that you had when you told ugg boots usa your family and friends about it (or even your boss!). There was a �religious� silence as each one savored some of the memorable moments of their profession. Even the boss, sitting at the back of the room

writing away!

B) OK, tell us your story, and share with us the feelings you felt! Following some time, I asked who wished to share their best-ever sale. Jean-Marc told us how a transport company that he had prospected months before with out success contacted our service and invited him to ask fo

appointment.

He said to himself that he might do a great day�s sale, perhaps 5-6000 euros. He was far under! The client wanted to restructure all his archives and be able to find all his documents in 2 seconds. It just happened to be that we had a numeric filing system with folders manufactured in polypropylene in different sizes adapted to his profession. In fact, the client bought 40000� worth of this innovative filing ugg boots usa system that Jean-Marc so

hat very day!

He told us that the same client, one month later sent a second order of the same quantity for another department! Mohamed told us how he drove by a company for the last 10 years hidden in a curve of the road. He truly sensed that this looked like an inte
sting prospect. But there was no way of stopping and he couldn�t see exactly where the entry road was. But one month of December, times were so difficult, and the sales had been so low, that he said he had nothing to lose to spend some time to attempt to find the entrance

this company.

He was warmly welcomed by the potential client and the he purchased every thing Jean-Marc had to sell. � You know, I don�t have time to go to town to get what I need. It doesn�t bother me to pay a bit more, if somebody comes to visit me. But it�s been ten ye
s that I�m here. I've ever seen a single salesman! � My colleague waived ten years of sales because he didn�t follow his intuition! This totally unexpected sale was equivalent to 3 weeks sales in normal times and it permitted him to appreciate Christmas time with his family. I recommended that they would put themselves two-by-two to share their best-ever sa

ith each other!

(It is much better than sharing your latest disaster, isn�t it?) No one saw the time fly. We were all on another planet! Even Mike (for once) had a great sales adventure to tell the others. Conclusion i) An infallible method to resist negative events durin

ur selling day.

ii) How never again miss a sale and always be on top of things. iii) Describe your best sale, write it down, and think of your feelings before and after. iv) Even when you feel depressed, you may be only a minute away from your best sale ever. What do yo

ink about that?

v) Write several of these stories to encourage you throughout difficult moments. Why not describe your best weekly sale? If you do not encourage your self, who will? AA/01/13 Andre Amsing is the writer of the articles on website and if you would want to find out the very best online profit model that John Chow shares in his new e book �The Ultimate Online Profit Model click right here: website top salespersons have the ability to resist negative influences

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