Giáo trình lý thuyết mô hình toán kinh tế

TRUONG DAI HOC KINH TE QUOC DAN K H O A T O A N K IN H T E PGS TS HOANG DiNH TUAN N H A X U A T B AN D A I H O C K IN H T E Q U O C D A N HA NOI - 2007 TRUONG DAI HOC KINH i t Q U 6c DAN BO m ON TOAN KINH t £ v>° cm 0 (4.139) Nhu v&y chinh phu sir cac chinh sach kinh te vT mo lam tang ty suat rich luy s se tao trang thai ben virng mod ung vdi k* mdi Ion hem Phan tich tac dong cua s tdi c* Theo (4.131), miic tieu dung tinh theo dau ngudi b trang thai ben vung c* se la: c*(s) = f(k*(s)) - (n+h)k’(s) (4.140) Ta se tim mric s cho c*(s) dat tdi da Ta co: dc* _ df(k*(s)) dk* _ ( n + h )d k ds dk ds ds hay dc ds df(k (s)) dk dk* dc (n + h) -, (4.131) n d n - = Okhi va chi khi: ds ds df(k*(s)) dk - ( n + h) = (4.141) Ky hidu nghiem cua (4.141) la sVJng va k* tuong ring la kv;ing sVang goi la ty suat tich luy “vang” Ta co: d f(k Vang) _ (n + h) dk (4.142) Di6u kidn (4.142) goi la “quy tic vang cua rich luy vo'n” Vdi sving, kv^ng ta co tieu dung theo dau ngirdi dat mric cao nhat, ky hieu la cvimg, ta co cv;ing = f(kvtog) - (n+h)kva,lg Mat khac ta lai co mile dau tu theo dau ngirdi ung vdi sVang, kVang la iVang= (n+h)kVang Nhu vay vdi ty suat tich luy “vang” sVang Trurdng Dai hoc Kinh te Quoc dan 331 GIAQ TRINH LY THUYET MO H1NH TOAN KINH TE _J he kinh te vita nghi toi the' he tuong lai (dau tu ivtag) vua quan tarn tai the he then tai m6t each toi da (tieu dung cving) Thi du 4.9 Ta hay xet mo hinh Solow - Swan voi ham san xuat dang Cobb - Douglas: Y =K“L l a vdi < a< l Ta co f(k) = k“ Phuong trinh vi phan doi vdi k la: k = sk“ - (h+n)k De giai phuong trinh tren ta dat z = k 1' trinh tren phuong trinh: co the bie'n doi phuong z + (1 - oc)(n+h) z = (1 - a)s Nghifm cua phuong trinh tren co dang: z(t) = [z(0) - (s/(n+h))] e ■(|-a)(n+h)t + (s/(n+h)) Suy ra: k 1' “(t) = [k(0)‘ ■“ - (s/(n+h))] e -(I-a>(n+h), + (s/(n+h)) Ta co k1' “(t) ->• s/(n+h) t -»+oo do k(t) -> [s/(n+h)]l/(l' a) t ->+oo Nhu valy: 1-a * s k n +h Ta co nhip tang trubng cua k: Theo (4.128) g k = k - (h + n) suy ra: g k = - ^ (h + n) = sk“ - (n + h ) k Nhip tang truong cua y: Theo (4.129), ta co a = 1- a suy gy= a g k = a [ s k a_! - ( n + h) ] Tai trang thai bdn vung ta co tieu dung theo dau ngudi c (s) = f(k (s)) (n+h)k*(s), suy ra: r a r “i s s l_a - (n / + i.\ h) n+h n+h 33a Trirdng Dai hoc Kinh te Qudc dan Ctw&ng tV MS hinh kinh SSng Ta xac dinh ty sua't tfch luy “vang”, theo (4.142): — ^ Vang^ = (n + h ) , dk ct-1 1-a suy a k “ = n + h Thay k bbi k’ ta dirge a n+h = (n + h ) , hay S Vang= a - Do kving= a 1-a n+h suy ra: a Oying ]-a n+h - (n + h) i 1-a a n +h C hu y: Neu ham san xuat co dang Y =AK“L'~a vbi A >0, < a < l cac chi tieu se dirge tinh befi cac cong thuc sau: i sA -a sA' -a sA -a - ( n + h) , gk = sAka' ‘ - (n + h) k* = C = n+h n+h n+h va g = a g k Thf du 4.10 Ta hay xet m6 hinh Solow - Swan doi vdi n6n kinh te co ham san xuat Y =K°’5L0’5, hang nam kh6ng co tang dan so, co ty le tiet kiem:15%, ty le khau hao von: 5% a Hay tinh ty le von/lao dong, thu nhap va lieu dung theo dau ngubi cs trang thai b6n virng b Neu hien tai ty 16 von/lao d6ng cua n6n kinh te' la 4, hay tinh thu nhap, tieu dung, dau tu theo dau ngubi va nhip tang trubng hien tai Phai mat khoang bao nhieu nam n6n kinh t6' se dat tbi trang thai b6n vung? Giai: Sir dung cac ky hieu cua mb hinh ta co: a = 0,5; h = 0,05; n =0 va k0 = a Theo thf du 4.9, a trang thai b6n vung ta co: Ty 16 vb'n/lao dbng k ’ s -a _n + h- '0 ,1 ' 0,05_ ,5 =9 Thu nhap y* = f(k ’) = (k*)“ = 90’5 = Trirdng Dai hoc Kinh id' Quoc ddn 333 GlAO TRlNH LY 7HUYI=T M HlNH toA N KINH t £ a Ti6u dung c* = s _n + h_ 1-a - ( n + h) S n+h = - , 05x32 = 2,55 b Hi6n tai k0 = do y0 = f (k0) = (k0)“ = 40,5 = 2, c0 = ( l - s ) f ( k 0) = 0,85(k0)a = 0,85x4°’5 =1,7 suyra: i0 = y0 - c0 = 0,3, day la muc dau tu tho tinli theo d&u nguoi, mdc dau tu rong se la: 0,3-hk= 0,3 - 0,1 = 0,2 Chi tieu the hien mile thu hut von diu tu cua n6n kinh te Ta co gk = ska_1- ( n + h) = 0,15x40,5-0 ,0 = 0,025 n6n nhip tang tnrcmg hien tai: gy= a g k = 0,5x0,025 = 0,0125 ~ 1,25%/nam Ta co tai nam t: y, = y0(l + gy)( , c&n xac dinh T de yT = y0(l + gy)T = y* Suy ra: T Ln (1 + gy) = Ln (y y 0) do: T = L n ( y * 1y ) _ Ln (3 / 2) _ 63 L n (1 + g y ) Ln ( 1, ) ~ tuc la mat khoang 33 nam ndn kinh te se tang truerng tod trang thai b6n vflng Ta co hinh ve minh hoa: Mo hinh tang trifdng kinh te Solow - Swan vdi tien bo cong nghe Chung ta hieu tien bo cong nghe (TBCN) la ta't ca nhftng gi d&n den viec tang san lupng Y ma khong can tang cac nhan t6' dupe sir dung Trong 334 Trifdng Dai hpc Kinh te Qud'c dan thdi dai hien nay, khoa hoc - cong nghe da trd nganh san xuat true tiep thi san pham cua nganh ctiinh la TBCN Viec san xuat va sir dung san pham dac biet doi hoi nhung y£u to v |t chat nhat dinh, phai co dau tu vdn (von vat chat va von ngucri) Thanh thir chung ta co the’ coi tac dong cua TBCN duoc vat chat hoa von va lao dong Su vat chat hoa cua TBCN lao ddng bieu hien a viec su dung lao dong hieu qu a hon Vdi mot so lao dong nhat dinh, tac dong cua TBCN se tuong duong vdi viec su dung nhi£u hon Nhu vay su tang tnrdng cua ngu6n lao dong ngoai viec tang tu nhidn theo mure tang cua dan so tang bed tac dong cua TBCN Ngu6n lao dong duoc goi la nguon lao dong hieu qua ky hieu la L, ham san xuat se co dang: Y = F (K, L) vdd L = A(t)L Vdi gia dinh nhip tang nguon lao dong TBCN la A, thi Nhip tang trudng cua nguon lao dong hieu qua se la: g£ = n + X (4.143) Phuong trinh vi phan bieu hien qua trinh tang trudng cua ti suat v6n/ lao dong hieu qua se co dang: k = s (k) f (k) - (n + h + A) k (4.144) vdi k se la K/ £ So vdi trudng hop tang trudng chua tmh den TBCN thi phuemg trinh tren co them hang so X d ve phai Do phan tfch hoan toan tuong tu nhu d tren ta se duoc cac ket qua tuong tu Di6u kien de dam bao cho nen kinh te tang trudng can dd'i trudng hop co tfnh den tac dong cua TBCN la giu'a ti suat tfch luy va ti suat von/ lao dong phai co moi lien he: s(k) f(k) = (n + h + X) k (4.145) Ky hieu n + h + X = v didu kien tren co dang: s(k)f(k) = vk (4.146) Neu ty sua't tfch luy s khong phu thuoc vao k thi phuong trinh co dang: k = sf (k) - vk Khi di6u ki6n de dam bao tang trudng can doi la: sf (k) = vk Ky hieu k* la nghiem cua phuong trinh, quy dao tang trudng can doi se la:k(t) = k* Cac quy dao tang trudng khac se hoi tu tdi quy dao tren T Trifdng Dai hoc Kinh te Quoc dan 335 GlAO TRiNH L? THUYST HlNH TOAN KfNH Tg Nhir vay diem khac biet d md hinh trudng hop co TBCN la tai trang thai bdn vung cac chi tidu Y,K,C se tang truong vdi nhip dp la n + X, turc la bang nhip tang cua lao ddng cong vdi nhip tang cua tidn bp c6ng nghp Hach toan tang trucfng a Khdi niem hach toan tang trudng (Growth Accounting) Qua trinh tang trudng kinh te cua nhidu quoc gia cho thay dong gop cho tang trudng ngoai nhan to von, lao dong co nhieu nhan to khac dupe goi chung la “nhan td tdng hop” Vai tro cua nhan td tdng hop tang trudng thudng dupe ly giai nhu tac dong cua tien bo va hi6u qua cua cong nghe Cac phuong phap, ky thuat tinh toan su dong gop rieng re cua nhan td vdn, lao dong va nhan td tdng hop tang trudng san lupng goi chung la hach toan tdng trudng Thuc hien hach toan tang trudng se giup ta xac dinh tarn quan cua cac nhan td dac biet la nhan td tdng hop tang trudng, tfir co the dd xua't cac chrnh sach thich hop nham phat huy tdi da hieu qua sd dung nhan td ndn kinh td phuc vu muc tidu tang trudng nhanh va bdn vung Ve phuong didn thuc hanh, vdi ham san dang tan cd dien va co sd du lidu day du chung ta cd thd thuc hidn hach toan tang trudng vdi tin cdy cao b Thuc hanh hach toan tdng trudng Phuong trinh hach toan tang trudng Trong chuong phan dd cap vd ham san xua't tan cd dien ta da biet: gv= gA+ gK «* + giA (4.147) vdi gY: nhip tang trudng san lupng (tang trudng kinh td), gK, gL: nhip tang trudng cua vdn, lao dong, sK, sL: hd sd co gian cua san lupng theo vdn, lao dong Td day ta cd: gA= gv - gK% - g A (4.148) Nhu vay ta cd thd tmh dupe tac ddng cua nhan td tdng hop tdi tang trudng kinh td Phuong trinh (4.147) dupe goi la phuong trinh hach toan tang trudng Phan duSolow Xet md hinh Solow vdi ham san xua't cd dang Y =AKaL l_ “ vdi A >0, < a < l Khi phuong trinh hach toan tang trudng se cd dang: 336 Trudng £>ai hoc Kinh ie Qu6c ddn Chitting tV Mo hinh kinh tedong Suy gY= gA+ a g K+ (1 -a)g L (4.149) gA= gY - a g K - (1 -a)gL (4.150) va dai lupng goi la phdn du Solow, phan lai tang trudng kinh te sau da khau trd phan dong gop cua von va lao dong Uac lugng phdn du Solow Vdi ham san xuat trdn, ky hidu LY = LnY, LK = LnK, LL = LnL va LA= LnA ta dupe: LY= LA + aL K + (l-a)L L Xet mo hinh kinh te lupng tuemg dng: LYt = p0 + p ,LKt + p2LLt + st (4.151) TO chuPi thai gian cua LY, LK va LL ta ude lupng mo hinh (4.151) thu dupe cac ude lupng: P0.P1.P2 Co th£ sd dung cac ude lupng de: - Kiem dinh tinh chat hieu qua khdng doi theo quy md cua ham san xudt mo hinh Solow (gia thidt: p,+p2= l) - l/d c lupng a phuang trinh hach toan do co the ude lupng ph£n du Solow Trong thuc te co the mot sd' gia thiet mo hinh Solow khdng dupe thoa man, thf du: ham san xuat co hieu qua tang theo quy md, ndn kinh te canh tranh khdng hoan hao de ude lupng phan du Solow can sd dung md hinh kinh te lupng co dang phde tap hon Trirdng Oai hoc Kinh te Qu6'c d in 337 GIAO TRINH LY'THUYETMO HINH TOAN KINH TE b Ai TAP CHGCNG IV Cho md hinh can bang rieng: D(t) = a - bp(t) S(t) = -c + dp(t) p = k(D (t) - S(t)) (1) vdi a,b,c,d, k > Cho p* = a + C , ky hieu r =k(b+d) b+d a Neu y nghia cua p* chdng to rang (1) co the vie't dudi dang: jjc P = r ( p ( t) - P )• b N6u dat A(t) = p(t) - p*, neu y nghia cua A(t) Chimg to rang (1) co the v id dudi dang: A - rA(t) = c Xac dinh quy dao cua A(t) va khao sat su 6n dinh Cho mo hinh: D(t) = a - bp(t) + ep S(t) = -c + dp(t) vdi a,b,c,d > a Neu toe thay doi gia ty 16 vdi mire dir cau, hay xac dinh quy dao gia b Vdi dilu ki6n nao cua e thi quy dao gia on dinh? Cho m6 hinh: D(t) = a - bp(t) - ep S(t) = dp(t) vdi a,b,d, e > a Neu thi trirdng ludn c&n bang tai moi thdi diem, hay xac dinh quy dao gia b Hay khao sat su on dinh cua quy dao gia 33& TrLfdng Dai hoc Kinh te Quoc dan Ctwtfng IV M6 hinh kinh tefddng Hay lap va phan tich cac m6 hinh kinh te lirong tucmg ling vdi mo hinh can bang thi truing vdi dy tfnh ve gia va co dy tru a Hay xac dinh co che gia, gia can bang (dai han) va tfnh on dinh cua cac mo hinh mang nh6n sau: 1) Dt = 18 - 3pt; St = -3 +4pt_, 2) Dt = 22 - 3pt; St = -2 + pt_, 3) D, = 19 - 6pt; St = -5 +6pt_, b N6u tai thdi diem bat dau xem xet co cu soc lam miic cung giam 12 Hay tfnh gia thi trircmg sau ky Xet mo hinh can bang thi trircmg vdi dy tfnh v i gia a N6u g = l, mo hinh co dang nao? co the coi mo hinh mang nhen la mot trircmg hop rieng cua mo hinh nay? Dieu kien on dinh cua m6 hinh la rong hon hay chat hon so vdi m6 hinh mang nhen? b Cho bang sd li6u tham so cua cac mo hinh: a b c d g I 102 40 120 20 0,15 II 100 75 0,22 III 60 12 45 0,34 Mo hinhXTham s6 1) Hay vi6t cac m6 hinh, xac dinh co ch£ gia, gia can bang dai han, quy dao gia va khao sat tfnh on dinh 2) N6u tai thcri diem bat dau xem xet thi triromg mdc cung la 20 va duoc ban het, toi thieu sau bao nhieu ky chenh lech giira gia thi trircmg va gia can bang dai han se nho hon 1,5%? a Hay xac dinh co che gia, gia can bang (dai han) va tfnh on dinh cua cac mo hinh can bang co dy trff vdi he s6 dieu chinh gia la 0,1 dudi day: 1) Dt = 18 - 3pt; St = -3 +4pt 2) Dt = 22 - 3pt; St = -2 + pt 3) Dt = 19 - 6pt; St = -5 +6pt b N6u tai thdi diem bat d£u xem xet co cu soc lam mure cung giam 12 Hay tfnh gia thi truemg sau ky Trirdng Dai hoc Kinh te Quoc dan S39 GIAO TRlNH L? THUYgT MO HlNH T0ANK1NHT£' Xet mo hinh: Dt = 21 - pt St = - + pt P t+i = Pt - 0,3 (QSt - QDt) hay xac dinh quy dao pt va khao sat su on dinh Xet mo hinh can bang thi trudng vdi du tru, ham cung la co dinh: Qa = k a Phan tfch quy dao gia pt b Vdi didu ki6n nao cua k quy dao tr6n co y nghTa kinh te? 10 Hay vidt va phan tich m6 hinh Keynes dau tir phu thuoc vao muc tang trirbng kinh te 11 Xet mo hinh Keynes: Yt = Ct + It; C, = a + bYt_, vdi a,b > 0, b < a Neu It la ngoai sinh, hay xac dinh quy dao cua Yt va khao sat tfnh dn dinh b Vdi a =40, b = 0,6, It = 134, hay xac dinh quy dao cua Yt Neu It = 110 hay xac dinh can bang lien thdi va minh hoa qua trinh hdi tu 12 Cho mo hinh: Yt = Ct + I0 + G0 + NX0 Ct = 400 + 0,6Yt_, G0 = 1000, NX0 = 300 va I0 = 600 a Hay xac dinh thu nhap can bang va khao sat tinh dn dinh b N6u ban dau ndn kinh te d trang thai can bang nhung co cu sdc nen chi tieu cua chinh phu giam 900 Tim thu nhap va tieu dung sau ky Tim ty le sai lech giua thu nhap sau ky vdi thu nhap can bang 13 Xet mo hinh dudng Phillips tdng quat: pt = 0,4 - 3,7Ut - 0,03 Ut+1 - U t = - 9(0,05 - p t+1) va dcm vi thdi gian t: nam a Hay xac dinh ty 16 lam phat va ty 16 tha't nghiep can bang va khao sat tfnh dn dinh 340 Trurdng Dai hoc Kinh Id' Quoc d3n Chitting IV M6 Mnh kinh d6ng b Ne'u hien ty 16 lam phat: 6,5%/nam, ty 16 that nghiep: 7%/nam Hay du doan hai ty 16 tren sau nam 14 Mot nen kinh te' co he so ICOR la 3,21 va tong san pham nubc (GDP) nam t la 32 ty USD a Hay giai thfch y nghla cua he sd' ICOR N6'u nhip tang trubng cua GDP cac nam tie'p theo la 8% thi d6'n nam (t +5) GDP se la bao nhieu? b Sir dung mo hinh Harrod - Domar khbng co tr6 de lap bang dir bao nhu cau dau tu tb nam (t+1) den (t+5) va ty 16 tie't kiem (ty 16 tfch luy) nham dam bao tang trirong kinh te' 8%/nam 15 Hay phan tfch mo hinh Harrod - Domar co tr6 dau tu va co khau hao von 16 Cho bang s6' lieu sau cua m6t nen kinh te: Nam t+1 t+2 t+3 t+4 t+5 ICOR 2,95 3,02 3,08 3,15 3,21 Ty 16 s 27,14% 27,97% 28,51% 29,05% 28,55% a Hay sir dung mo hinh Harrod - Domar (co tr6) de tfnh von can dau tu hang nam de t6ng san pham nude (GDP) co nhip tang 8% nam b Hay tfnh nhip tang cua GDP cac nam Neu ty le khau hao von la 0,3%/nam thi nhip tang cua GDP cac nam la bao nhi6u? c N6'u dau tu kh6ng co tr6, hay tfnh nhip tang cua GDP cac nam 17 Xet mo hinh Solow - Swan doi vdi n6n kinh te' co ham san xuat Y =K0,5L0,5, hang nam dan s6' tangl% , co ty 16 tie't kiem: 15%, ty 16 khau hao v6'n: 5% a Hay tfnh ty 16 von/lao dong, thu nhap va tieu dung theo dau ngudi o trang thai b6n vung b N6'u hi6n tai ty 16 v6'n/lao dong cua n6n kinh te' la 4, hay tfnh thu nhap, tieu dung, dSu tu theo dau ngubi va nhip tang truemg hi6n tai Phai mat khoang bao nhi6u nam n6n kinh te' se dat tai trang thai ben vung? 18 Cho ham san xuat: Y = L05K0,5 a Ham san xuat vai san luang tfnh theo dau ngubi (ham y = f(k), k = K/L) co dang nhu th6' nao? Trifdng Dai hoc Kinh te Quoc dan GlAO TRlNH LV THUY^T UO HiNH TOAN KiNH t £ b Hay s i dung m6 hinh tang truing Solow - Swan de tra ldi cac cau hoi: - NS'u nude A, B co ciing ham san suat nhu tren va cung he so khau hao: 5%, khong co tien bd c6ng nghe, khong co tang dan so Nude A co ty IS tiet kieni s: 10%, cua nude B la: 20% Hay xac dinh ty IS vd'n, tiSu dung trnh theo dau ngudi cua mdi nude d trang thai bSn vung - NS'u nude dSu bat dau tu trang thai vdi k =2 thi tai muc thu nhap va tiSu dung tfnh theo d;tu ngudi la bao nhiSu? Cac chi tiSu biSn ddng nhu thS nao cac nam tiSp theo? Hay so sanh thu nhap ti'nh theo dau ngudi cua nude 342 Trifdng Dai Kinh id' Quoc ddn Tai liiu tham khao tAi lieu tham khAo Nguygn Van Sinh: De curong giao trlnh Ly thuyet mo hinh toan kinh te (Ban thao) NguySn Kh&c Minh: Mo hinh Toan kinh te - giao trinh DH KTQD Nguybn Van Quy: M6 hinh kinh te - NXB GD, Ha n6i 1999 Hoang Tuy: Phan tfch he thong va urng dung - NXB KH-KT, Ha noi 1987 F S Mishikin: Tien te, ngan hang va thi trilorng tai chlnh - NXB KHKT, Ha noi -1995 Joseph E Stiglitz: Kinh te hoc cong cong - NXB KH-KT, Ha noi 1995 Lancaster K.: Toan hoc kinh te - NXB KH-KT, Ha noi 1984 D Begg - S Fisher - R Dombusch: Kinh te hoc T1,T2 - NXB DH va G D C N ,H anoi 1992 Allen R.D: Mathematical Economics - M artin’s Press INC, NewYork 1959 10 Chiang A.C: Fundamental Methods of Mathematical Economics McGraw-Hill, 1985 12 Chris Birchenhall - Paul Grout: Mathematics for Modem Economics Philip Allan 1984 13 H R Varian: Microeconomic Analysis - Norton & Company, Inc 1992, New York 14 K Arrow - F Hahn: General Competitive Analysis - San Francisco Holden Day 1971 15 T Atkinson - J Stiglitz: Lectures on Public Economics - McGraw Hill 1980 16 Geoffrey Jehle: Advanced Microeconomics Theory - Prentice Hall 1990 17 A Dixit: Optimization in Economic Theory - Oxford University Press 1990 18 A.Steverison - M.Gregory: Macroeconomic Theory and Stabilization Policy - Philip Allan Book 1990 Trirdng Dai hoc Kinh te Quoc dan 343 giAo trinh LY THUYET MO HINH TOAN KINH TE nhA xuAt BAN DAI HOC KINH t £ qu6 c DAN Dja chi: 207 Birdng Giai Phong, Ha Noi Bien thoai: (04) 8696407 - 6282486 Fax: (04) 6282485 so G9 os Chiu trach nhiem xuat ban: GS.TS NG UYEN TH A N H D O Chju trach nhiem noi dung: PGS.TS HOANG OiNH TU A N Bien tap noi dung: Bien tap ky thuat: Che ban: Thiet ke bia: SCfa ban in va doc sach mau: PGS.TS HOANG OINH TUAN ThS TRAN QUANG YEN QUANG KET QUANG KET PGS.TS HOANG O'lNH TUAN In 1.000 cuon, kho 16 x 24cm ta i XcfSng in NXB D hoc KTQD So" dang ky ke hoach x u a t ban: 666 - 2007/CXB/21 - 130/DHKTQD In xong v a nop litu chieu quy III n am 2007 ... HlNH TANG TRLTdNG KINH t £ 313 I tang trirdng kinh te va mo hinh tang trudng kinh te 313 II Mo hinh tang truong kinh te Harrod - D om ar 316 III Mo hinh tang truong kinh te Solow - Swan... dung kinh tenhif: - Trong chwang 3- Mo hinh cdn bang kinh te: tac gid da bo sung them mo hinh IS-LM dang mo hinh kinh tehtang - Trong chwang 4- Mo hinh kinh te dong: bo sung them cac mo hinh kinh. .. ke't luan kha gan vdi chan ly III MO HlNH KINH VA MO HINH TOAN KINH TE Mo hinh kinh te Mo hinh cua cac doi tuong linh vuc hoat dong kinh te' goi la mo hinh kinh te Cac van de lien quan tdi nhung