M hnh tng trng SolowBi:

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M hnh tng trng Solow l mt m hnh thuyt minh v c ch tng trng kinh tdo Robert Solow v Trevor Swan xy dng ri c cc hc gi kinh t khc b sung.Solow nhn c gii Nobel v kinh t nm 1987 nh cng hin ny. M hnh nycn gi l M hnh tng trng tn c in v mt s gi thit ca m hnh da theo llun ca kinh t hc tn c in. M hnh ny cn c cch gi khc, l M hnh tngtrng ngoi sinh, bi v khng lin quan n cc nhn t bn trong, rt cc tng trngca mt nn kinh t s hi t v mt tc nht nh trng thi bn vng. Ch cc yut bn ngoi, l cng ngh v tc tng trng lao ng mi thay i c tc tng trng kinh t trng thi bn vng.

K hiu

* Y l sn lng thc t (hoc thu nhp thc t).

* K l lng t bn em u t.

* L l lng lao ng.

* y l sn lng trn u lao ng.

* k l lng t bn trn u lao ng.

* S l tit kim ca c nn kinh t.

* s l t l tit kim.

* I l u t.

* i l u t trn u lao ng.

* C l tiu dng c nhn trong nn kinh t.

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* c l tiu dng c nhn trn u lao ng.

* l t l khu hao t bn.

* l lng t bn tng thm rng.

* n l tc tng dn s, ng thi l tc tng lc lng lao ng.

H gi thit

Gi thit 1

Gi c linh hot trong di hn. y l mt quan im ca kinh t hc tn c in. Khiny, lao ng L c s dng hon ton, v nn kinh t tng trng ht mc tim nngv n nh.

ng thi, lc ny, ton b tit kim S s c chuyn thnh u t I (quy tc Say trongkinh t hc tn c in) V do , sY = I.

Mt khc, gi c lao ng (tc tin cng thc t) v gi t bn (tc li sut i vay) lcny cng s linh hot. V th, c th kt hp hai yu t ny sn xut mt cch tythch.

Gi thit 2

Mc sn lng thc t Y ph thuc vo lng lao ng L, lng t bn K vi nng sutlao ng A. T , ta c mt hm sn xut v m Y = F(A,L,K).

Gi thit l hm ny c dng Cobb-Douglas, tc l:

Y=AK^aL^{1-a}\,

Vi hm s dng Cobb-Douglas, nu ta nhn cc s nhn trong v phi vi cng mt s,th tch s bn v tri s tng ln cng s ln. Do vy, nu nhn 1/L vi L v K, thv tri s thnh Y/L tc l sn lng thc t trn u lao ng y. Cn K/L tc lng tbn trn u lao ng k. Hm sn xut v m s c dng sau:

Y=AK^aL^{1-a}\ \leftrightarrow y=Ak^a

Gi thit 3

Nn kinh t ng ca v khng c s can thip ca Chnh ph. Do , tng sn lng Ybng tng ca tiu dng c nhn C v u t I hay Y = C + I tng ng vi Y = C +sY v li tng ng vi C = (1-s)Y.

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Nu tnh trn u lao ng L, th s c tiu dng c nhn trn u ngi c bng snlng thc t trn u ngi y nhn vi 1-s hay c = (1-s)y.

Lu l 0 < s < 1.

Gi thit 4

C s khu hao t bn. Vi t l khu hao , mc khu hao s l K.

u t I lm tng lng t bn trong khi khu hao K lm gim lng t bn, nn mct bn thc t tng thm K s bng I - K.

C th vit quan h trn thnh:

\Delta K=sY-\,\delta K\,

Gi thit 5

T bn K v lao ng L tun theo Quy lut li tc bin gim dn. C ngha l khi khitng k th ban u y tng rt nhanh n mt lc no n tng chm li.

Gi thit 6

Hm y = f(k) l mt hm tng. th ca n c dng ng cong. Hm i = sf(k) = sycng nh vy, bi v u t trn u lao ng i l mt b phn ca sn lng trn ulao ng y.

Ch rng hm s y = f(k) l hm tng th o hm bc mt y' phi ln hn 0, mtkhc do n tun theo quy lut nng sut cn bin gim dn nn o hm bc hai y phinh 0. th ca hm s y = f(k) c hnh dng nh trong hnh v.

Gi thit 7

Thay i trong lc lng lao ng L th hin bng phng trnh sau:

L_{t+1}=L_t(1+gL)\,

trong , gL l hm s ca L.

ng thi gi thit l tc thay i lao ng ng bng tc thay i dn s n.

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Xc nh m hnh

Khi t bn trn u lao ng k tng, th gi tr khu hao k tng, hn na, dn n tbn mi trn u lao ng nk tng. Gi k + nk hay (+n)k l u t cn thit, v n bp phn ti sn b hao mn v p ng vn cho lao ng mi tng thm.

im A trn Hnh 1 l giao ca ng u t cn thit (+n)k v ng u t trn ulao ng i. N cho thy l mt s cn bng.

Ti trng thi vn trn u lao ng k1 nh hn k*, th u t i = sy ln hn u t cnthit (+n)k, c ngha l k = sy (+n)k > 0 do dn n k tng.

Ngc li, ti trng thi vn trn u lao ng k2 ln hn k*, th u t i = sy nh hnu t cn thit (+n)k, c ngha l k = sy (+n)k < 0, do k gim.

Ta c, k tng ln n mc k*, v ngc li khi n gim, th gim n mc k*. C haitrng hp tng v gim u t n mt trng thi cn bng. V ngi ta gi l imn nh hay trng thi n nh.

Ti trng thi n nh k*, chng ta nhn thy rng u t v u t cn thit cn bngnhau, hay ?k = sy (+n)k* = 0, tc tng ca sn lng trn lao ng bng khng(gy = 0), v tc tng ca vn trn mi lao ng bng khng (gk = 0).

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M hnh tng trng SolowS lcK hiuH gi thitGi thit 1Gi thit 2Gi thit 3Gi thit 4Gi thit 5Gi thit 6Gi thit 7

Xc nh m hnh