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Intermediate Macroeconomics Notes Week #9

by: Zachary Hill

Intermediate Macroeconomics Notes Week #9 ECON 3020

Marketplace > Tulane University > Economcs > ECON 3020 > Intermediate Macroeconomics Notes Week 9
Zachary Hill
GPA 3.88

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About this Document

These notes cover an in-depth look at the Solow Growth Model, continuing over from the notes for Week #8.
Intermediate Macroeconomics
Antonio Bojanic
Class Notes
Econ, ECON 3020, 3020, Macroeconomics, Economics
25 ?




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This 5 page Class Notes was uploaded by Zachary Hill on Sunday March 13, 2016. The Class Notes belongs to ECON 3020 at Tulane University taught by Antonio Bojanic in Fall 2015. Since its upload, it has received 18 views. For similar materials see Intermediate Macroeconomics in Economcs at Tulane University.


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Date Created: 03/13/16
ECON 3020 Notes for Week #9  7 March 2016  The Solow Growth Model (continued)  0.3 0.7 ● We know that in the US Y = F(K, L) = AK L   ● Then g = g + 0.3g + 0.7g ; this is called the growth accounting equation  Y A K L 0.3Y 0.7Y ● Remember that MP = K K  and MP = L L   ● Then, from Y = AK L 0.3 0., ΔY = ∂Y ∙ ΔA + ∂Y ∙ ΔK + ∂Y ∙ ΔL  ∂A ∂K ∂L 0.3 0.7 0.3 0.7 ○ ∂A = K L = AK A = A   ∂Y ∂Y ∂Y Y ○ so ΔY = ∂A ∙ ΔA + ∂K ∙ ΔK + ∂L ∙ ΔL = A ∙ ΔA + MP ∙ KK + MP ∙ ΔL L  A ∙ ΔA + 0K3Y∙ ΔK + 0L7Y∙ ΔL  1 ΔY ΔA ΔK ΔL ○ when you multiply both sides by  , you Yet  Y = A + 0.3 K + 0.7 L   ○ so g =Yg + A.3g + 0.Kg   L ● A, the total factor productivity, is not directly observable, so it is difficult to measure g   A 0.3 0.7 ● We can rearrange Y = AK L  to get A = 0.3 0.7in order to specify, we will notate this  K L Yt as A t K0.L0.7 where t is some time; A  is talled the Solow Residual and has the  t t greatest impact on g   Y ● The Solow Growth Model tries to explain what allows K  per worker to grow over time  ● Assume L is fixed over a period of time  Y C I K ● Because we are working with per worker values, Y = t, C = t, i = t, and K = t  t Lt t Lt t Lt t Lt Y 0.3 0.7 0.3 0.3 ● Then Y = t L t= AK L = AK0.3= AK t   t L ●   ● Assume we are working with a closed economy with no government   ● Then Y = t + it  t ● Solow assumed households would save a fixed fraction of their disposable income, so  Y −tC = St  wheretS is the savings rate  ● Then i = SY , which we know to be true in a closed economy  t t 0.3 ● Then i = tAK t         9 March 2016  The Solow Growth Model (continued)  ● A is given in the Solow Growth Model  ● Solow assumed depreciation would be a constant fraction of the existing capital stock;  depreciation = dK   t 0.3 ● Remember that i = SAK t t ; this establishes a relationship between investment per  worker and capital per worker  ●   ● For the capital to grow, the economy must invest at a rate higher than the depreciation of  existing capital  ● ΔK =ti −tdK ; ttis is the capital accumulation equation  0.3        = SAK t − dK t ● At point S, capital stock stays the same; referred to as the steady state, where  0.3 SAK t = dK  t ● If a country is operating at K , i > 1K ,tso capttal stock is increasing until it reaches the  steady state  ● If a country is operating at K , i < dK , so capital stock is decreasing until it reaches the  2 t t steady state  ● Then, in the long run, all economies will tend toward the steady state, or the point where  0.3 SAK t = dK  t ● Remember that Y = C + i , so C = Y − i = Y − SY = Y (1 − S)  t t t t t t t t t ●   ● So when K  goes to K , Y  and C  increase; when K  goes to K , Y  and C   * 1 t t 2 t t decrease  Application:  ● 2 countries with the same production functions  ● Country A (the US) performs at a K < K ; country B (China) performs at a K << K   * * ● They should both converge at K  in the long run  * ● Country A will only achieve a certain level of growth per year because it is close to K   ● Country B’s growth level will be higher than that of country A because it is further away  * from K   ● There will be conditional convergence; across similar countries there will be the same  convergence; between dissimilar countries there will not be convergence between the  two  ● Best example supporting Solow’s theory is Japan and Germany post WWII        11 March 2016  Classes Cancelled 


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