Giáo trình lý thuyết mô hình toán kinh tế

Khi Ufa chon noi dung bien soan giao trinh, tdc gid can cu vao yen can va chuong trinh mon hoc “Ly thuyet mo hinh toan kinh te” da dupe dong dao cdc nha khoa hoc thong nha't trong khuon

TRUONG DAI HOC KINH TE QUOC DAN

K H O A T O A N K I N H T E PGS TS HOANG DiNH TUAN

N H A X U A T B A N D A I H O C K IN H T E Q U O C D A N

H A N O I - 2 0 0 7

TRUONG DAI HOC KINH i t Q U 6 c DAN

Mite luc

h g c Lgc

lOin o ioAu 7

LOl TUA CHO TAl bAn LAN THUNHAT 9

Chuong I: GIGfl THIEU PHlTONG PHAP MO HINH VA H EP CAN HE THONG TRONG NGHIEN C0U KINH TE 11

§1 PHLTONG PHAP MO HlNH VA Y NGHlA 11

I Cac phuong phap nghien curu khoa hoc .11

II Y nghia cua phuong phap mo hinh trong nghien curu kinh t e 15

§ 2 KHAl NI$M MO HINH KINH t£ VA MO HlNH TOAN KINH t£ 16

I Mo hinh cua doi tuong 16

II Mo hinh hoa doi tuong • nhumg van de can chu y 16

III Mo hinh kinh te va mo hinh toan kinh te 18

§ 3 CAU TRCJC MO HlNH TOAN KINH 24

I Cac bien so cua mo hinh - phan loai va do ludng bien 24

II Moi lien he gitta cac bien so va hinh thufc bieu d i^n 29

§4 PHAN LOAI MO HlNH TOAN KINH .32

I Phan loai mo hinh theo dac diem cau true va cong cu toan hoc sii d u n g 32

II Phan loai mo hinh theo quy mo yeu to, theo thoi han 33

§5 N0I DUNG COA PHLTONG PHAP MO HlNH TRONG NGHIEN COl VAPHAN TlCH KINH t£ 34

I Noi dung co ban cua phuong phap mo h in h 34

II Thi du minh hoa 35

§6 MO HlNH HOA D(5l TUONG THEO CACH Tl£P CAN H | TH0NG 37

I Cac khai niem lien quan tdi he thong 38

!

II He thong kinh te 47

§ 7 PHlfCfNG PHAP PHAN TICH MO HlNH 50

I Giai mo h in h 50

II Phan tich so sanh tin h 55

III Mo phong mo hin h 66

Bai tap chircfng 1 68

Chirang II MO HINH TOIUU TRONG KINH TE 73

§1 GICJI THI$U CHUNG v£ MO HlNH T6l LTU 73

I Su lira chon cua tac nhan kinh te 73

II Mot so gia thiet va van d6 lien quan den mo hinh toi iru 79

§2 MO HlNH PHAN TICH HANH VI COA H0 GIA BlNH 89

I Mo hinh hoa so thich, thi hieu cua ho gia dinh - ham lqi ich tieu dung 90

II Phan tich hanh vi tieu dung - Mo hinh xac djnh Ham lqi ich gian tiep va ham cau M arshall 93

III Phan tich hanh vi tieu dung - Mo hinh xac dinh Ham chi tieu va ham cau Hicks 101

§3 MO HlNH PHAN TICH HANH VI COA DOANH NGHlEP - HANH VI SAN XUATKINH DOANH 118

I Hanh vi va vj the cua doanh nghiep 118

H Mo hinh mo ta cong nghe 120

HI Mo hinh phan tich chi phi cua doanh nghep 131

IV Mo hinh phan tich quyet dinh cua doanh nghiep • Mo hinh xac dinh mire cung 144

Bai ta p ch tro n g II 159

chinmg hi mo m m cam bang o n te i69

§1 GIOI THI$U CHUNG V^CANBANGVAPHAN TICH CAN BANG 169

I Khai niem ve cam bang n ma h a h cam b a ag 169

GIAOTRiNH LY THUYI-T MO HiNH TOAn KiNH Tg

Muc luc‘ * »

II Phan tich can b a n g 171

§2 GI0I THI$U CHUNG V£ MO HiNH CAN BANG TH| TRLfONG 173

I Su hinh thanh thi truong va cau true cua thi trudng 173

II Nguyen tac thiet lap va phan loai mo hinh can bang thi tru d n g 177

§3 MO HlNH CAN BANG TH| TRl/ONG Rl£NG VA ONG DUNG 179

I Mo hinh can bang thi trudng canh tranh hoan h ao 179

II Can bang tren thi truong doc quyen ve phia cu n g 182

III Can bang thi trudng va phuc lqi xa hoi 183

IV IJng dung phan tich so sanh tinh - Phan tich chinh sach dieu tiet thi truong cua nha nude 187

§4 MO HlNH CAN BANG T6NG TH^ - MO HlNH CAN BANG WALRAS 200

I Su trao doi hang hoa (nguon) gifta hai tac nhan - Mo hinh “Hop Edgeworth” 201

II Mo hinh can bang W alras va phuc lqi 203

III Khuyet tat cua kinh te thi trudng va vai tro cua nha nude 209

§4 M0 HlNH CAN BANG KINH t£ VT M0 211

I Vai tro cua mo hinh can bang kinh te vT mo 211

II Mo hinh can bang vi mo 212

Bai tap chirdng III 254

Chirong IV MO HINH KINH TE DONG 265

§1 GlOl THI$U CHUNG V£ MO HlNH DONG VA PHAN TICH B0NG THAI 265

I Dong thai cua cac qua trinh hoat dong kinh t e 265

II Cau true mo hinh don g 266

III Phan tich mo hinh dong - Phan tich dong th a i 267

IV Mot so cong cu toan su dung phan tich dong th a i 270

§2 MO HlNH CAN BANG THj TRl/ONG VCJI CO CHg GlA CA - PHAN

TfCH S I/6 n B|NH COATH! TRUONG 278

I Mo hinh ctf che gia ca 278

/ / II Ap dung mo hinh co che gia trong phan tich can bang thi truong rieng 285

§3 MO HlNH CAN BANG Vi MO B0NG 293

I Duong cong Phillips - Dong thai cua thi truomg lao dong 294

II Mo hinh can bang vi mo dong 301

II Mot so mo hinh can bang vi mo dong dang don gian 306

§4 MO 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 o m ar 316

III Mo hinh tang truong kinh te Solow - Swan 321

Bai tap chirdng I V 338

TAl LIEU THAM KHAO 343

GlAOTRiNHLyTHUYgTMOHiNHTQANKlNHTg

LCJI n 6 i dau

Doi tugng nghien citu trong kinh te ngay cang da dang va phitc tap cd

ve quy mo lan cdc moi lien he De cd the nhan thi'tc mot each tuong doi day

du doi tugng nham dap itng muc tieu nghien citu ddi hoi phi tong phap tie'p can mdi vdi lap liian logic chat che va de Idem cluing trong thuc te. Mo hinh hoa kin h te la phucfng phap tie'p can ngay cang to ra hitu ich, dqc biet khi

co sit hd trg ciia cac nganh khoa hoc khac nlut: todn hoc, khoa hoc quan ly, edng nghe thong tin Tuy nhien trong ITnh vice nay, cac tai lieu lien quan bang tieng Viet edn rat it Cuo'n sach “Ly thuyet mo hinh toan kinh te”

dugc bien soan nham muc dich cung cap mot gido trinh chuan cho mdn hoc

“Ly thuyet mo hinh toan kinh te” trong chuang trinh ddo tqo eft nhan Todn kinh te'va Toan tai chinh cua Dai hoc Kinh te quo'c dan Ngoai ra gido trinh

cd the dugc sit dung nlut tai lieu tham khao bo ich ciia sinh vien, hoc vien cao hoc thude cac chuyen nganh khac trong Dai hoc Kinh te quoc dan cung nlut cua cac nha nghien citu, phdn tich kinh te co quan tarn Vdi thdi lugng

120 tie't gido trinh gidi han 6 viec de cap tdi nhitng ndi dung co ban mang tinh khdi quat cua mot so' Idp mo hinh todn kinh te cung nlut khd ndng van dung trong thuc tien Dugc trang bi nhung kie'n thi'tc co ban nay ngitdi hoc

cd the ket hgp vdi cac kie'n thi'tc ve kinh te lugng de trite tie'p dp dung trong phdn tich kinh te, kinh doanh; dong thdi cd the tie'p tuc nghien citu chuyen sau ve cdc mb hinh kinh te thong qua tham dit cac chuyen de hoqc tit tim hieu Nhitng kie'n thi'tc todn sit dung de phdn tich cdc mo hinh trong gido trinh thudng chi dung d mite do vita dii can thie't nham tranh nhitng khd khan cho ngitdi hoc cung nlut tranh viec xa rdi muc tieu chinh la phdn tich y nghia kinh te'va ling dung Cdc mo hinh kinh te hit site da dang va phong phu nen cd nhieu tieu chi de phdn loai Gido trinh can cit vao dqc diem can true cua mb hinh cung nhit cong cu todn dugc sit dung phdn tich de phdn chia mo hinh thanh cdc Idp tuong itng vdi cdc chitong Gido trinh bao gom cdc ndi dung sau:

Chuong I: Gidi thieu phiromg phap mo hinh va tie'p can he thong trong nghien curu va phan tich kinh te

Noi dung ciia chitong gidi thieu nhitng kie'n thitc co ban ciia qua trinh

GlAO TRiNH L Y THUYET MO HINH TOAN K1NH TE

mo hinh hod kinh te Vdi cdc kie'n I hue nay ngudi hoc co the dp dung de thiet lap va phan tich cdc mo hinh kinh tetheo linh vice va yen can rieng.

Chircmg II: Mo hinh toi iru trong kinh te: de cap toi mo hinh toi itu ling dung trong phan tich kinh te, hanh vi toi i(u ciia tdc nhdn kinh te va phan tich tdc dong cua mot so yen to ngoai sinh tai hanh vi nay.

Chuo'ng III: Mo hinh can bting kinh te: tap trung phan tich mot so mo hinh can bang thi trudng dong thdi phan tich cdc tdc dong ngoai sinh, dqc biet la la phan tich chinh sdch.

Chuong IV: Mo hinh kinh te dong: de cap mot so khdi niem co ban, phuong phap phan tich dong thdi cua mo hinh va se phan tich chi tie't mo hinh can bang thi trudng dong ciing nhum pt so mo hinh tang trudng kinh te Cd'u true cdc chuong co dang modun kie'n tlu'tcmang tinh doc lap tuong doi vi vay tuy thupevao thdi lupng, doi tuong, muc tieu ngudi sit dung gido trinh co the chon nhilng noi dung thich hop Phan dan ciia cdc chuong II, III, N deu gidi thieu chung ve cac lop mo hinh tuong ung ciing vdi cong cu todn va phuong phap phan tich; phan sail ciia moi chuong de cap toi mot so lop mo hinh cu the Muc dich phan tich mo hinh nliam tim hieu y nghia kinh

te de van dung trong thuc te nen viec tim Idi gidi bang so khong phai Id trong tarn Trong moi chuong deu co nhieit thi du niinli hog de giiip ngudi hoc co the nam bat nhanh nhilng kie'n ihuc dupe gidi thieu ciing nhu tao lu'tng thu trong hoc tap.

Khi Ufa chon noi dung bien soan giao trinh, tdc gid can cu vao yen can

va chuong trinh mon hoc “Ly thuyet mo hinh toan kinh te” da dupe dong dao cdc nha khoa hoc thong nha't trong khuon kho hoi thdo quo'c gia “Iloan thien muc tieu, chuong trinh,phuong phap giang day Toan - Thong ke - Tin hoc d trudng DH KTQD” dupe to chiic tai Dai hoc Kinh te quo'c dan (tliang 10/2001) Mac dii vay day la Ian ddu gido trinh dupe bien soan va phat hanh nen khong trdnh khoi nhitng han che va khie'm khuye't Tdc gid mong dupe sit gop y ciia ngudi doc de co the hoan thien cudn sdch Tdc gid xin cam on cdc dong nghiep trong va ngoai trudng da dong vien, dong gop nhilng y kie'n quy ban trong qua trinh xay dung de cuong va bien soan gido trinh.

Tac gia

Lot tu'a cho tai ban Ian thunhat

LCJl TOA CHO TAI b A n l A n THl/ NHAT

Sau khi cuon Ly thuyet m6 hinh toan kinh te xuat ban va di(a vao sit dung nhw mot giao trinh tai Dai hoc kinh te'qud'c dan, tac gid da nhan d it etc sit ling ho ciia dong ddo ban doc thuoc nhieu doi twang: sinh vien, hoc vien cao hoc, nghien citu sinh, can bo giang day vd cac nha nghien citu kinh te Ben canh viec sit dung cuon sach nhu mot tai lieu hoc tap, nghien citu, nhieu ban doc cdn mong muon khai thac noi dung cuon sach trong thitc hanh nghien citu, phan tich kinh te Tit kinh nghiem thu ditac qua thitc te giang day ciia tac gid cho nhieu doi twang trong then gian qua, de dap ling tot han yen cau ciia chwang trinh mdn hoc ciing nhw mong muon ciia ban doc, tac gid cho tai ban cuon sach vdi mot so s/fa doi, bo sung:

Thit nhat, cac loi in trong cuon sach xuat ban Ian 1 da dwac chinh sita Dong thai tac gid bo sung them nhieu thi du minh hoa noi dung ciing nhw phan bai tap sau moi chwang ciia cuon sach.

Thit hai, mot so mo hinh da dwac bo sung, met rong khong nhitng v i hinh thitc dien dat ma cdn ve noi 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 tehtang twang itng vdi cac mo hinh da co.

Vdi viec bo sung noi dung (dac biet Id cac mo hinh kinh te Iwang) k it hap vdi kie'n thitc ve kinh telite/ng ciing nhw cac cd sd dit lieu se giiip ngitdi doc co the van dung tot han cac mo hinh trong itng dung thitc te Tac gid tie'p tuc mong doi nhitng y kie'n dong gop ciia ban doc de co the hoan thien cuon sach.

Ha Noi, thang 8 nam 2007

Tac gia

Chuong I Gioi thieu phuong phap mo hinh va tiep can.

Chvorng I

GIOI THIEU PHU0NG PHAP MO HINH VA TIEP CAN HE THONG

TRONG NGHIEN CIlTU KINH TE

I CAC PHl/ONG PHAP NGHIEN CUE KHOA HOC

1 Quy luat va nghien cufu khoa hoc

Nghien cdu khoa hoc noi chung va nghien cun kinh te noi rieng la qua trinh tim kiem, phat hien nhQng su kien mdi tren co so cac su kien da biet,

da dupe nhan thde Ket qua nghien cdu se giup ta giai dap cac cau hoi: su kien mdi co ton tai hay khong? sir kien nay nhu the nao?

Ngirdi thvrc hien viec nghien cun muon dat ket qua co gia tri can nhan thuc dupe cac quy luat chi phoi mdi quan he giua cac hien tupng, cac su kien Muc dich chinh ciia nghien ciiu khoa hoc la phat hien cac qui luat

Vay chung ta quan niem quy luat la gi?

a K hai niem quy luat va mo ta quy luat bang ngon ngu toan hoc

Theo nghia hep, qui luat la mdi quan he tat yeu thiedng xuyen giua cac hien titqng, sickien. De mo ta, dien dat quy luat bang ngon ngu toan ta co the sir dung quan he hai ngdi giua cac phan tir trong tap cac hien tupng, su kien

Ky hieu 76la tap cac hien tupng, su kien Mot quy luat tren 76la mot quan

he hai ngdi p giua cac phan tu thude 76 Gia sir ta co cac hien tupng

A,B,C € 76 va quy lu$t p tren 76 , khi do de bieu didn quy luat p, ta viet-

p(A,B) Tuy thude vao dac diem cua p va 76 chung ta se co cac quy luat khac nhau va trong thuc te tuy cung quy luat p nhung cac bieu hien cu the cua quy luat se khac nhau tren cac tap 76khac nhau De phat hien, nhan thuc quy luat chung ta can nhan biet quan he p cung cac dac diem cua no Thong thudng, quan he p can phai dap ung cac yeu cau cua logic bien chung va logic hinh thde Muc dich cua viec nghien cdu quy luat khong chi ddng lai d cho phat hien quy luat ma con van dung quy luat de dieu chinh hoat dong nham dat cac muc tieu nhat dinh

GIAO TRiNH LY THUYET MO HiNH TOAn KINH TE

b Phart loai qui luat

Can cu vao dac diem cua tap 7(> cung nhu quy luat p chung ta co the phan loai cac quy luat thanh cac nhom N6u 7(> la cac hien tupng tur nhien thi

p goi la quy luat tu nhien, neu 7C la cac hiSn tupng xa hoi thi p goi la quy luat xa hoi. Neu A ,B e 3*3 va co p(A,B) nhung khong co p(B,A) thi p goi la

quy luat nhan-qua; A goi la nguyen nhan (“nhan”), B la ket qua (“qua”) Ta

co the bi^u di6n quy luat nhan-qua bang so do: A —> B Chu y rang trong thuc te co the co quy luat nhan-qua ma trong do mot “nhan” nhung nhieu

“qua” Vi du:

CTrong thuc te co the nhan thirc duoc B trudc C nen rat d6 ngo nhan B la nhan cua C Viec phat hien qui luat nhan- qua co the giup ta tim ra phuong thdc tac dong vao "nhan" de dupe "qua" mong muon Neu p chi xac lap vdi mot so lupng Ion cac phan tu- cua 7C> thi quy luat p goi la qui luat thong ke

Nhu vay quy luat nay la qui luat thuoc v6 cac hien tupng tap the, dam dong,

no phan anh xu the tat yeu cua da phan Trong llnh vuc KT-XH, cac quy luat dupe bieu hien thong qua hoat dong cua-tap the ngufri tham gia vi vay hau nhu chung d6u la cac quy luat thong ke C6ng viec chinh cua cac nha nghien ctru, phan tich kinh te" xa hoi la tim ra qui luat nhan qua mang tinh thong ke giua cac hipn tupng va khong chi vi muc dich nghien curu khoa hoc ma con

de hudng dkn thuc hanh

2 Mot s o qui luat pho bien trong kinh te - xa hoi

a Qui luat bao toan van dong

Noi dung cua quy luat: Moi qua trinh van dpng trong tu nhien xa hoi

d6u khong tu nhien sinh ra va cung khong tu nhien mat di ma chung chi chuyPn hoa cac hinh thuc van dong

Cac bieu hien cu the cua quy luat nay la quy luat bao toan vat chat, quy luat bao toan nang lupng trong khoa hoc tu nhien va ky thuat, quy luat “bu”

- “trur” , “danh doi” trong khoa hoc xa hoi

b Qui luat khan hiem

Noi dung cua quy luat: Moi hoat dong cua con ngucti, trong do co hoat

Trirdng Oai hoc Kfnh te Q i^ c dan 12

Chu&ng l G iai thieu phucfng phap m o hinh va tiep can.

dong kinh te dSu phai su dung cac nguon luc Cac nguon luc ddu khan hiem,

co gidfi han, dac biet la cac nguon tu nhien kho hoac khong the tai sinh

Su khan hiem cac ngudn luc la do:

+ Dan sd tang d in tdi nhu c^u su: dung ngu6n luc tang

+ Do canh tranh de dap ung nhu cau mdi, cac tac nhan trong hoat dong kinh te phai cai tidn, thay doi phucrng thdc hanh dong vi vay nhu cau sir dung nguon luc tang

c Qui luat hieu qua, Iffi suat giam dan

+ Noi dung cua quy luat

Su khan hiem ngudn luc sir dung trong hoat ddng noi chung va hoat dong kinh t£ noi rieng keo theo chi phi co hoi khi chung ta sir dung cac nguon nay Thien nhien rat hao phong nhung cung nghiem khdc trong viec cung cap cho chung ta nhung nguon luc va tao hoa luon luon doi hoi tra

"gia" dat hem khi chung ta muon sir dung them cac nguon V ai quan niem viec su dung nguon ludn kem theo chi phi ca hoi thi quy luat hieu qua giam dan mang noi dung nhu sau:

Neu nhung dieu kien khac khong thay doi, khi chung ta tang mdc sir dung cac nguon thi chi phi co h6i se ngay cang tang vdi nhip d6 ngay cang cao

+ Mot so bieu hien cu the cua quy luat trong KT - XH

Su bieu hien tac dong cua quy luat het sue da dang trong nhieu lmh vuc tu nhien cung nhu xa h6i Chung ta se d6 cap t6i mot so bieu hien cu the cua quy luat qua cac hien tupng sau day:

+ Luat Malthas

Malthus cho rang khi dan sd tang, san lupng se tang nhung tang ch&m hon bdi vi dan sd tang thi lao dong cung tang nhung ddt dai co han nen ty le lao dong - dat dai tang Do tac dong cua quy luat, san pham tang them se giam

Malthus ket luan: sdc ep dan sd se day nen kinh te tdi chd lam cho ngudi lao dong phai song b muc tdi thieu

+ Quy luat xu lutdng giam siit ciia ty suat loi nhuan (Marx)

K Marx cho rang doi vdi nen kinh te TBCN, trong qua trinh tfch luy tu ban, cdu tao huu co cua tu ban tang va do do ty suat lpi nhuan se giam Neu

GIAO TRiNH LY THUYET MO HiNH TOAN KINH l£

xem xet lqi nhu&n nhuf la ket qua, hieu qua cua viec dau tu tu ban (bat bien, kha bien) cua nha tu ban thi khi tu ban bat bien tang nhanh han tu ban kha bien (c£u tao huu co tang) do tac dbng cua quy luat, hieu qua se giam

+ Quy luat bien dong cua chi phi trung binh - dang chit U cua dudng chi phi trung binh

Do'i vori nhieu qua trinh san xuat, khi tang quy mo se tan dung duqc uu the cua san xuat 1cm do do chi phi' trung binh se giam Tuy nhien den mot gidfi han nhat dinh, khi- uu the cua san xuat 1cm da tan dung het, neu tiep tuc tang quy mo, chi phi trung binh se tang Neu ta bieu didn bang do thi moi quan he giua mbc san luqng (quy mo san xuat) va chi phi' trung binh tuong ling thi do thi nay se co dang chu U, the la co diem day (didm thap nhat).+ Quy luat lqi ich can bien giam dan

Viec tibu thu m6t loai hang hoa se dem lai mot mdc lqi l'ch nhat dinh doi vdi ngucri ti6u dung Tuy nhien, neu ngubti tieu dung tiep tuc tieu thu them loai hang hoa do thi mdc gia tang cua lqi l'ch se giam dan do tac dong cua quy luat lqi suat giam ddn

+ Quy luat ve hieu qua sit dung mot bien phap, mot phitong tien

Hieu qua sir dung mot bien phap phu thuoc vao muc do sir dung Ban dau, hieu qua tha'p vi con phai thang sue y, sau do tang nhanh dan va den mot mure nhat dinh bat dau giam dan; cuoi cung gan nhu khong con hieu qua (bao hoa) Khi hieu qua cua mot bien phap da den giai doan bao hoa thi can phai cai tien, bo sung hoac thay doi

3 Cac phirdng phap nghien cuxi

a Phitffng phap theo doi, quan sat

Ngay tir then xa xua, con ngucri trong qua trinh muu sinh da biet quansat, theo doi cac hien tuqng xay ra quanh minh Cac hien tuqng duqc ghi nhan de rut ra nhung kinh nghiem ling xu va luu truydn lai cho cac the hesau Nhung kinh nghiem due ket qua nhieu the he chi'nh la nhung thong tin

ve viec phat hien cac quy luat

Han che lorn nhat cua phuemg phap quan sat la no doi hoi ngucri nghien cuu phai true tiep theo doi, quan sat doi tuqng trong thbi gian dai do do rat kho co the chu dong trong nghien cuu

b Phuemg phap tien hanh thi nghiem, thu nghiem co kiem soat

Theo phuemg phap nay, ngudi nghien cuu tao ra va tien hanh cac thl

Chuong l Gidi thieu phuong phdp m o hinh va tiep can.

nghiem nhSm tac dong vao doi tuong nghien cun va theo d5i, ghi nhan ket qua TO cac ket qua tong ket co the rut ra cac quy luat dang nhan - qua Diem quan trong trong phuong phap nay la ngubi nghien cun phai hoan toan co the kiem soat duqc thf nghiem, tuc la co the tao ra va giu dupe cac dieu kien giong nhau trong cac lan thf nghiem (giu dupe “nhan” giong nhau) Phuong phap nay dupe ap dung pho bibn trong khoa hoc tu nhien va trong ky thuat

c Phuong phap suy luan logic

Phuong phap suy luan xuat phat tb nhung dibu da biet (hoac gia dinh la

da biet) thdng qua qua trinh suy luan logic (logic bien chung, logic hinh thu"c) rut ra nhung he qua, nhung ket luan Suy luan logic gom suy luan di6n dich: suy luan tu- cai chung, khai quat den cai rieng, cu the; va suy luan quy nap: suy lu^n tCr nhung cai rieng, dac thu d6n cai chung, khai quat Phuong phap suy luan logic voi cong cu suy luan la mo hinh ciia doi tuong nghien ci(u goi la phuong phap mo hinh. Voi phuong phap mo hinh, cac doi tuong trong hien thuc co lien quan tori hien tuong, van de ta quan tarn nghien curu

se dupe thay the bbi “ hinh anh “ cua chung: cac Mo hinh cua doi tuong

II Y NGHIA CUA PHUONG PHAP MO HINH TRONG NGHIEN CtJU KINH TE

Hien thuc kinh te lien quan den van d i nghien cun thuong phiic tap Co rat nhieu hien tuong va vo so moi quan he dan xen, chong cheo giua chung

vi vay neu chi quan sat thi cMc chan chung ta khong the nSm bat dupe ban chat va do do rat kho tim ra quy luat chi phoi cac moi quan he Khi nghien cun cac hien tuong, van d6 KT-XH, phuong phap thf nghiem thuong kho ap dung va no khong dem lai ket qua nhu mong muon, bdi vi:

- Qui mo cua nhung vdn d6 KT-XH doi hoi chi phf cho thuc nghiem rat lern va nhieu khi nhung sai sot trong qua trinh thuc nghiem se gay ra hau qua khong the luomg trude dupe

- Ngay ca trong truong hop co du di6u kien tien hanh cac thuc nghiem trong nghien cuu kinh te thi chung thuong la nhiing thf nghiem khong kiem soat dupe vi cac hien tuong KT-XH g&n lidn voi hoat dong cua con ngubi Khi didu kien thuc te khac biet vdi dieu kien thuc nghiem, con ngubi co phan ung khac han nhau do do ket qua thu dupe trong hai truong hop se khac nhau

GIAO TRiNH LY THUYET MO HiNH TOAN KINH TE

De nghien cun cac hien tupng, cac va'n <36 kinh te' thuong la phai sit dung phuang phap mo hinh. Ndi dung ca ban cua phuang phap mo hinh bao gom:

- Xay dung, xac dinh mo hinh cua dd'i tupng Qua trinh nay goi la mo hinh hod doi tuang.

- Dung mo hinh lam cdng cu suy luan phuc vu yeu cau nghien cuu Qua trinh nay goi la phan tich mo hinh.

Phuang phap mo hinh khac phuc dupe han che' cua cac phuang phap tren Dong theti voi viec phan tich mo hinh, phuang phap tao kha nang phat huy tot hieu qua cua tu duy logic, ket hop nhuan nhuyPn giua cac phuang phap phan tich truyen thong voi hien dai, giua phan tich dinh tfnh vdi phan tich dinh lupng M uon sh dung co hieu qua phuang phap mo hinh trong nghien cull kinh te, van de cot loi la xac lap duac mo hinh cua doi tuang nghien eftu. De hieu ro qua trinh nay chung ta can d6 cap toi mot so khai niem ca ban co lien quan

§ 2 KHAI NIEM MO HINH KINH TE VA MO HINH TOAN KINH TE

I MO HINH CUA DOI TUONG

Co rat nhi6u quan niem v6 mo hinh cua dp'i tupng, tu: hinh thtre don gian, true quan den hinh thde khai quat, co sd dung cac khai niem toan hoc trim tupng Vdi yeu cau bude ddu lam quen vdi phuang phap mo hinh, chung

ta se de cap tdi quan diem kha don gian v6 mo hinh Theo quan diem nay thl: mo hinh cua mot do'i tupng la su phan anh hi6n thuc khach quan cua doi tupng; sit hinh dung, titdng titang doi tuang do bang y nghT cua ngudi nghien cun va viec trinh bay, the hien, dien dat y nghT do bang Idi van, chu viet, sa

do, hinh ve hoac mot ngon ngu chuyen nganh. Nhu vay mdi mo hinh bao gom noi dung cua mo hinh va hinh thuc the hien noi dung

II MO HINH HOA DOI TUONG - NHUNG VAN DE CAN CHU Y

Viec nM n thuc, mo ta doi tupng bln g mo hinh (mo hinh hoa doi tupng) la cot de hieu rd hon ve do'i tupng, de co the tac dong den no, lam cho

Chwang I, Gidi thieu phuong phap md hinh va tiep can

no van dong theo chidu hudng ma ta mong muon, tdc la bao gib cung nhlm

muc tieu nhat dinh Hien thuc khach quan vo cung phut tap va sinh dong, trinh do nhan thuc cua con ngudi b mdi thbi ddu co gidi han; vi vay chung ta khong the va cung khong can thiet phai hi^u biet mot each tudng tan moi chi tiet cua doi tupng nhtr chung von ton tai Doi vdi mdi doi tupng, mdi van dd can nghien cdu, bao gid cung co mdt so' it chi tiet quan trong va mot sd' ldn chi tiet co the bo qua Nhung chi tiet quan trong se mo ta cac dqc diem co ban cua doi tugng, the hien ban chat cua doi tugng lien quan din van de can nghien cuu. Viec xac dinh nhung chi tiet nao va bo qua nhung chi tiet nao cua doi tupng tuy thuoc vao muc tieu nghien citu, trinh do cua ngitdi nghien citu va nhilng thong tin san co ve doi tugng. Cung mot doi tupng, chi tic't nay

co the la quan trong dd'i vdi vdn d6 nghien cun nay va rat co the la khong quan trong d van d6 khac Do do co the xay dung nhiSu mo hinh phan anh cung mot dd'i tupng nhung su dung vdi muc tieu nghien cuu khac nhau Tuy nhien, cung can phai y thuc rang khong phai bao gid chung ta cung nhan thuc ro rang muc tieu ngay ttr dau Kinh nghiem cho thay rang, nhidu khi phai kinh qua hoat dong thuc tidn mdi dan dan hieu ro dupe muc tieu Chung

ta co lam mdi rd va cang lam cang sang to minh can lam gi, se di tdi dau va dat muc tieu gi Do cung la mot dac tinh trong hoat dong cua con ngudi Bdi vay khi mo hinh hoa dd'i tupng can co gang xac djnh muc tieu nhung cung khong nen cho rin g muc tieu chi xac dinh mot lan la xong Trai lai, phai thudng xuyen xem xet de nlm vung han muc tieu va theo do ma hidu chinh, cai tien md hinh Dd'i vdi nhung van de ldn va phde tap, day la mot nguyen tic lam viec chu khong phai chi la mot ldi khuyen dan thuan Mot trong nhung each de hi^u ro muc tieu la phan chia no va chi tiet hoa dan dan thanh mot loat nhung muc tieu cu the sip xep theo mot thu tu hinh cay goi la cay muc tieu.

Khi md hinh hoa dd'i tupng can tranh hai khuynh hudng cue doan:

“Thay cay ma khdng th ly rung”: md hinh qua chi tiet, vun vat, khong tap trung vao nhung yeu to co't loi nhat

“Theo cac dudng mon qua dan gian”: md hinh qua dan gian, so lupc, khdng phan anh dupe thuc te, khdng chda'dung thong tin dang gia

Mo hinh hoa la lupc bdt chi tiet, nhung chi lupc bdt nhung gi khdng quan trong doi vdi van de nghien cuu Md hinh hoa bao gid cung co tmh chat ly tudng hoa, nhung ly tudng hoa khdng nhat thiet la thoat ly thuc te ma

GlAO TRiNH LY THUYE-T MO HINH TOAN KINH TE

chi gat bo cai thda, cai thu yeu va gan loc cai Mn thiet, cai tinh tuy Viec don gian hoa, ly tudng hoa trong qua trinh mo hinh hoa cac doi tuong la bien phap ctin thiet de dat tdi nhan thuc sau sac thuc tien Khong nen tranh don gian hoa, ly tuong hoa, ma van de la viec don gian hoa, ly tuong hoa co co

so thuc te' den mdc nao va co the giup ta hieu them thuc te' den mdc nao Chang han, mo hinh tai san xuat cua Marx tuy dua tren mot so gia thiet ly tudng nhung da giup phat hien mot so qui luat cua tai san xuat; mo hinh can bang thi trubng canh tranh hoan hao vdi nhibu gia dinh ly tuong nhung cung giup chung ta thong tin ve hoat dong cua co che' thi trubng va vai tro cua nha nude trong dieu tiet hoat dong kinh te'

Co the co ngudi cho rang ne'u doi tuong cang ldn, cang phuc tap bao nhieu thi de phan anh sat thuc te, mo hinh cang can phai phuc tap M y nhieu That ra khbng han la nhu vay Mo hinh phurc tap den dau tuy thuoc vao yeu cau nghien cdu va van de c^n giai quyet Thi du, khi doi tuong la toan bo nen kinh te' quoc dan, nhung yeu c^u la khao sat mdt so xu the' chung de gqi

y cho cac nha hoach dinh chinh sach mot so van de ve phuong hudng phat trien thi mo hinh co the tuong doi don gian (mo hinh tong cung-tong cau,

mo hinh can doi ); neu nhu yeu cau la tinh toan cac chi tieu chi tiet de'n nganh thi mo hinh co the rat phuc tap vdi hang ngan chi tieu Do phtre tap cua mo hinh khong the dac trung cho chat luong cua no Nhidu khi mo hinh qua phtre tap de'n n6i khong the sir dung dupe hoac sir dung sai

Phuong phap dien dat, the hien cac mo hinh cung rat phong phu Viec lua chon phuong phap nao cung phu thuoc vao muc tieu va trinh do cua ngucri nghien cun Tuy nhien, du lua chon phuong phap nao, cac mo hinh cung phai dong vai tro la phuong tien cho ngudi nghien ciru suy lurin tCr nhimg dieu da biet de'n nhung dieu chua biet, tdc la tir nhung tien de, nhiing gia thiet co the rut ra nhung he qua logic Ne'u mo hinh chua dung nhung yeu to' co ban cua hien thuc khach quan co lien quan de'n van de can nghien ctru thi chung ta co nhieu hi vong rang nhung ke't luan rut ra trong qua trinh sir dung mo hinh de phdn tich se phu hop vdi thuc tien d mdc dp dang tin cay, tdc la nhung ke't luan nay kha gan vdi chan ly

III MO HlNH KINH VA MO HINH TOAN KINH TE

Chirang I. G/d/ thieu phuang phtfp m6 hinh va tiep c a n

kinh te - von dT la nhung va'n dd het sire phuc tap, dac biet la nhung van dd dirong dai Do do khi phac thao mo hinh kinh te, chung ta can phai sir dung nhung kien thud khoa hoc kinh te da tich luy duoc Tuy nhien cac If thuyet, cac hoc thuyet thudng mang tfnh khai quat, trim tuong vi v&y chung bo qua nhieu chi tiet cua nhung trudng hop cu the ma rat co the doi vdi nhung van

dd chung ta c<in nghien cun lai la quan trong Vi the de xay dung mo hinh kinh te chung ta con can phai thu thap, si( dung cac thong tin ve nhitng cong trinh nghien ci'cu co lien quan, cac df( lieu da dwqc cong bo va thqm chi phai sic dung kien tliiic cua cac nganh khoa hoc khac.

2 Mo hinh toan kinh te

Cac yeu to co ban cua doi tuong trong linh vuc kinh te la chat lieu chu yeu de xay dung mo hinh kinh te va cung chinh la phan noi dung cua mo hinh Viec lua chon hinh thdc the hien noi dung kinh te phu thuoc vao van d6 nghien cun va ngucri nghien cun Duong nhien chung ta mong muon chon hinh thuc the hien sao cho vita thuan tien vua hieu qua trong qua trinh nghien cun, giai quyet van de

Mo hinh toan kinh te la mo hinh kinh te ditcfc trinh bay bang ngon ngu toan hoc. Viec sir dung ngon ngu toan hoc tao kha nang ap dung cac phuong phap suy lu$n, phan tich toan hoc va ke thira cac thanh tuu trong linh vuc nay cung nhu trong cac linh vuc khoa hoc co lien quan Doi vdi cac van de phuc tap co nhieu moi lien he dan xen tham chi tidm an ma chung ta cSn nghien cun, phan tich chang nhiing v6 mat dinh tinh ma ca ve mat dinh luong thi phuong phap suy nghT thong thuctng, phan tich gian don khong du hieu luc de giai quyet Chung ta can den phuong phap suy luan toan hoc Day chinh la diem manh cua cac mo hinh toan kinh te Chung ta co the thay

rd hon thong qua thi du sau

T h i du 1.1

Gia su chung ta muon nghien cun, phan tich qua trinh hinh thanh gia

ca cua mot loai hang hoa A tren thi trucmg vdi gia dinh la cac yeu to khac nhu didu kien san xuat hang hoa A, thu nhap, sd thich cua ngudi tieu dung

da cho trudc va khong thay doi

Doi tuong lien quan tdi van dd nghien cun cua chung ta la thi trudng hang hoa A va su van hanh cua no Chung ta c^n mo hinh hoa doi tuong nay.+ Mo hinh bang Idi: Xet thi trudng hang hoa A, noi do ngudi ban, ngudi mua gap nhau va xuat hien mdc gia ban dau Vdi mdc gia do luong

GlAO ' RiriH LY THUYErT M 6 HiNH TOAN KINH TE

hang hoa ngubi ban muon ban goi la mbc cung va luong hang hoa ngubi mua muon mua goi la mbc cdu Neu cung lbn hon cSu, do ngubi ban muon ban dirge nhieu hang hon nen phai giam gia vi v&y hinh thanh mbc gia mbi thSfp hon Neu c£u lbn hon cung thi ngubi mua san sang tra gia cao hon de mua duoc hang do vay mot mbc gia cao hon duoc hinh thanh Vbi mbc gia mbi, xuat hien mbc cung, cSu mbi Qua trinh tiep dien den khi cung bang cau b mot mbc gia goi la gia can bang

+ Mo hinh bang hinh ve\ Mo hinh mang nhen

Tb nhbng dieu mb ta bang lbi trong mb hinh tren ta se the hien bang hinh ve

Ve dubng cung S va dubng cau D tren cung he true toa do trong do true hoanh bieu thi cac mbc gia, true tung bieu thi mbc cung, mbc cau hang hoa bng vbi cac mbc gia Qua trinh hinh thanh gia can bang duoc the hibn qua so do minh hoa dubi day:

Giai thfch so do:

Neu b thbi diem bat dau xem xet thi trubng, gia hang la p, va gia sb

S, = S(p,) > D, = D(p,), khi do dubi tac dong cua quy luat cung - cau, gia p se phai ha xuong mbc p2

6 mbc gia p2 do S2= S(p2) < D2= D(p2) nen gia se tang len mbc p3

Ci mbc gia p3 do S3 = S(p3) > D3 = D(p3) nen gia se giam xuong mbc p4

Chwang l Giai thieu phirong phap m 6 hinh va tiep can

Qua tr'inh cb tiep dibn cho den khi p = p , tai mbc gia nay co can bang cung cau

+ Mo hinh toan kinh te {Mo hinh can bang thi trubng)

Goi S,D la dubng cung, dubng cau tuong bng Nhu vay bng vbi tbng mbc gia p ta co: S = S(p), do ngubi ban san sang ban vbi mbc gia cao hon nen S la ham tang theo p, the la S’(p) > 0; D= D(p), do ngubi mua se mua ft hon neu gia cao hon nen D la ham giam theo p, the la D'(p) < 0 Tinh huong can bang thi trubng (muc cung bang muc cau) se co neu: S = D Viet gon lai

ta se co mo hinh can bang thi trubng, ky hieu la MH IA dubi day:

S = S(p); S'(p)= dS/dp > 0

D = D(p); D'(p)= dD/dp < 0

S = DVbi mo hinh dibn dat bang lbi hoac bang hinh ve ta khong the biet chac rang qua trinh hinh thanh gia tren thi trubng co ket thuc hay khong, tuc

la co can bang thi trubng hay khong Doi vbi mb hinh toan kinh te v6 can bang thi trubng, ta se co cau tra lbi thong qua viec giai phuong trinh S = D

va phan tich dac diem cua nghiem

Khi muon db cap tbi tac dong cua thu nhap (M), thue (T) tbi qua trinh hinh thanh gia, ta co the mb rong mo hinh bang each dua cac yeu to nay tham gia vao cac moi lien he vbi cac yeu to san co trong mb hinh phu hop vbi cac quy luat trong ly thuyet kinh te, chang han: S=S(p,T), D=D(p,M,T) Khi nay mb hinh, ky hieu la MH IB se co dang:

S = S(p,T); 5S/5p > 0

D = D(p,M,T); bD/bp < 0

S = DThi du 1.2

Mb hinh hoa “Qui luat hieu qua, lqi suat giam dan” va vtng dung

1 Mo hinh hoa quy luat

Gia sir chung ta co mot mibn lua chon muc sir dung n nguon (phuong tien, cong cu): S c Rn+ Kf hieu x e S la vec to mure su dung cac nguon Xuat phat tb quan niem cho rang su lua chon mbc sir dung nguon giua hai muc cho phep la co the chap nhan dupe, ta co the gia dinh S la tap lbi Viec xem

GIAO TRiNH LY THUYE'T MO HINH TOAn KINH TE

xet tfnh hieu qua khi su dung cac nguon co the de cap tren hai phuong dien Mdt la, co th6 xet tdi chi phi cho viec su dung, khi do ta co ham chi the hien

su mat mat, thua thiet, cai ta phai bo ra Hai la, neu ta quan tarn tdi lqi fch thu dupe khi su dung nguon thi se sd dung ham thu bieu thi cai ta se nhan dupe Nhu v(iy vdi x e S ta co y=f(x), ham so nay co the la ham chi hoac ham thu Trong ca hai trudng hop ta ddu co the gia dinh rang khi gia tang mdc su" dung cac nguon ddu keo theo su gia tang mdc chi hoac mdc thu; co nghia la f(x) tang theo tung thanh phSn cua x Gia dinh nay co the dupe th6 hi6n bdi gia thiet cty/dX; > 0 vdi moi i

Tyl e thay the (chuyen doi) can bien va tac dong cua qui luat

Vdi viec su dung ngudn x, ta dat mot mdc y0= f(x) (thu hoac chi) Ta co th^ giu nguyen mdc y0 bang each thay doi co c&'u cua x thong qua viec bdt su dung nguon nay va tang sd dung ngudn khac De phan anh su kien "danh doi" nay vd mat dinh lupng, chung ta su dung ti le thay the (chuyen doi) can bien S^ Ti le nay cho ta biet, de giu nguyen mdc y0 ta co the them (bdt) 1 don

vi ngudn i va giam (th6m) don vi ngudn j Cong thde tfnh Sj j la:

vdi f;, fj la cac dao ham rieng cua f theo xi5 Xj

Tac dong cua qui luat

Dudi tac dong cua qui luat hieu qua giam dan, su "danh doi" d tren buoc chung ta phai tra gia ngay cang cao hon theo mdc su dung cac ngudn Dieu nay co nghTa la neu y0 la mdc chi thi de giu nguyen mdc nay, ti 16 thay the cua ngudn j cho ngudn i se ngay cang tang theo mdc sd dung ngudn i; neu y0 la mdc thu thi de giu nguyen mdc nay ti le thay the cua ngudn j cho ngudn i ngay cang giam theo mdc su dung ngudn i Mat khac, tu cong thuc tren ta thay rSng ti le thay the can bien chinh la do doc cua dudng mdc y0 = f(x) Vi vay tac dong cua qui luat se dupe thd hien bdi vi6c do ddc cua dudng mdc se tang neu y = f(x) la ham chi va se giam ndu y = f(x) la ham thu Dae tfnh nay cua cac dudng mdc tuong dng vdi dac tfnh cua cac ham tang, tua loi hoac.ham tang, tua lorn Do do ta co the mo hinh hoa qui luat bdi ham tang, tua loi hoac tua lorn tuy trudng hop Ta co the minh hoa cac tinh hudng nay trong hinh 1 - 2

Ch trong I Gioi thieu phudng phap mo hinh va tiep can.

HINH 1 - 2

Mot so ting dung

+ Bieu thi tac dong cua qui luat trong phan tfch kinh te:

Trong nhi6u phan tfch kinh te co sir dung mo hinh toan kinh te' lam cong cu, doi vdi cac chi tieu tircmg umg vdi cac khoan thu (chi), de phan anh tac dong cua qui luat ta chi c&i gia thiet la cac ham tucmg ung la ham tua lorn (tua loi) Mat khac ta cung biet gia thiet tua lorn (tua loi) nhe hon gia thiet lorn (loi) do do vdi gia thiet nay se bao quat nhi6u tinh huong, nhi6u

mo hinh hem Hem nua gia thiet tua 15m (tua l6i) dong vai tro het sdc quan trong trong viec phan tfch cac mo hinh toi uu

+ Phat hien qui luat trong phan tfch kinh te:

Khi phan tfch mot hien tuong kinh te bang mot ham kinh te, chang han

tu viec phan tfch du lieu ta uoc luong dupe ham kinh te; neu muon tim hieu xem hien tuong kinh te co bi chi phoi beri qui luat hieu qua giam dan hay khong va muc do chi phoi la bao nhieu, ta chi can ki6m tra tfnh tua lorn (tua loi) cua ham va ude lupng cac ti le thay the

Thi du 1.3

Mo hinh hod “Quy luat xu htidng giam silt cua ty sua't loi nhuan ”

Goi P la gia tri hang hoa, khi do P = c + v + m, trong do c: tu ban bat bien, v: tu ban kha bien, m: gia tri thang du chda dung trong hang hoa

Ta co ti suat lpi nhuan la - va cau tao huu co cua tu ban la —

Chia ca tur va mSu so cho v ta dupe:

GlAO TRiNH LY THUYET MO HiNH TOAN K1NH TE

Do — tang cham hem

v

§ 3 CAU TRUC MO HINH TOAN KINH TE

Cung la san pham cua qua trinh mo hinh hoa nhung mo hinh toan kinh

te co nhung diem khac biet so vdi cac loai mo hinh khac Quan sat mo hinh

MH IA trong thi du 1.1 chung ta co the thay ro di6u nay Mo hinh chua mot

so yeu to mang tinh dinh luqng (S,D,p,S’, D ) - cac bie'n cua mo hinh - va cac

he thhc toan hoc giua chung (cac phucmg trinh va bat phuong trinh) Day la dac trung co ban, la hinh thuc ket cau cua mo hinh toan kinh te, do do ta co the dung dac trung nay de hinh dung mot each cu the hon v6 mo hinh toan kinh te' so vdi khai mem da dupe gidi thieu d muc trude Ta se quan niem mo hinh toan kinh te la mot tap gom cac bien so'va cac he thitc toan hoc lien he giifa cluing nham mo ta doi twang lien quan tdi sw kien, hien twang kinh te

Chung ta se phan tich chi tiet cau true nay cua mo hinh de’ dinh rd vai tro cua tirng bo phan cau thanh nham trq giup qua trinh mo hinh hoa

I CAC BIEN SO CUA MO HINH - PHAN LOAI VA DO LUCiNG BIEN

De mo ta doi tuqng va phan tich dinh luqng cac hien tuqng va van de kinh te lien quan tdi do'i tuqng, chung ta can phai xem xet va lua chon mot

so yeh to ca ban dac trung cho doi tuqng va It tang hod chung Cac yeu to' nay sau khi duqc luqng hoa goi la cac dai luqng, cac bien so' (kinh te) cua

mo hinh Chung co the thay doi gia tri trong pham vi nhat dinh Nhd duqc luqng hoa nen ta co the quan sat, do ludng va thuc hien tinh toan giua cac bien so' nay Chung ta co the can cu vao noi dung, vai tro thuc tidn, dac diem toan hoc cua yeu to ma bien so' dai dien de phan loai cac bie'n va xac dinh phuong phap do ludng thich hop

1 Bie'n djnh ludng va bien djnh tinh

Theo quan niem bien chdng, doi tuqng luon co mat “luqng” va mat

“chat” va hai mat nay g&n bo hum co vdi nhau Tuong ung vdi cac ye'u to' cau

m

mv

Chifong I G iai thieu phuong phap mo hinh va tiep can

thanh mat “luong” va mat “chat” cua doi tupng chung ta co cac bien dinh lu'png (bien so luong) va bien dinh tinh (bien chat luong) vdi thudc do va phuong phap do ludng khac nhau

a Bien dinh luong va do ludng

Bien dinh luong la bien dai dien cho cac yeu to von dT da mang tinh dinh luong, chung the hien mat luong cua van d6, cua hien tupng Cac bien the hien chi phi, lpi nhuan, san luong, muc cau la cac thi du ve bien dinh luong Doi vdi cac bien dinh luong viec do luong co the bieu thi dudi dang hien vat (dung thudc do theo ban chat tu nhien cua bien, thi du: san luong than co thP do bang tan, san luong dien do bang KW „) hoac gia tri Dang hien vat cua cac bien co han che ldn la ta khong the so sanh tri s6' cua cac bien vi chung khong co cung thudc do Dang gia tri cua bien co tfnh chat tuong doi vi no phu thuoc vao khdng gian (dia diem) va thdi gian (thdi diem) cua viec do ludng bien Do do de dam bao tfnh nhat quan va co the so sanh, tfnh toan giffa cac bien chung ta can quy doi gia tri cac bien theo dia diem, thdi diem co dinh Khi nay do ldn cua cac bien goi la dp ldn thuc Ngoai ra, cac bien dang gia tri ddu dung tidn te lam thudc do ma ban than tidn te co gia tri theo thdi gian do do cac bien dang gia tri co the do theo gia tri hien hanh hoac gia tri hien tai Viec quy doi giua hai loai gia tri nay can tuan thu

nguyen ly chief khau theo mot ty le nhat dinh

b Bien dinh tinh va do litong

Ngoai yeu to' “luong”, con co nhieu yeu to' phan anh mat “chat” cua do'i tupng Nhung yeu to' nay bieu thi cac thuoc tfnh, dac diem cua doi tupng d cac cap do khac nhau (cac pham trii) Cac yeu to dinh tfnh co the la gidi tinh, trinh do tay ngh6, hoc van, dia ban hoat dong cua cac nhan; la lTnh vuc phat trien con ngudi, kha nang canh tranh cua n6n kinh te, tinh trang dan chu, nhan quy6n, mdc do md cua, moi trudng dau tu, tinh trang tham nhung cua quo'c gia Van dp co ban la ta can phai phan tich sit tuang tac gifta cac yen to nay trong cung mot doi tifo'ng va so sanh cac yen to nay giita cac doi tuang de co the phan loai, sap xep doi tuong theo tieu chi chat luong. De lam dupe viec nay ta din su dung cac bien dinh tfnh nhSm luong hoa cac yeu to' “chat” cua do'i tupng Viec xac dinh va do ludng cac bien dinh tfnh chrnh la qua trinh “bien so hoa” cac yeu to “chat” No doi hoi nang luc, ky thuat phan tich, tong hop cac mat kinh te - xa hoi va cac kien thtre nhat dinh trong toan hoc, thong ke va kinh te luong Ve co ban qua trinh

“bien so' hoa” duoc tien hanh nhu sau:

GlAO TRiNH LY THUYIrT MO HlNH TOAN KINH T£

- Y6u td' “chat” cua dd'i tugng dirge gan cho bien y Theo quy luat tit duy bi6n chdng, mat “lirgng” va mat “chat” cua doi tirgng co moi li6n he khang khit, gdn bo huu co vdi nhau (quy luat bien ddi “lugng” thanh “chat”

va ngugc lai); dong thdi tren co sd phan tich thuc ti6n ta co the gia thiet y co lien quan tdi mot loat cac yeu to dinh lirgng the hi6n bdi cac bien X „ X2, ,

XN Vdi cac gia tri khac nhau cua bien dinh lugng, yeu to “chat” - bien y - the hien cac cap do khac nhau (cam nhan dugc v6 mat dinh tinh) Nhu vay

co the cho rang giua y va X,, X2, , XN co moi lien he ham: y = f(X,, X2, , XN) va y dugc xem nhu mot chi tieu, tieu chi tong hgp vdi cac chi tieu thanh phan (cac “chieu”) la X l5 X2, , XN Van d6 quan trgng la xay dung ham f nhu the nao de co the danh gia, phan loai doi tugng mot each khach quan theo tieu chi la yeu to “chat” ke tren Neu trong tinh huong cu the, so lugng cac bien dinh lugng li6n quan tdi y la rat lbn, khi nay ta co th^ dung ky thuat phan tich nhan to trong phan tich thong ke da bien de loai bbt Viec lam nay khong nhirng giup chung ta tinh toan don gian hon ma con tranh nhung sai sot co the gap trong phan tich so lieu

- Ham y = f(X,, X2, , XN) can phai thoa man mot so yeu cau sau:+ Ham y = f(X,, X2, , XN) chi can xac dinh tren khoang gia tri thuc te

co the co (tinh tai khong gian, thdi gian cu the) cua cac bien X l7 X2, , XN

Ta khong can phai xet toan bo gia tri cho phep v6 mat logic cua bien X r Thi du: neu X f la thu nhap binh quan hang thang cua ho gia dinh tai Ha noi trong khoang thdi gian tir 1990 den 2001 thi ve mat logic Xj e[0 , +oo) Tuy nhien can cur vao tinh hinh thuc te tai dia phuong ta co the chi can xet Xj e[0, 10(trieu d6ng)]

+ Ham y = f(X,, X2, , XN) thudng la'y gia tri tren khoang [0, 1] de tien sap xep, phan loai doi tugng tren bang tong sap

+ Neu chi tieu thanh phan X; co moi lien he “t6't”, “tich cue” vdi y tuc

la khi gia tri X ; tang, y nghTa tich cue vd phuong dien kinh te - xa hoi cua y tang thi Xj gpi la thanh phan “tdt”, “tich cue”; trai lai, ggi la thanh phan

“xa'u”, “tieu cue” Thi du: khi xem xet ‘chat lugng cuoc song’ cua dan cu - tuong umg vdi bien y - cac chi tidu thanh phan nhu thu nhap dau ngudi, tuoi thg, ty Id ngudi biet chu, ty 16 so dan dugc dung nude sach, so' bac si tren mot ngan dan la nhung thanh phan “td't”; ty 16 ngudi ngheo, ty 16 toi

Chuong I G iai thieu phuong phap mo hmh va tiep can.

pham la thanh phan “xau” Yeu cau hop ly la ham y = f(X,, X2, , XN) phai dong bien theo bien “to t’ va nghich bien theo bien “xau”

Dei xay durng ham f trudc tien ta phai “chi so hoa” cac bien (cac

“chidu”) Phuong phap thudng dupe ap dung la:

X - Min X ;Neu X: la bien tot thi dat x, =

Max X, - Min X,

Neu X; la bien xau thi x, = Max X ; - X,

Max X; - Min X ;vdi Min X, va Max X, tinh trong khoang gia tri thuc te cua X,

Vdi each tinh nhu tren ro rang x- <e[0, 1] va ta co the sir dung x t de sap xep doi tupng theo tung thanh phan rieng re Doi vdi cac bien X, co khoang bien thien ldn, su thay doi cua X| co the co tac dong manh, yeu khac nhau doi vdi y tuy thuoc gia tri hien co cua X t (do tac dong cua quy luat lpi su&'t giam dan); de the hien anh hudng nay, trong cac cong thuc tren ta thay Xi? Min Xi7 Max Xj bang logarit co so' tu nhien (co so e) cua cac dai lupng nay

Su thay the nay vita phan anh thuc te sat thuc hon vira giam nhe tinh toan (thay the phep tmh nhan, chia bang phep tinh edng, trit)

Sau khi da co dupe cac chi so' thanh phan x t, y thudng dupe tinh theo trung binh cong, binh quan gia quydn, trung binh nhan hoac trung binh hdn hop cua cac xr Cac trong sd' trong binh quSn gia quy6n dupe tinh toan cho phu hop vdi vai tro cua chi so' thanh phan

Thi du 1.4

Chi so phdt trien con ngudi (HDI: Human Development Index)

De phan loai va sSp xdp cac qud'c gia theo trinh do phat trien kinh te va mdc do thu hudng cua ngudi dan doi vdi su phat trien nay, td nam 1997 to chdc Chuong trinh phat trien cua Lien hop qud'c (UNDP) da sd dung chi tieu

“Chi so phdt trien con ngudi” (HDI) HDI la bien chat lupng va dupe tinh dua vao 3 chi so thanh phan:

x (: chi so' v i tuoi tho trung binh cua ngudi dan, vdi X, la tuoi tho trung binh cua ngudi dan va X, e [25, 85]

2 X -h Xx2: chi so' vd trinh do hoc va'n cua ngudi dan, vdi x2 = —^ — , x2l

la chi so' cua ty le % so dan biet chd (X21) , X2, e[0% , 100%]; x22 la chi sd

GlAO TRlNH L? THUYET MO HINH TOAN KINH t£cua ty le % so dan di hoc (trubng pho thong, dai hoc, cao dang) (X22), X22 e[0% , 100%]

x3: chi so vS GDP tfnh theo dau ngucti vbi GDP theo dau ngubi X3 e[100$(PPP),40.000$(PPP)]

Theo each tfnh nay cua UNDP, HDI cua Viet nam lien tuc tang hang nam ke tit khi chung ta tie'n hanh cong cuoc doi mbi HDI cua nude ta nam

1985 la 0,583, nam 1990 la 0,605, nam 1995 la 0,649, nam 2001 la 0,682, nam 2002 la 0,688 va nam 2004 la 0,709 xep hang thu: 109 trong tong so

177 quoc gia duoc UNDP tfnh HDI

2 Bien noi sinh, bien ngoai sinh va tham s o

Can cu- vao vai tro cua bien so trong mo hinh ta co the phan chia bien

so thanh:

- bien noi sinh (bien duoc giai thfch): do la cac bien ma ve ban chat chung phan anh, the hien true tiep su kien, hien tuqng kinh te va gia tri cua chung phu thu6c vao gia tri cua cac bidn khac co trong mo hinh Neu biet gia tri cua cac bien khac trong mo hinh, ta co the xac dinh gia tri cu the bang so' cua cac biS'n noi sinh bang each giai cac he thde Trong mo hinh MH IA, chung ta thay cac bien S,D,p, S ,D’ deu true tiep phan cinh trang thai cua thi trudng va chung phu thuoc lln nhau do do chung deu la cac bien noi sinh

- bien ngoai sinh (bien giai thfch): do la cac bien doc lap vdi cac bien khac trong mo hinh, gia tri cua chung duoc xem la ton tai ben ngoai mo hinh Trong mo hinh MH IB, cac bien M,T co gia tri khong phu thuoc vao cac bien khac do do chung duoc goi la cac bien ngoai sinh

Xet theo dac diem cau true toan hoc, mot mo hinh co tat ca cac bien deu la noi sinh goi la mo hinh dong, vf du mo hinh MH IA; mo hinh co bien noi sinh va ngoai sinh goi la mo hinh met, vf du mo hinh MH IB la mo hinh mb

- tham so (thong so'): do la cac bien so' ma trong pham vi nghien cdu do'i tuong chung the hien cac dac trung tuong do'i on dinh, ft bien dong hoac

la co the gia thiet la nhu vay cua do'i tuong Cac tham so' cua mo hinh phan anh xu hubng, mire do anh hubng cua cac bien tdi bien noi sinh Thf du, neu trong mo hinh MH IB ta co S = a p ^ T Y, khi nay cac bien a,P,y la cac tham so' cua mo hinh vi gia tri cua chung quyet dinh muc do tac dong cua bien ngoai sinh T tori bien noi sinh S,D,p, S',D\

Chu&ng I Gidi thieu phucfng phap md hinh va tiep can

Luu y rang cung mot bien so, trong cac mo hinh khac nhau co the dong vai tro khac nhau; thdm chi trong cung mot mo hlnh no cung co the co vai tro khac nhau do muc di'ch sir dung md hlnh khac nhau

3 Phan loai bien theo cac dac diem khac

Cac bien cua mo hinh co the phcin loai theo dac diem vd hinh thud cung nhir noi dung cua chung Theo each nay chung ta co bien lien tuc - bien rfri rac, bien tat dinh - bien ngSu nhien, bien don - bien gop, bien luru lupng (bien luong) - bien ton lupng (bien kho), bien dong - bien tlnh

II MOI LIEN HE GIUA CAC BIEN SO VA HINH THUG BIEU DlfiN

Phan cot loi va phuc tap nhat cua mo hinh la phan mo ta cac quan he dinh luqng the hien su tuong tac, anh hudng qua lai giua cac bien so Cac quan he nay phan anh quan he kinh t enky sinh trong qua trinh hoat dong kinh te giua cac ca nhdn, giua ca nhan vdi Nha nude, giua cac khu vuc, bo phan cua n6n kinh te va giua n6n kinh td cua cac quoc gia Chung ta co the phan loai quan he kinh te theo cac qui luat, qui tac hinh thanh chung Cac quan he kinh te chu yeu bao gom:

- Quan he hanh vi: la cac quan he hinh thanh khi chu th6 thuc hien hanh vi kinh te Thi du: quan he giua mile cung va loi nhuan cua doanh nghiep khi doanh nghiep muon dat mile loi nhuan cao nhat, quan he giua thu nhap va tieu dung Cac quan he tren la quan he hanh vi vi chung la he qua cua hanh vi san xuat, tieu dung

- Quan he ki thuaf. phan anh moi lien he mang tinh kT thuat giua cac yeu to Thi du: quan he giua mure sir dung cac yeu to dau vao va san lupng, quan he giiia gidi tinh, tuoi tac va mdc ti6u thu hang hoa

- Quan he dong nhat (quan he dinh nghTa): don thuan la cac quan he dupe dinh nghTa, dupe gan cho cac yeu to Thi du: doanh thu la tong so ti6n thu dupe khi ban hang, lpi nhuan la doanh thu trir chi phi, thu nhap kha dung

la thu nhap trir di cac khoan chi tra

- Quan he dinh che: cac quan he hinh thanh do qui dinh cua luat phap, cac van ban phap qui hoac do cac qui dinh, qui ude , thoa thuan giua cac doi tac Thi du: quan he giua thu nhap va thue thu nhap, quan he giua tien do cap von va tien do thi cong, quan he giua tai san the; chap va khoan vay Neu xem xet hoat dong kinh te theo hinh thit'c cac giao dich kinh te

giua cac chu the, chung ta co the dd cap tdi cac quan he sau:

GIAO TRINH LY THUYET MO HiNH TOAN K1NH T£'

- Quan he mua-ban, trao doi hang hoa, dich vu

- Quan he thue mudn lao dong, thiet bi, dat dai, vung bien, viing trdi

- Quan he vay muon von, tai san

- Quan he chuyen nhupng: trp cap, di san, thira ke, cho tang, bieu, vientrp

Cac quan he ke tren hinh thanh va diSn bien tao ra quan he giua cac bien so lien quan Cac quan he nay chfnh la sir the hien cua cac qui luat trong qua trinh hoat dong kinh te Chung ta co the dung cac bieu thCrc, cac

he thuc toan hoc mot each thfch hop tir don gian den phuc tap de the hien moi quan he giua cac bien trong mo hinh Qui luat bao trum, chi phoi sir van dong cua tu nhien, xa hoi la qui luat bao toan van dong. Theo qui luat nay,

su van dong (hinh thanh, phat trien, diet vong) cua cac qua trinh trong tu nhien va xa hoi khong n g lu nhien sinh ra va mat di, chung chi chuyen tfir dang nay qua dang khac Cac moi quan he kinh te' va do do cac quan he giiJa cac bien cung chiu su chi phdi cua qui luat bao toan Bao toan, neu neu cam nhan theo true giac chung ta co the hieu la co su bang nhau, can bang (theo thude do thfch hop) giua cai nay-cai kia, giua trude-sau (trude -sau theo nghia qui ude nao do) Vi vay hinh thurc the hien kha pho bien moi quan he giua cac bien la cac phuong trinh (dau bang giua hai ve^ va chung dupe goi

la phuffng trinh can true cua mo hinh C) dang don gian, phuong trinh cau true la nhung ham so' (ham kinh te), d dang phde tap hon la phuong trinh hoac he phuong trinh dai so', vi phan hoac sai phan, phuong trinh ham Quan he giua cac bien sd co the la cac moi quan he true tie'p hoac gian tie'p thong qua cac bien so' khac theo mot hoac nhieu khau trung gian Chung

ta co the bieu dien quan he giua cac bie'n dudi dang so do cac moi lien he (so

dd cac k6nh lien he) Thf du:

Thud' - > Tieu dung

Thu nhap

Vo'n

Gia yeu to san xuat

NChi phi san xuat —► Mure cung —► Lai nhuan

Chwang i Gidi thieu phucfng phap m o hinh va tiep can

Trinh dd cong ngh6

Cac quan he giua cac bien thuemg diSn bien theo thbi gian, vi vay khong nha't thiet chi co cac quan he mbt chibu (nhan- qua) ma co the co ca cac quan he tuang tac hai chi6u (lien he nguqc) Thf du:

Dau tir -► Thu nhap -► Tiet kiem

t : i

D<§ xac dinh duqc quan he giua cac bien so chung ta can:

- Dua vao ly thuyet kinh te, cac qui luat kinh te da duqc thua nhan mot each rong rai

- Su dung cac k it qua phan tick Kinh te luong xac lap cac moi quan he vdi mdc do tin cay phu hop vdi muc dfch nghien cuu

Thdng thuemg, cac quan he giua cac bien so kinh te th^ hien su lien quan, tac d6ng tuong h6 giua chung trong nhung tinh huong nhat dinh nhu tinh huong can bang, tinh hubng chi phoi cac quyet dinh cua chu the kinh te Vi vay sd dung cac phuong trinh giua cac bien so chung ta co the bieu thi cac mbi quan he phuc tap, dan xen lan nhau

Tuy thuoc vao y nghTa thuc tibn cua mbi quan he giua cac bien co trong phuong trinh, chung ta co the phan loai cac phuong trinh trong mo hinh nhu sau:

+ Phuong trinh dinh nghTa (dong nhat thuc): phuong trinh the hien quan he dinh nghia giua cac bien sd hoac giua hai bieu thtre o hai ve cua phuong trinh Thf du: lqi nhuan (II) duqc dinh nghTa la phan hieu so' giua tong doanh thu (TR) va tong chi phi (TC); ta co the viet: n = TR -TC, phuong trinh nay la mot d6ng nhat thut Mot thf du khac, xuat khau rong cua mot quoc gia (NX) la khoan chenh lech giua xuat khau (EX) va nhap khau (IM) cua qubc gia do Thong thuemg xuat, nhap kh^u phu thuoc vao thu nhap (Y), mbc gia ca (P), ty gia hoi doai (ER) do do theo dinh nghTa cua xuat khau rong, ta co the viet: NX= EX(Y,P,ER) - IM(Y,P,ER) Trong

Trtfdng Dai hoc Kinh te Quoc dan

GIAO TRiNH L? THUYET MO HINH TOAN KINH TE

mo hinh MH IA, cac phircmg trinh S'(p)=dS/dp, D'(p)=dD/dp la cac phuong trinh dinh nghTa

+ Phucfng trinh hanh vi: phirong trinh mo ta quan h6 giua cac bien do tac dong cua cac quy luat hoac do gia dinh Tir phirong trinh hanh vi ta co the biet sir bien dong cua bien noi sinh - “hanh vi” cua bien nay- khi cac bien so khac thay doi Sir bien dong nay co the am chi su phan dng trong hanh vi cua con ngudi (vi du: trong hanh vi tieu dung, neu thu nhap tang len thi ngudi tieu dung se chi tieu nhibu hon), nhung cung co the chi la the hien quy luat v6 moi quan he phu thuoc lSn nhau giua cac bien so Trong mo hinh

MH IA, cac phuong trinh S=S(p);D=D(p) la cac phuong trinh hanh vi vi chung the hien su phan ung cua ngucfi’san suat va ngubi tieu dung trubc su thay doi cua gia ca

+ Phucfng trinh dieu kieir. phuong trinh mo ta quan he giua cac bien so trong cac tinh huong co nhirng di6u kien, rang buoc cu the ma mo hinh d6 cap Trong mo hinh MH IA, phuong trinh S = D la phuong trinh dibu kien vi

no the hien dieu kien can bang thi trubng

§4 PHAN LOAI MO HINH TOAN KINH TE

Chung ta co the phan loai m6 hinh theo cac can cir khac nhau phu thuoc vao noi dung, hinh thtrc, quy mb, pham vi, cong dung cua chung

I PHAN LOAI MO HINH THEO DAC DIEM CAU TRUC VA CONG

CU TOAN HOC SET DUNG

1 Mo hinh toi iru

Mo hinh phan anh su lira chon each thde hoat dong nham toi uu hoa mot hoac mot so chi tieu dinh trude Cau true co ban cua mo hinh la bai toan toi

uu co the bao gom bai toan quy hoach, bai toan dieu khien toi uu Khi phbn tfch mo hinh toi uu, cong cu chinh dupe sir dung la cac phuong phap toi uu trong toan hoc

2 Mo hinh can bang

Trong mo hinh lien quan toi doi tupng, neu quan he giua cac bien so' dupe thiet lap, gia tri cua cac bien noi sinh dupe xac dinh va chung khong thay doi neu gia tri cua bien ngoai sinh, tham so cho trude va co' dinh thi doi

Chuang I GJai thieu phuang phap m o hinh va tiep can.

tuong duac goi la d trang thai can bang Mo hinh the hien doi tuong trong trang thai can bang goi la mo hinh can bang Trong nhom mo hinh nay bao gom cac mo hinh can bang thi trudng, mo hinh can doi Cong cu thudng su dung de phan tich mo hinh la cac phuang phap giai he phuang trinh, tim diem bat dong

Luu y rang co nhidu chuyen gia toan kinh te vdi quan niem tong quat

ve trang thai can bang nen coi nhom mo hinh toi uu thuoc ldp mo hinh can bang Tuy nhien theo dac diem cau true toan hoc, chung ta se tach rieng hai nhom nay

3 Mo hinh tat djnh, mo hinh n g lu nhien

Md hinh vdi cac bien la tat dinh (phi ngSu nhien) goi la mo hinh tat dinh, neu co chua bien ngSu nhien goi la mo hinh n g iu nhien

4 Mo hinh toan kinh te va mo hinh kinh te lirong

Vdi quan niem duac di6n dat d tren v6 mo hinh toan kinh te, ve mat hinh thde, ta co the xem cac mo hinh kinh te luang cung la cac mo hinh toan kinh te va thude ldp mo hinh ng lu nhien Tuy nhien, trong thuc te ngudi ta thudng phan bidt chung vi ly do ky thuat phan tich va ung dung Doi vdi cac

mo hinh toan kinh te, cac tham so cua mo hinh hoac la cho trude hoac duac gia dinh rin g da biet va khi phan tich ta sir dung cac phuang phap toan hoc thuan tuy; trong khi do doi vdi md hinh kinh tc luang cac tham so lai chinh

la cac an so, gia tri cua chung duac xac dinh nhd cac phuang phap suy doan thdng kd can cd vao gia tri qua khu cua cac bien khac trong md hinh

5 Mo hinh tTnh (theo thdi gian), md hinh dong

Mo hinh cd cac bid'n md ta hien tugng kinh te tdn tai d mot thdi diem hay mot khoang thdi gian da xac dinh (thdi gian cd dinh) goi la md hinh tlnh Md hinh md ta hien tuong kinh te trong do cd cac bien phu thuoc vao thdi gian goi la md hinh dong

GIAO TRINH LY THUYET MO HINH I GAN KINH t£

Ngoai ra, co the phan loai m6 hinh theo cac chuan muc khac ma chung

ta khong de cap a day

§5 NO I DUNG CUA PHl/ONG PHAP MO HINH TRONG NGHIEN CCTU VA PHAN TICH KINH TE

I NOl DUNG CO BAN CUA PHUONG PHAP MO HINH

De ap dung phuong phap md hinh trong do su" dung mo hinh toan kinh

te lam cdng cu nghien curu, phan tich cac van d6, cac hien tupng kinh t6' chung ta can tiein hanh cac birdc sau:

1 Dat van de

Chung ta cdn di6n dat ro van d6, hien tupng nao trong hoat dong kinh

te can quan tarn, muc dich la gi, cac nguon luc co the huy dpng de tham gia nghien cuu (con ngudi, tai chrnh, thong tin, thofi gian )

2 Mo hinh hoa

Sau khi da xac dinh dupe muc dich, yeu cau can nghien cuu, chung ta

se tien hanh qua trinh mo hinh hoa doi tupng lien quan tdi van d6 Ve co ban, qua trinh gom cac cong viec:

- Xac dinh cac y6u to, su kidn can xem xet cirng cac moi lien he true dep giua chung ma ta co the cam nh(Ln bang true quan hoac can cu vao co scf

ly luan da lua chon

- Lupng hoa cac yeu to nay, coi chung la cac bien cua mo hinh Trong thuc te co nhieu yeu to von dl mang ban chat dinh lupng vi vay van de chi la xac dinh don vi do lucmg thich hop; tuy nhien co the co nhung ybu tb dinh tinh ma nhidu khi ta can sit dung cac phuong phap trong thong ke, kinh te lupng de lupng hoa chung

Chifong l Gidi thieu phlfdng phtfp rndhinh va tiep can

- Xem xet vai tro cua cac bien so va thie't lap cac he thdc toan hoc - chu ye'u la cac phuong trinh- mo ta quan he giua cac bien Day thudng la phan quan trong va kho khan nhat cua qua trinh mo hinh hoa De co the lam tot khau nay chung ta can dua vao co sd ly lu&n du manh va dang tin cay ca

ve phuong dien kinh te' lln toan hoc Ket thuc c6ng viec nay ta se co dupe

md hinh ban dau

3 Phan tich mo hinh

Sir dung phucmg phap phan tich mo hinh (se dupe trinh bay chi tiet b

phan dudi) de phan tich Kg't qua phan tich co the dung de hieu chinh mo hinh (thay doi vai tro cua bien, them, bbt bien, thay doi dinh dang phuong trinh ) cho phu hop vbi thuc ti6n

4 Giai thich ket qua

Dua vao ket qua phan tich mo hinh ta se dua ra giai dap cho van d6 can nghien cuai Neu ta thay doi van d6, hoac muc dich nghien cuu nhung doi tupng lien quan khong thay doi thi vSn co the sir dung mo hinh s;In co

D at van de

De dap dng yeu cau trdn, chung ta can phan tich tac dong true tiep

(ngan han) cua thue' doi vdi viec san xuat va tieu thu loai hang hoa A trdn thi trudng

M o hinh hod

Do'i tupng lien quan den van dd can phan tich la thi trudng hang hoa A cung su hoat ddng cua no trong trudng hop cd xudt hien yeu to' thue, chung

ta se mo hinh hoa doi tupng nay

GIAO TRlNH LY THUY^T MO HiNH TOAN KINH T£'

Theo ly thuyet kinh te vi mo, chung ta biet rang co moi lien he khang khft giua vibe san suat (mire cung), tieu thu (mue cau) va gia ca hang hoa tr6n thi trubng va no bi chi phbi bbi quy luat cung-ctiu, hon nua, thue anh hubng tbi gia ca va do do tac dong tbi mue cung va mue cau M at khac thue ti6n di6n bien cua thi trubng cung cho thay la cac thi trubng trong qua trinh hoat dong co xu the hirdng v6 trang thai can bang Cac yeu to (bien so) ta can xem xet la muc cung (S), muc cau (D), gia ca (p) va thue (T) Bang each lap luan tuerng tu nhu trong thi du 1.1, ta co mo hinh:

S = S(p,T) (S''= dS/dp > 0)

D = D(p,T) (D’ = dD/dp < 0)

S = Dtrong do S,D,S ,D ,p la cac bibn noi sinh, T la bien ngoai sinh

De dinh dang cu the cho cac ham trong mo hinh ta co the sb dung cac phuong phap trong kinh te lupng

Phan tick

Giai phuong trinh can bang, gia sir dupe nghiem la p Ro rang p se phu thuoc vao T n6n ta co the viet p = p(T) Thay p vao cac ham cung, cSu

ta tmh dupe lupng can bang:

Q = S(p(T),T) = D (p(T ),T) Vbi cac gia thiet thich hop ve mat toanhoc, ta co the tfnh dupe cac bieu thue: d p /d T , d Q /d T va chung phan anh tac dpng cua thue T tbi gia va lupng can bang

Giai thich ket qua

De phan tfch tac dong cua thue T tbi gia ca va lupng hang hoa luu thong tren thi trubng, vb mat dinh tfnh ta chi can xet dau cua cac bieu thue

d p /d T , d Q /d T Neu muon co danh gia v6 lupng ta can co thong tin, du lieu

cu the cua cac bien de co the dinh dang chi tiet va ubc lupng (dang so) mo hinh Tac dong cua T dupe minh hoa trong hinh ve: T thay doi lam dich chuyen cac dubng S,D sang vi trf S*, D* do do dich chuyen diem can bang E sang E*

Tri/dng Dai hoc Kinh to Quoc dan

36

Ch trong \ Gi&i thieu phtrang phap m d h 'mh va tiep can

§6 MO HINH HOA OOI Tl/O NG THEO CACH TIEP CAN

HE THONG

Cac van dd nay sinh trong hoat dong kinh te - xa hoi thircmg la phiic tap trong do t6n tai nhieu moi quan he phai giai thfch va phan tfch; nhieu phirong dien phai xem xet; c6 nhidu yeu to bat dinh va dong thcri co nhi6u each thuc va phirong an de can nhac, lira chon trong di^u kien thong tin khong d^y du (thong tin khong hoan hao) khi giai quyet van de Nhiing van

de chua dung cac yeu to, quan h6 dinh luqng va co the mo ta chat che blng ngon ngO toan hoc (hinh thurc hoa duqc) duqc coi la van de co cau true chat che Tuy nhien trong thirc te co khong it van dS ham chda nhieu quan

he dinh tmh rat kho hinh thuc hoa Nhung van de nay goi la "van de co ca'u true ye'u" hoac rong hon la “khdng xac dinh duqc cau true, khong co cau true” De co the phan tfch, tim giai phap cho cac van de thude nhom co cau true yeu hoac khong co cau true chung ta co the sir dung phuong phap tiep can he thong trong qua trinh mo hinh hoa doi tuqng lien quan Day la phuong phap kha hien dai duqc ap dung rat thanh c6ng trong khoa hoc tu nhien, trong ky thuat va bude dau xam nhap vao khoa hoc quan ly, khoa hoc xa h6i - nh&n van Tiep can he thong doi tuqng nghien curu la each thuc xem xet va xii ly cac van d6 tren co scr day du cac dac diem he thong cua doi tuemg (coi doi tuong la mot he thong) cung nhit sit dung cac phuong

GlAO TRiNH LY THUY^T JUl6 HiNH TOAN KiNH TE

phap phan tick lien quan (phan tick he thong). De c6 the hieu ro noi dung

va ling dung cua each tiep can he thong chung ta c^n xet mot so khai niem lien quan

I CAC KHAI NIEM LIEN QUAN TCfl HE THONG

1 Khai niem he thong

a Thi du ve he thong

+ Dong ho: chie'c dong ho (co hoac dien td) g6m nhidu linh kien g&n ket vdi nhau, hoat dong theo cac quy luat co hoc, dien tu nh&m thuc hien chdc nang do thdi gian

+ Ca the con ngi(di(hoac co the sinh vat): co the gom nhieu bo phan chuc nang lien quan vdi nhau va lien he voi moi truong song, hoat dong theo cac quy luat sinh, hoa, ly giup sinh vat ton tai va phat tri^n

+ Cac thi tntdng: he thong cac thi trudng co lien he vdi nhau, hoat dong theo quy luat cua kinh te thi trudng thuc hien viec trao doi, mua ban hang hoa dap dng nhu cau cua ngudi mua, ngudi ban

+ Cac chinh sach kinh te: he thong cac chmh sach cua nha nude duoc ban hanh gSn bo, lien quan dong bo vdi nhau nhSm thuc hien vai tro quan ly, di6u tiet cac hoat dong kinh te cua nha nude

b K hai niem he thong

TCr cac thi du tren ta co the dua ra khai niem he thong He thong la mot tong the gdm nhi6u yeu to', bo phan hop thanh (goi la cac phan tu) va mo'i quan he tuong tac giua chung vdi nhau, vdi moi trudng xung quanh mot each

co quy luat d ! tao thanh mot the thd'ng nhat (chinh the) nham thuc hien mdt so' chdc nang hoac muc tieu nha't dinh

Theo quan niem tren, cac phan td cua he thd'ng duoc hieu theo nghTa rat rong Phan tu cua he co the la cac doi tuong co cau tao vat chat, cac pham tru trong tu duy, cac khai niem cua cac bo mon khoa hoc Co hai diem can nhan manh khi chung ta xem do'i tuong nhu la mot he thd'ng:

+ Sau khi xac dinh cac phan tu cua he thd'ng, can chi ra moi lien he tuong tac theo quan he nhan - qua giua chung Bat ky su thay doi nao trong cac phan td cung nhu trong moi lien he ddu keo theo su thay doi cua cac phan td va cac moi lien he con lai

Trirdng Dai hoc Kinh t6' Quoc dan 3$

Chutmg i Gidi thieu phudng phap md hinh va tiep can

+ Cac phdn tit c6 the rat khac nhau vd hinh thuc ton tai nhimg khi hop thanh he thong thi tao thanh mot the thong nhat va c6 tmh chat mdi khac vbi tmh chat ban dau Dae tfnh nay cua he thong goi la “tmh troi” Tmh troi cua

he thdng chmh la bieu hien cua quy luat “lupng” ddi thanh “chat” trong tu duy bien chirng

Ndu ban than phan tu hoac mot nhom phan tu1 co tfnh doc lap tuong doi trong mdi quan he cung nhu there hien chuc nang thi ta co the coi chung

la he thong con (phan he) cua he ldn Nguqc lai, mot he thong co the la mot phan tit, mdt hd con cua hd thong ldn hon (sieu hd) Vide phan ra - chia tach

he thanh cac hd con, long ghep, gop cac he thanh sieu he trong nghien cdu tuy thuoc vao muc tidu Vi du, khi nghien cun, phan tich qua trinh hoat dong san xuat, kinh doanh cua doanh nghiep thi doanh nghiep dupe coi la

hd thong; nhung khi ta muon phan tich tac dong cua cac chmh sach kinh te' tdi qua trinh nay thi phai xem doanh nghiep la phan tit cua he thong cac doanh nghidp

2 Mo hinh hoa he thong

a M di trif&ng cua he thong

Mdi trubng cua he thdng la tat ca nhirng gi n3m “ben ngoai” he thong Tuy thude muc dich nghien cun, ta se gidi han van de, ddi tuong nghien curu

va coi do la he thdng Phfo con lai cua he thdng ldn hon hoac cac van de lien quan dupe xem la mdi trudng Trong thuc hanh co the van dung each thuc sau day de phan biet mot yeu to, mot bo phan thude hd thdng hay thuoc mdi trudng Ta dat 2 cau hoi: yeu to co lien quan tdi vide thuc hien chile nang hoac muc tidu cua he thdng hay khong? Phan tu cua he thdng co the chi phoi yeu to nay hay khong? Neu ca hai cau hoi deu co cau tra ldi la “khong” thi

ta khdng can xem xet tdi yeu to vi no khdng phai la phan tu- cung nhu khong thuoc mdi trudng cua he thdng Ndu cau tra ldi thu nhat la “co” va thil hai la

“khdng” thi yeu td thuoc mdi trudng Neu ca hai cau tra ldi la “co” thi yeu to dupe xem la phan tur cua hd thdng

b So'do he thdng - mo hinh hod he thdng bang hinh ve

Ta co the dung hinh ve de minh hoa hd thdng va mdi trudng va goi la

so do he thdng. Cac phan td ky hieu la a,b,c dupc bidu didn bang cac hinh vuong hoac hinh tron nho, mdi lien he dupe bieu didn bang mui ten

GIAO TRiNH L? THUYET MO HiNH TOAN KINH TE

Cach bieu didn nay mang tmh true quan cao, bubc dau giup ta hinh dung, dinh dang cac moi lien he cung nhu yeu cau suu tap thong tin, du lieu lien quan Thiet lap so do he thong (dang phac thao) la viec lam diiu tien trong qua trinh mo hinh hoa he thong

c M o hinh hod he thong - tiep can toan hoc

1 Dau vao, dau ra ciia he thong

Dau vao cua he thong la tac dong cua moi trufrng doi vdi he thong Tac dong nay co the la vat li6u, nang luong, thong tin D&u ra cua he la phan ung cua he dap lai dau vao doi vdi moi trudng DSu ra co the la dap ling, ket qua, muc tieu

2 Mo hinh hop den (mo hinh vao - ra)

Theo each tiep can nay, ta coi he thbng la mot co cau bien doi d^u vao thanh dau ra Ta chi quan tarn tori su thay d6i ddu vao, dau ra cua he cung moi lien he giua chung con bo qua co cSu to chtic ben trong cua he, coi he nhu mot “hop den” Mo hinh hop den cua he thong dua tren gia thuyet quan trong la dau ra hoan toan duqc xac dinh tit dau vao Vdi each mo ta mang tlnh be ngoai nay, ta co the hinh dung dau vao la “nhan”, dSu ra la “qua”

N di dau vao duoc mo hinh hoa thanh mot vecto X, dSu ra la Y thuoc cac khong gian nhat dinh (thucmg gia dinh la khong gian metric hoac khong gian Banach) khi nay he thong dupe mo ta bdi anh xa:

F: X -> YAnh xa F goi la phep bien doi he thong

Ta co the minh hoa so do he thong

—>

Chifong l GidS thieu phtro’ng phap m6 hinh va tiep can

Trong each mo ta tren co the coi X la vecto bien ngoai sinh, Y la vecto bien noi sinh Trong thirc te, anh xa F thirong dirge gia thiet la loan tit tuyen tinh va chung ta se ky hieu Y = F(X)

Thi du:

Khi phan tfch tinh trang c6ng nghe cua nen kinh te ta co the coi n6n kinh te nhu- mot hop den va dac trung cho cong nghe bbi ham san xuat

Y = F(K,L) vdi K,L la mire sir dung von, lao dong; Y la thu nhap

Sir dung mo hinh hop den de minh hoa quan diem “Con ngudi la tong hod cac moi quan he xa hoi”

Ta xem CON NGUCil nhu mot hop den voi m6i truong la moi trubng tu nhien, xa hoi, dau vao la cac moi quan he vdi moi trubng, dau ra la hanh vi ung xu

Uu diem cua mo hinh hop den la d§ xac dinh va nghidn chu va thuan tien khi ta muon lap ghep he thong Song mo hinh co nhugc diem la chi thich hop khi xem xet va'n d6 tinh va moi quan tarn chu yeu la su tuong tac giua he thong v6i moi truong

3 Phitang phap lap ghep he thong

Tir cac he thong con chung ta co the nhom gop va lap ghep thanh mot sieu he thong Cac phuong phap ghep co ban bao gom:

- Ghep nd'i tiep: So do ghep

HINH 1 - 4