MC LC .................................................................................................................................................. 2CHNG 1 - NHNG VN C BN CA KINH T HC QUN L .................. 3CHNG 2 - K THUT TI U HA........................................................................... 13CHNG 3 - LC TH TRNG: CU V CUNG....................................................... 31CHNG 4 - PHN TCH CU NH LNG .............................................................. 55CHNG 6 - L THUYT SN XUT .......................................................................... 102CHNG 7 - LP K HOCH A SN PHM V QUY HOCH TUYN TNH ................................................................................................................................................. 121 LI M UKha hc ny trnh by sc tch v r rng mn kinh t qun l. Mn kinh t qun l c th gi di nhiu tn gi khc nhau nh kinh t kinh doanh, phn tch kinh t trong quyt nh kinh doanh, kinh t hc cho quyt nh qun lcho c sinh vin cha tt nghip v sinh vin tt nghip.Kha hc tp trung vo nhng vn nn tng v thit yu gip hc vin nhn thc c qu trnh ra v ng dng quyt nh kinh doanh thng qua cc cng c kinh t v nh lng. N minh ha cc quyt nh bng nhiu vn c gii quyt nhm kim tra v gip sinh vin cng c li kin thc v mn hc. Hn na, nhiu chuyn gia kinh doanh cng c th hc hi t kha hc ny. Ngi c nn lm mt s bi tp kinh t cp bt u. Mc ch ca vic lm ny l nhm c c mt khi lng ti thiu kin thc nn ton hc v thng k cp i hc. Kha hc trnh by ng dng ca l thuyt kinh t v cc khi nim vo quyt nh kinh doanh thc t mt cch bao qut v chuyn su. Bao gm cc cu hi, vn km theo gii php. 2/142CHNG 1 - NHNG VN C BN CA KINH T HC QUN LMC TIU HC TPSau khi hc chng ny bn c th:1. Gii thch v lit k cc hm lin quan n kinh t hc qun l2. Xc nh cc ngun lc v a ra cc v d v li nhun k ton3. M t vai tr ca li nhun kinh t4. Tnh ton v nh ngha khi nim gi tr ca tin theo thi gian 5. Phn tch v m t chi tit quy trnh pht sinh gi tr hin ti6. M t chi tit v gii thch gi tr ca mt hng7. Hiu v gii thch c khi nim ti a ha li nhun8. Hiu r cch ti a ha gi tr ti sn (c ng)9. Gii thch v cho v d v phn tch cn bin10. Xc nh v p dng cc chin lc ti u ha li nhunKinh t hc qun l (hoc kinh t hc kinh doanh) l mn kinh t hc p dng trong ra quyt nh. N l mt nhnh ca mn kinh t hc p dng l thuyt kinh t v phng php lun khoa hc vo vic ra quyt nh nhm gii quyt nhng vn qun l v kinh doanh. Mc tiu ca mn hc nhm lp khong trng gia l thuyt kinh t tru tng v thc t qun l. Kinh t hc qun l nghin cu mt cch c h thng cch phn b cc ngun lc sao cho c hiu qu nht nhm t ti mc tiu qun l.Chng ta thng thy rng l thuyt v cc cng c kinh t khng gii quyt tt c cc vn qun l. Chng ta vn phi mn nhiu cng c v k thut ca ti chnh, nghin cu hot ng, v cc quy tc kinh doanh. iu ny c ngha l l thuyt v cc cng c kinh t, v c cc nguyn tc kinh doanh u lin quan n vn kinh t qun l.3/142QU TRNH RA QUYT NH QUN LCc bc c bn trong qu trnh ra quyt nh gm:Bc 1Nhn din vn . Khi kt lun c vn tn ti, b my qun l nn chun b xc nh c th hoc thng bo chnh xc v vn . V d, cng ty nn sn xut bao nhiu sn phm? Bc 2La chn mt mc tiu. Mc tiu ti a ha li nhun hay ti thiu ha chi ph?Bc 3Xc nh cc hn ch. S la chn ca b my qun l lun lun b gii hn bi s sn c cc ngun lc, lut l, cc o lut iu chnh, cc gi tr o c, hoc mong mun ca b my qun l. Cn phi xc nh bt c hn ch no c kh nng tn ti.Bc 4Xc nh cc phng n thay th hoc lm r cc bin quyt nh khc nhau m hng cn tho g.Bc 5La chn phng n ph hp vi cc mc tiu ca doanh nghip hay xc nh phng n ti u (v d, phng n ti a ha li nhun hay ti thiu ha chi ph).LI NHUN Li nhun (profits) thng c coi l vn mu cht ca hng. Khi li nhun c to ra mt cch hp php v hp l, em li g cho cc doanh nghip? u tin, n l thng ip r rng cho thy cng ty ny ang cung cp nhng sn phm v dch v m con ngi ang cn hoc mong mun - c bit mc gi m h sn sng chi tr. Cng vy, mt mc li nhun tt c ngha l chi ph ca cng ty theo ng k hoch d tnh. 4/142CC CNG C V L THUYT KINH TL thuyt v nhu cuL thuyt v doanh nghipL thuyt sn xutC cu th trngKinh t hc v mCC CNG C V KHOA HC QUYT NHTi u haCc phng php thng kD bo v c lngTi chnh v u tCc cng c ra quyt nh khoa hc khcKINH T QUN LS dng cc cng c v l thuyt kinh t cng phng php lun khoa hc trong vic ra quyt nh gii quyt cc vn kinh doanh v phn b ngun lc ti uN cng c ngha l hiu qu. Ti sao cc doanh nghip cn phi to ra mt mc li nhun cao?VAI TR CA LI NHUNMc li nhun cao cho php cc cng ty:1. em li li nhun cho nh u t khi dm mo him u t vn2. Nghin cu, pht trin hng ha - dch v mi v tt hn. 3. To cng n vic lm, thng v m rng c hi thng tin cho nhn vin.4. ng vin kp thi i vi nhng hot ng c hiu qu.LI NHUN K TON V LI NHUN KINH TCn phn bit c li nhun k ton v li nhun kinh t. Li nhun k ton (Accounting profits), cn gi l li nhun kinh doanh, l phn chnh lch gia tng doanh thu v chi ph sn xut hng ha hoc dch v. Li nhun k ton c ghi dng cui cng trong bn bo co thu nhp ca mt doanh nghip. Li nhun kinh t (Economic profits) th ngc li, l phn chnh lch gia tng doanh thu v tng chi ph c hi (opportunity costs). Chi ph c hi ca vic s dng mt ngun lc to ra chi ph kinh t bao gm chi ph tng minh ca ngun lc v chi ph n ca phng n s dng ngun lc tt nht b b qua. V l do ny chi ph c hi ni chung thng cao hn chi ph k ton hay chi ph trn s sch. V d, chi ph c hi ca vic tham d kha hc h l chi ph cho gio vin v gio trnh cng vi s tin m l ra bn kim c nu nh i lm sut k ngh h. TI A HA LI NHUN V PHN TCH CN BINMc ch ca mt cng ty l ti a ha li nhun (profit maxinmization). y l l thuyt truyn thng khc vi l thuyt hnh vi ca mt cng ty. Phn tch cn bin (marginalanalysis) cho bit nn ra quyt nh kinh doanh v hnh ng nh th no khi doanh thu cn bin (MR) vt qua chi ph cn bin (MC). (MR l phn doanh thu thm khi bn thm mt n v u ra v MC l chi ph u vo dng sn xut thm mt n v u ra).Nu MR=MC, quyt nh a ra s ti a ha li nhun cng ty. V D 1Gi TR(Q) l tng doanh thu m mt cng ty c c t vic sn xut Q n v u ra v gi TC (Q) l tng chi ph sn xut Q n v u ra . Do , li nhun ( ) l: (Q) =TR(Q) - TC(Q).Nh qun l phi i mt vi tnh hung nh tm tt trong ct 1 n ct 3 bng 1 mun xc nh c sn lng u ra cho php ti a ha li nhun.5/142BNG 1PHN TCH CN BINQ(1)TR(Q)(2)TC(Q)(3) (Q)(4) = (2) - (3)MR MC0 0 0 0 - -1 90 10 80 90 10 MR>MC2 170 30 140 80 203 240 60 180 70 304 300 100 200 60 405 350 150 200 50 50 MR=MC6 390 210 180 40 607 420 280 140 30 708 440 360 80 20 809 450 450 0 10 9010 450 550 -100 0 100 MR0 x->0iu ny c ngha o hm dy/dx=y=f (x)ca mt hm y = f(x) ti x0 l gii hn ca thng vi phn y/ x khi x tin v 015/142CH :ohm l t l thay i tc thi ca mt hm ti mt im (x = x0), trong khi thng vi phn l t l thay i trung bnh trong mt khong (x0, x0 + x) no . Ch trong trng hp ng thng, hai t l ny mi ng nht. Trn th, o hm l dc ca ng tip tuyn vi ng ti im x0.QUY TC TNH VI PHNQuy tc 1 (Quy tc hng s): y= f(x) = c, l mt hng so hm dy/dx = y= f (x) = 0. o hm ca mt hm hng s bng 0. Ngha l, t l thay i trong mt hng s lin quan n s thay i trong bin c lp (hay bt c bin no, trong trng hp ny) bng 0V d: Nu y = 13, th dy/dx = 0Quy tc 2 (Quy tc hm s m bin): y = f(x) = cxn.o hm: dy/dx=cnxn-1.V d:Nu y = x3, th dy/dx = 3x2. Nu y = x, th dy/dx = 1x0 = 1.Quy tc 3 (Quy tc o hm ca tng cc hm s): y = f(x) + g(x).Hm s: dy/dx = f (x)+ g(x), khi f (x) = df(x)/dxvg(x) = dg(x)/ dx. Quy tc ny quy nh o hm ca mt tng hai hm s khc nhau ca cng mt bin c lp bng tng hai o hm ca cc hm ring l. V d:Nu y = x4 + 2x, dy/dx = 4x3 + 2.Nu 4x - 5x2, th dy/dx = 4 - 10x.Quy tc 4 (Quy tc o hm ca mt tch): y = f(x)g(x).Hm s: dy/dx = f (x)g(x) + g(x)f(x).Quy tc ny ch ra rng o hm mt tch 2 hm s khc nhau ca cng bin c lp l tng ca tch ca o hm hm th nht nhn vi hm th 2, sau cng vi tch ca o hm hm th 2 nhn vi hm th nht. V d:Nu y = x2(2x - 3), th dy/dx = x2(2 - 0) + (2x - 3)(2x) = 2x2 + 4x2 - 6x = 6x2 - 6x = 6x(x - 1)Quy tc 5 (Quy tc o hm mt thng): y = f(x)/g(x).o hm:2)] ( [) ( ) ( ' ) ( ) ( ' '/x gx f x g x g x fdx dy16/142V d: Nuy = 5x/(2x + 1), th 5(2x+1)-2(5x)dy/dx= =5/(2x+1)2(2x+1)Quy tc 6 (Quy tc tnh o hm hp): y =g(z), trong z = f(x)o hm: dy dzdy/dx= . =g'(z)f'(x)dz dxQuy tc ny ch ra rng x thay i s ko theo z thay i, n lt n, z li ko theo y thay i. Do vy, dy/dx, hay t l thay i ca y tng ng vi x, c xc nh theo t l thay i ca z tng ng theo x, dz/dx nhn vi t l thay i ca y theo z, dy/dz.V d: Nu y = 10z - 2z2 - 3, trong z = 2x2 - 1, thdy/dx = (10 - 4z)(4x) =[10 - 4(2x2 - 1)](4x) = (10 - 8x2 + 4)(4x) = 40x - 32x2 + 16x = 56x - 32x2.Quy tc 7 (Quy tc o hm nghch o): x = f--1(y), trong f1 l hm nghch o ch khng phi l 1/f(y).o hm c dng:dx dydy dx/1/ V d:Nu y = 5x + 3, th x = 1/5 y- 3/5, v dx/dy = 1/5.V d sau y cho bit cch dng o hm tm ra t l thay i.V D 1Cng ty cung cp dch v lau dn Peruvian l nh phn phi ch yu cht ty ra quan trng cho nhng ngi qut dn khp min nam nc M. Cht ty ra ny dng to ra lp bo v bn ngoi cho cc hm lm lnh sut ma h c m cao. Peruvian cung cp cht ty trong nhng chic xe tc, v mi khch hng phi mua t nht 100-gallon (1 gallon = 3.78 lt M). Gi tin mi gallon l $12. Khch hng mua khi lng ln hn 100 gallon s c chit khu $0.05 mi gallon. Phn trm chit khu ny ch p dng cho nhng lng hng ln hn mc ti thiu; 100 gallon u tin vn c gi l $12 mi gallon bt k tng s gallon c mua l bao nhiu i na.B phn qun l thit lp hm ton hc sau y v tng doanh thu t mi khch hng da vo nhng thng tin trn nh sau:17/142TR $12(100) + [$12 $0.05(x100)] (x100) = 500 + 22x 0.05x2y l mt hm bc 2. o hm ca dng hm s ny l:dTR/dx22 0.10x.CH :o hm ca hm tng doanh thu cho bit doanh thu cn bin (MR), v d, phn tng ln trong TR c c t mt n v tng thm ca u ra. Tng t, chi ph cn bin bng o hm ca hm tng chi pho hm ny phn nh mt thc t rng mc thay i khng phi l mt hng s. C ngha l mc thay i ph thuc vo gi tr ca x, v vy mc thay i t n s thay i khi gi tr ca g thay i. Tnh a dng trong mc thay i l do mc thay i ca mt hm bc 2 thay i lin tc. tm ra mc thay i trong TR khi mt s lng gallon c th c bn cho ngi mua, thay x trong o hm bng lng gallon ny. V d, tm mc thay i (mi gallon) trong TR ti 105 gallon, php tnh da trn o hm sau l cn thit. 22 0.10(105) 22 10.5011.50.Ngha l tng doanh thu thay i $11.50 vi doanh s 105 gallon. Ti mc bn 110 gallons, mc thay i l $11, 22 0.10(110) 22 1111.Ni cch khc, tng doanh thu thay i t l $11 khi doanh s bn l 110 gallons, ngc li so vi t l $11.50 khi doanh s l 105 gallonsCC TR CA MT HM S V KIM TRA BNG O HM BC NHT Gi tr cc tr t c ca mt hm (gi tr ln nht hoc nh nht) rt quan trng trong ra quyt nh kinh t. Phn ln kinh t hc gii quyt vn ti u ha, l ti a ha li nhun hoc ti thiu ha chi ph. IU KIN KIM TRA BNG O HM BC NHTPhp th o hm bc nht (first derivative test - hay iu kin bc nht ) dng xc nh cc im cc tr ca mt hm (Xem hnh 3). dy/dx = y= f (x0) = 0 ti im cc i hoc cc tiu v x0 gi l cc tr ca hm. Gm 3 bc: (1) tm o hm, (2) t biu thc bng 0 v (3) tm gi tr ca x.o hm bc 2 c c t vic p dng quy tc vi phn cho o hm bc nht ch khng phi i vi hm ban u. Kt qu vi phn o hm bc nht cho ta o hm bc 2, c dng d2y/dx2 = y= f(x).V D 2Gi s y = f(x) = 3x2. Th, dy/dx = f (x) = 6x. 18/1426x l kt qu ca o hm bc nht. o hm bc 2 l d2y/dx2 = y= f(x) = 6.CH :o hm bc 2 dng nh gi o hm bc nht. Ni cch khc o hm bc 2 o lng t l thay i ca dc hm gc f(x). HNH 3IM CC I V CC TIUIU KIN BC HAIChng ta cn xc nh xem gi tr cc tr l cc tiu hay cc i. C th tm c thng tin ny thng qua vic tm o hm bc 2 (hay iu kin bc 2). Php th nh sau:1. Hm y = f(x) t cc i ti im x = x0 no nu f (x0) = 0 v f (x0) m.2. Tng t nh vy, f(x) t cc tiu ti mt im x0no nu f (x0) = 0 v f (x0) dng.3. Nu c hm bc nht v hm bc 2 u bng 0 th ta ch c mt im un ch khng c gi tr cc i hoc cc tiu, tc lf (x0) = 0 v f (x0) = 0. Mt v d v hm khng c im cc i v cc tiu l y = f(x) = x3.V D 3Xem li v d 1 :TR =500 + 22x 0.05x2.TR/dx = 22 0.10x = 019/142Ta cho o hm bc nht bng 0 v tm c gi tr x, nh sau:22 0.10x 00.10x 22x 220.Ch rng d2TR/dx2 = -0.1. V o hm bc 2 m, gi tr cc tr ca hm (x* = 220) l gi tr cc i. Thay x bi x* = 220 trong hm gc chng ta c doanh thu cc i nh sau:500 + 22(220) 0.05(220)2500 + 4,840 0.05(48,400)$1,920V D 4Cho y = f(x) = x3 - 12x2 + 36x + 18 c gi tr ti hn chng ta tm o hm bc nht v cho o hm ny bng 0.dy/dx = f (x) = 3x2 - 24x + 36 = 0 = (3x - 18)(x - 2) = 0, cho thy phng trnh bc 2 ny c 2 nghim. Cc nghim kp l: (3x - 18) = 0 v (x - 2) = 0; do , x1 = 6 v x2 = 2. khng nh xem chng l im cc i hay cc tiu hay khng, chng ta cn th li o hm bc 2 nh sau:d2y/dx2 = f(x)= 6x - 24Ti x1 = 6, f(x)= 6(6) - 24 = 8 > 0, l im cc tiuTi x2 = 2, f(x)= 6(2) - 24 = -12 0O HM RING V TI U HA NHIU BINNhiu hm c cha nhiu bin c lp phc tp. Khi nim ti u ha nhiu bin (multivariate optimization) v qu trnh ti u ha cho ng thc vi nhiu bin quyt nh l rt hu ch. C th dng tng chi ph nhn cng trc tip trong mt hng sn xut minh ha cho hm c 2 bin c lp, c tn l (1) s lng gi 20/142lao ng trc tip c thc hin v (2) t l lng mi gi lao ng. Kt qu l, ti u ha nhiu bin c s dng trong qu trnh ti u ha. Trong qu trnh ny c cha vi phn ring. Chng ta mun bit nh hng ring r m mt s thay i trong bin c lp tc ng ln bin ph thuc (trong khi cc yu t khc c coi l hng s). Qu trnh gi l vi phn ring. Tn gi ny ch ra thc t rng hm ny b vi phn tng ng vi mt phn (c th hn l mt bin) trong mt nhm cc bin c lp. Kt qu ny c gi l vi phn ring k hiu l , ch khng phi l d.CH :Cc quy tc vi phn ring l ging nhau vi iu kin cc bin c lp khng tham gia vo php vi phn c xem nh l nhng hng s.V D 5 minh ha cho hm tng doanh thu l TR 2x2y2z., trong x = chi ph qung co trong giai on trc, y = chi ph i li cho nhn vin kinh doanh, v z = l s hng ha m i th cnh tranh bn thi im hin ti. Gi thit rng ban qun l cn bit gii hn ti a m doanh thu thu c t x c th t ti (chi ph qung co trong giai on trc). Quy trnh tm gi tr cc i nh sau:1. Vi phn ring tng ng vi bin ca thu nhp 2. Ly o hm ring bng 0 v tm bin thu nhp3. Xc nh gi tr hm gc ti gi tr ny tm cc trXem y v z l hng s, h s y ca x2 l 2y2z. o hm ring tng ng vi x, bin s ca thu nhp trong v d ny l:TR/x = 4xy2z.Ly o hm ring bng 0 v tm c x nh sau:4y2zx 0x 0.Do hm doanh thu t cc tr khi x = 0. hiu r thm v kt qu ny, vic xc nh cc tr l cc i hay cc tiu rt hu ch. Nh gii thch trn, du ca o hm bc 2 (o hm ring bc 2 trong trng hp c nhiu bin) gii quyt c vn ny. o hm ring bc 2 c xc nh nh sau.2TR/ x2 = 4y2z.V o hm ring bc 2 l dng nn gi tr cc tr ca hm l cc tiu. Thc t rng gi tr cc tr ca hm t c khi x = 0 c ngha l chi ph qung co bng 0 trong giai on trc khng ng gp c g cho tng doanh thu. 21/142Hn na n ch ra rng ng gp ca chi ph qung co trong tng doanh thu giai on tip theo s tip tc tng ln min l chi ph qung co phi tip tc tng ln. iu ny cho thy chi ph qung co ca mt doanh nghip c nh hng tch cc ti doanh thu. (Cn nh rng qu trnh vi phn coi y v z l hng s, v vy khng c kt lun g v nh hng ca nhng thay i trong cc bin s i vi hm doanh thu).TI A HA LI NHUNMc tiu ca mt hng l ti a ha li nhun. L thuyt kinh t ni rng nn ra quyt nh kinh doanh v thc thi quyt nh ch khi doanh thu cn bin vt qu chi ph cn bin. Nu iu ny xy ra, quyt nh a ra s ti a ha li nhun ca hng. tm ra sn lng u ra c th ti a ha li nhun, chng ta nn dng php tnh vi phn.V D 6Xt hm tng doanh thu (TR) v tng chi ph (TC) sau y:TR(Q) = $1,000Q - $5Q2v TC(Q) = $20,000 + $200Q.Hm li nhun ( ) l:(Q) = TR(Q) -TC(Q) = $1,000Q - $5Q2- ($20,000 + $200Q) = $1,000Q - $5Q2- $20,000 -$200Q= -$20,000 + $800Q - $5Q2Ly d /dQ = 0 v tm c Q c th l Q* = 80 n v nh sau:d /dQ = $800 - $10Q = 0; Q* = 80 n vGi tr o hm bc 2 ca hm li nhun ld2 /dQ2 = -10 < 0, cho bitQ* = 80 l im ti a ha li nhun.Hnh 3 biu din th ca (a) tng doanh thu, tng chi ph v hm li nhun gi thit v (b) cc hm doanh thu cn bin, chi ph cn bin v li nhun cn bin.22/142HNH 4TNG DOANH THU, TNG CHI PH, DOANH THU CN BIN, CHI PH CN BIN V TI A HA LI NHUNTI U HA B RNG BUCNhiu hng phi i mt vi nhng hn ch trong cc phng n quyt nh. Chng hn nh hn ch v ngun lc (nh tin, thit b, nng lc sn xut, nguyn liu v nhn s) sn c i vi hng. Ti u ha b rng buc (Constrained optimization) l ti a ha li nhun km theo nhng hn ch trong s sn c v ngun lc, hoc ti thiu ha chi ph km nhng yu cu ti thiu cn c tha mn. Nhng k thut nh phng php nhn t Lagrange v quy hoch tuyn tnh (c tho lun trong chng 7) c dng cho mc ch ny.Vn chung l tm ra im cc tr ca hm f(x,y) tng ng vi cc ng thc dng g(x,y) = 0Khi cc rng buc di dng ng thc, ta dng cc phng php ti u ha c in tm phng n ti u. Hai phng php thng dng l: (1) Phng php th v (2) Phng php nhn t Lagrangean. PHNG PHP THDng phng php th khi hm mc tiu ch ph thuc vo mt biu thc rng buc tng i n gin. Bng cch th, chng ta gim c mc rc ri ca hm mc tiu. Phng php ny gm 2 bc: (1) tm ra c mt trong nhiu bin quyt nh tha mn nht sau (2) thay gi tr ca bin ny vo hm mc tiu. Qu trnh ny chuyn t hm 23/142ban u sang hm ti u ha khng b rng buc p dng c php tnh vi phn c p dng nhm tm ra phng n ti u.V D 7Gi s mt hng sn xut vi 2 dy chuyn lp rp t ng v hot ng vi hm tng chi ph c dng TC(x, y) = 3x2 + 6y2 - xy, trong x =sn lng u ra ca dy chuyn th nht v y = sn lng u ra ca dy chuyn th 2. Cc nh qun l cn phi quyt nh phng php kt hp x v y sao cho tn t chi ph nht, vi iu kin rng tng u ra phi l 20 n v.Vn ti u ha vi iu kin rng buc trn c th c gii quyt nh sau:Ti thiu ha TC(x, y) = 3x2 + 6y2 - xyRng buc: x + y = 20Th nht, gii biu thc rng buc tm x, c x = 20 y v th vo hm mc tiu.TC(x, y) = T(y) = 3(20 - y)2 + 6y2 - (20 - y)y= 3(400 -40y + y2) + 6y2 -20y +y21,200-120y+3y2+ 6y2 -20y +y2 = 1,200 - 140y + 10y2Ly o hm ca hm th gin lc v cho n bng 0, ta c:dTC/dy = -140 + 20y = 0y = 7 n vTh ngc tr li vo x: x = 20 - y = 20 - 7 = 13 n v.Do vy x = 13 v y = 7 l phng n ti u cho vn ti thiu ha chi ph b rng buc.CH :Hn ch ca phng php th l n ch thc hin c khi ch c mt rng buc v ch c th gii ra mt bin. T 2 iu kin tr ln v/hoc c cu trc rng buc phc tp th s dng phng php nhn t Lagrangean. PHNG PHP NHN T LAGRANGEMt phng php gii quyt cc vn ti u ha b rng buc m trong c rng buc i vi hm mc tiu ban u (lm cho hm mc tiu bng 0 khi tha mn). Hm mc tiu mi thm rng buc c gi l hm Lagrange, s to ra mt bi ton ti u ha khng b rng buc c cu trc nh sau:L(x, y, ) = f(x, y) + g(x, y)H s ca ng thc rng buc g(x,y), (c l lamda), gi l nhn t Lagrangean. V ng thc rng buc bng 0 nn khi thm g(x, y) vo hm mc tiu f(x, y) khng lm thay i gi tr ca hm.Bin gi ny cho bit s thay i cn bin trong gi tr ca hm mc tiu c c t s thay i ca mt n v trong gi tr ca rng buc. S dng phng php Lagrange khi 24/142(1) khng dng c phng php th v (2) khi c nhiu rng buc. Hn na, phng php ny cn cho bit cc thng tin kinh t th v. Phng php Lagrange c minh ha bng v d trn. V D 8T v d 7, ta c rng buc x + y = 20. Trc ht, cn bin i sao cho ng thc c mt v bng 0, g(x, y) = 0. Khi x + y = 20 c dng 20 - x y = 0.Tip theo, chng ta xc nh bin gi v xy dng Hm Lagrange (L):L(x, y, ) = TC(x, y) + g(x, y) =3x2 + 6y2 - xy + (20 - x-y)Ch rng1. Min l g(x,y) lun bng 0, hm L(x,y, ) s khng thay i gi tr so vi hm tng chi ph ban u TC(x,y). Ti thiu ha L(x, y, ) s dn n ti thiu ha TC(x, y).2. Ly o hm ring theo v cho n bng 0, c c rng buc ban u.V L(x, y, ) l mt hm vi 3 bin quyt nh nn ti thiu ha hm ny cn:a. Vi phn ring theo mi binb. Cho cc biu thc o hm ring bng 0 c. Gii cc ng thc tm cc gi tr x, y v Cc o hm ring l:L(x, y, )/x = 6x - y - = 0L(x, y, )/y = 12y - x - = 0L(x, y, )/ = 20 - x - y= 0Gii ng thi 3 o hm ring ny ta c x= 13, y =7, v = 71. o lng mc thay i cn bin trong gi tr ca hm mc tiu theo s thay i ca mt n v trong rng buc. Trong v d ny, =71 ch ra rng chi ph s tng thm $71 khi sn xut thm mt n v, ngha l tng u ra t 20 ln 21 n v.CH :Nu mt bi ton ti u ha b rng buc c t 2 rng buc tr ln th mi rng buc s c mt ring v kt hp vi nhau trong hm L. Cc gi tr c v l cc bin kp trong quy hoch tuyn tnh (LP) v th hin cc mc gi m ca cc ngun lc khan him. 25/142PHN TCH CN BIN V PHN TCH TNG TINPhn tch cn bin (Marginal analysis)lin quan n mt n v u ra tng thm. Nh qun l cc cp, ngi c trch nhim a ra cc quyt nh chuyn mn (nh marketing, k hoch hot ng, sn xut, vt t, ti chnh, u t, nhn s ) phi lun lun cn i chi ph cn bin v doanh thu cn bin. Tuy nhin nhiu quyt nh qun l cn xem xt n nhng thay i c quy m ln. Chng hn nh, nh qun l mun tm hiu nh hng ca 20% doanh thu tng ln hay ca vic tung ra mt dng sn phm mi i vi li nhun ca hng.Phn tch tng tin (Incremental analysis) thng c dng trong mi tng quan thc t vi phn tch cn bin. N lin quan n mt quyt nh qun l c th, c th bao gm s la chn gia 2 sn lng u ra ring r (v d gia 10,000 n v v 15,000 n v). y l qu trnh kim tra nh hng ca cc quyt nh la chn phng n thay th i vi doanh thu, chi ph hay li nhun. N ch ra nhng thay i hay khc bit gia cc phng n. Cc nh qun l phi cn i c chi ph tng thm lin quan n quyt nh la chn vi doanh thu tng thm. V vy phn tch cn bin thng c gi l phn tch tng tin.CU HI1. nh ngha thut ng ti u ha.2. Tho lun qua v php th hm bc nht v hm bc hai.3. Ti u ha b rng buc l g? Hai phng php gii quyt vn ti u ha b rng buc4. nh ngha nhn t Lagrangean. Ci g c coi l bin kp trong quy hoch tuyn tnh?5. o hm l g? N dng o lng ci g?6. Phn bit gia phn tch cn bin v phn tch tng tin.BI TP1. ABC Boutique bn mi sn phm vi mc gi $20. Tng chi ph sn xut Q n v c th hin trong hm: TC = 40 + 4Q +0.02Q2. Cn phi sn xut bao nhiu n v ti a ha li nhun?Li nhun ti a mc sn lng ny l bao nhiu?2. Chng minh rng y l im cc i ch khng phi l im cc tiu bng cch tnh o hm bc hai ti gi tr x.3. Tm cc im cc i v cc tiu ca hm s y = 1,500 - 600x - 15x2 + x3, v tnh o hm bc 2 phn bit chng.4. B phn phn tch kinh t ca mt hng sn xut c tnh tng doanh thu l TR(Q) = 3,200Q - 6Q2 v tng chi ph l TC(Q) = 90 + 2Q226/142a. Sn lng Q no ti a ha li nhun?b. Doanh thu cn bin mc sn lng Q l bao nhiu?c. Chi ph cn bin mc sn lng Q l bao nhiu?d. Mc li nhun no l ti a?5. Jon Electronics hot ng vi hm TR v TC sau:TR = $200Q - $0.5Q2 v TC = $1,000 - $40Q + $0.5Q2a. Xc nh sn lng Q (sn lng u ra) ti a ha doanh thu.b. Xc nh sn lng Q ti thiu ha chi ph. c. Xc nh sn lng Q ti a ha li nhun. d. Chng minh rng MR bng MC ti sn lng Q lm ti a ha li nhun.6. Mc ch ca k hoch lu kho l to ra cc chnh sch nhm t c khon u t ti u cho sn lng lu kho. C th t c mc tiu ny bng cch xc nh mc lu kho ti u cn gim thiu ha chi ph lu kho. Tng chi ph lu kho hng nm (TIC) bao gm chi ph vn chuyn + chi ph t hng, v d TIC = C (Q/2) + S (D/Q), trong C = chi ph vn chuyn mi n v, S = chi ph t hng ca mi n hng, D = cu hng nm tnh theo n v v Q = s lng n hng. Lp cng thc xc nh s lng n hng kinh t Q* (EOQ) bng cch ti thiu ha TIC.7. S dng phng php L tm im cc trTi a haz = xyRng buc x + y = 68. Mt hng c hm li nhun trong bin li nhun Z l mt hm ca mc sn lng u ra gm 2 loi sn phm x v y: Z = -60 + 140x + 100y - 10 x2 - 8y2 - 6xy. Gi thit rng trong cung cp ngn hn, hng ny ch c nguyn liu th hn ch l 200 n v. Cc sn phm x v y ln lt cn 20 n v v 40 n v nguyn liu th sn xut mt n v u ra. Hng mun xc nh phng php kt hp cc sn phm ti a ha li nhun. a. Gii quyt vn nh cch gii quyt hm ti u ha b rng buc b. S dng phng php th xc nh sn lng x v y s ti a ha li nhun (Z)c. Gii bi ton bng phng php L d. Din gii gi tr kinh t ca tm c trong phn (c).27/142TR LI1. Ti u ha l ti a ha hoc ti thiu ha mt mc tiu c th (v d nh li nhun hay chi ph).2. Th o hm bc nht nhm mc ch xc nh mt hay nhiu im cc tr (cc i hay cc tiu) trong mt hm. Th o hm bc 2 nhm xc nh im cc tr tm c l cc i hay cc tiu.3. Tiu ha b rng buc l tm phng php ti u ha vi cc rng buc cho trc v s di do ca cc ngun lc v cc iu kin khc. Cc phng php nh LP v L c dng gii quyt vn ny.4. Phng php L o lng s thay i cn bin trong gi tr ca hm mc tiu khi c s thay i ca mt n v trong gi tr ca hm rng buc. y l cc bin kp trong quy hoch tuyn tnh v i din cho gi m ca ngun lc khan him cho trc.5. Hm dy/dx o lng s thay i cn bin trong y dn n s thay i nh trong x. V c bn l dc ca hm. 6. Phn tch cn bin lin quan n mt n v u ra, trong khi phn tch tng tin lin quan n mt quyt nh qun l c th, c th bao gm s la chn gia 2 sn lng u ra ring r (v d gia 10,000 n v v 15,000 n v). Phn tch tng tin thng c dng trong mi lin quan vi phn tch cn bin. GI TR LI 1.Tng li nhun ( )= Tng doanh thu (TR) tng chi ph (TC)= $20Q - (40 + 4Q + 0.02Q2) = -40 + 16Q - 0.02Q2Ly o hm theo Q v t n bng 0 ta c, d /dQ = 16 - 0.04Q = 0, tm c Q* = 40.Li nhun ti a ti Q* = 40 l: * = -40 + 16Q - 0.02Q2 =-40 + 16(40) - 0.02(40)2 = 568.2.t dy/dx = 0: dy/dx = 75 - 0.5x =0; x = 150. V d2y/dx2= - 0.5 < 0, ti x = 150 t im cc i.3.t dy/dx = 0 xc nh c im cc i v cc tiu dy/dx = -600 - 30x + 3x2 = 0hoc(3x + 30) (x - 20) = 0cc nghim kp l x = -10; x = 20.28/142Ly o hm bc 2 ta c d2y/dx2 = -30 + 6xTi x = -10, d2y/dx2 = -30 + 6x = -30 + 6(-10) = -90 < 0 (cc i)Ti x = 20, d2y/dx2 = -30 + 6x = -30 + 6(20) = 90 > 0 (cc tiu)4.a. Cho: TR(Q)=3,200Q - 6Q2 v TC(Q) = 90 + 2Q2 C MR v MC nh sau:MR = dTR/dQ = 3,200 -12Q v MC = dTC/dQ = 4QTi sn lng u ra ti a ha li nhun, MR = MC, do vyMR = 3,200 - $12Q = 4Q = MCTm c Q* = 200 n v, l sn lng u ra ti a ha li nhun.b. MR = 3,200 -12Q = 3,200 - 12(200) = 800c. MC = 4Q = 4(200) = 800d. Li nhun = TR - TC =3,200Q - 6Q2-(90 + 2Q2)=-90 + 2,300Q -8Q2.Khi Q*=200, li nhun l -90 + 2,300(200) - 8(200)2 = $139,910.5.a. t dTR/dQ =$200 - Q = 0; Q = 200b. t dTC/dQ = -$40 + Q = 0; Q = 40c. Tng li nhun( )= TR - TC = $200Q - $0.5Q2 - ($1,000 - $40Q + $0.5Q2) = -$1,000 + $240Q - Q2t d /dQ =$240 -2Q = 0; Q =120d. Ti Q*=20, ch rng:MR = dTR/dQ = $200 - Q = $200 - 120 = $80MC = dTC/dQ =-$40 + Q = -$40 + 120 = $806. V vy, MR = MC = $80Cho TIC =C(Q/2) + S (D/Q), ly o hm ca TIC theo Q v t n bng 0, c:dTIC/dQ =C/2 - SDQ-2 = 0 ----> Q2 = 2SD/C----> Q* = EOQ =C SD / 27.Hm L l:L(x, y, ) = xy + (6 - x - y)29/142Ly o hm bc nht ln lt theo x, y, v ta c:L/x = y - = 0L/y = x - = 0L/ = 6 - x - y = 0ng thi gii cc o hm ta c: x = 3, y = 3, v = 3.8.a. Bi ton c dng:Ti a ha Z = -60 + 140x + 100y - 10x2 - 8y2 - 6xy.Rng buc 20x + 40y = 200 b. Tm c x theo y v th vo phng trnh Z 20x + 40y = 200 ----> x = 200/20 - 40y/20 = 10 - 2y Z =-60 + 140x + 100y - 10 x2 - 8y2 - 6xy = -60 + 140(10 -2y) + 100y - 10(10 - 2y)2 - 8y2 - 6(10 - 2y)y = 340 + 160y - 36y2S dng iu kin bc nht tm im cc tr, ta c dQ/dK v t chng bng 0:dQ/dK =160 - 72y = 0, ngha l y =2.22 n v v x = 10 - 2y =10 - 2(2.22) =5.56 n v c. Hm L l:L(x, y, ) = -60 + 140x + 100y - 10x2 - 8y2 - 6xy+ (200 - 20x- 40y)Dng o hm ring:L/x = 140 - 20x - 6y + 20= 0L/y = 100 -16x -6y + 40= 0L/ = 200 - 20x - 40y = 0Gii ng thi 3 phng trnh tm c x = 5.56, y =2.22, =0.774d. =0.774 ngha l li nhun c th tng ln $0.774 nu thm vo mt n v nguyn liu th; ngha l tng t 200 n v ln 201 n v nguyn liu. 30/142CHNG 3 - LC TH TRNG: CU V CUNGMC TIU HC TP:Sau khi hc chng ny bn c th:1. nh ngha hm cu2. Minh ha biu cu3. Xy dng v gii thch ng cu4. Xc nh cc yu t dch chuyn cu5. Tnh ton doanh thu bnh qun6. Hiu r khi nim doanh thu cn bin7. Gii thch v cho v d v hm cu tuyn tnh8. Tnh ton v gii thch khi nim co gin im ca gi9. Hiu v tho lun co gin on10. Tnh ton co gin thu nhp11. Tnh ton v cho v d v co gin qung co12. Gii thch khi nim co gin lin tc13. nh ngha v cho v d v hng ho thay th14. Minh ha cng dng v li ch ca hng ho b sung15. nh ngha v cho v d v hng ho thng thng16. Xc nh v minh ha hng th cp17. Tnh ton mc gi ti u18. V th ng cung 19. Xc nh cc nhn t dch chuyn cungPhn tch cu hu ch trong vic d on doanh s, nh gi, v lp k hoch li nhun di hn. Phn tch cu bao gm:1. Lng ha nhu cu c th2. Tnh ton h s co gin ca cu 3. c lng cc hm s ca cu4. D bo doanh s5. Quyt nh giTrong chng ny chng ta s tho lun 2 ch im u. Cc ch im khc s c cp cc chng sau. 31/142HM CUL thuyt kinh t ch ra rng cu ca mt sn phm ph thuc vo gi ca n, v d.Qd = f(P)L thuyt kinh t cn cho bit rng ngoi gi, cu cn ph thuc vo cc yu t khc:Qd = f (P, PC, Y, A,...)Trong P = gi ca sn phm, PC = gi ca hng thay th v b sung; Y = thu nhp, A = qung co. Hm cu l mt mi quan h ton hc cho thy lng cu ca mt hng ha hay dch v s thay i nh th no khi cc nhn t trn thay i. Cc nhn t phi gi gi l nhn t dch chuyn cu. nh hng ca mi nhn t phi gi n lng cu c th c c lng thng k da vo cc d liu cho hoc theo dng thi gian.BIU CUBiu cu (Demand schedule) l mt bng hay biu th hin lng cu cc mc gi khc nhau trong mt khong thi gian nht nh, vi iu kin cc yu t khc khng i. C th dng s liu t biu cu xy dng ng cu. NG CUng cu (demand curve) l ng m t biu cu, th hin mi quan h nghch o gia gi v lng cu trong mt khong thi gian, vi iu kin cc yu t khc khng i. Gi nm trn trc tung, lng cu nm trn trc honh. Ch rng s thay i t im A n im B trn ng cu l do s thay i ca gi. S thay i t im A n C trn ng cu li khng phi do gi m do cc nhn t phi gi lm dch chuyn cu.S DCH CHUYN CUS thay i ca mt nhn t phi gi bt k ca sn phm (gi l cc nhn t lm dch chuyn cu demand shifters) s dn n cu i vi sn phm tng hoc gim. Cc nhn t ny bao gm 1. Thu nhp ca ngi tiu dng, 2. Gi ca hng b sung hay thay th 3. Th hiu ca ngi tiu dng. Trn s , s dch chuyn ca cu c th hin bng mt ng cu song song vi n.32/142HNH 1NG CU V CC NHN T DCH CHUYN CUNG CU TH TRNGng cu th trng ca mt sn phm th hin s lng hng ha khc nhau m nhm ngi tiu dng sn sng v c kh nng mua cc mc gi khc nhau ti mt thi im c th khi cc nhn t nh hng n hnh vi tiu dng khng i. Do vy, ng cu th trng phn bit mi quan h gia gi v lng cu gia cc nhm ngi tiu dng. N c xc nh bng cch ly tng s lng hng ha ca mt sn phm m mi ngi tiu dng sn sng v c kh nng mua ti cc mc gi khc nhau.CU V DOANH THUTng doanh thu ca mt hng lin quan cht ch n cu i vi sn phm hay dch v ca hng . TR l hm ca gi v lng cu, tc l:TR = f (P, Q) = P x QV d, nu P = 500-0.02Q, khi TR = PQ = (500 - 0.2Q)Q = 500Q - 0.02Q2 33/142DOANH THU BNH QUNDoanh thu bnh qun (AR) l tng doanh thu ca mi n v u ra, bng tng doanh thu thu chia cho u ra, v d, AR = TR/Q = (500Q - 0.02Q2)/Q = 500 - 0.02QDOANH THU CN BINDoanh thu cn bin l t l thay i ca tng doanh thu theo s thay i ca lng cu, tc l: MR = dTR/dQ = d(P x Q)/dQ = 500 - 0.04QHNH 2DOANH THU BNH QUN, DOANH THU CN BIN V TNG DOANH THU34/142S CO GIN CA CUVic xc nh xem nn gim gi hay tng qung co mt sn phm ph thuc nhiu vo s co gin ca cu (elasticity of demand) sn phm . Mt trong nhng khi nim quan trng nht v cu l s co gin cho bit tnh nhy cm ca lng cu i vi s thay i ca mt nhn t trong hm cu. Nhng nhn t ch yu dn n s co gin ca cu l: 1. Gi c ca hng ha (trong trng hp co gin theo gi)2. Gi c ca hng ha thay th (trong trng hp cu co gin cho)3. Thu nhp (trong trng hp co gin theo thu nhp)4. Qung co (trong trng hp co gin theo qung co)CO GIN THEO GICo gin theo gi (price elasticity), k hiu l ep, l t l phn trm thay i trong lng cu (Q) tng ng vi phn trm thay i trong gi (p), t l ny nhn gi tr dng. Chng ta phn loi co gin ca cu theo gi thnh 3 nhm:Co gin ca cu theo gi Mc co ginep>1 Co ginep=1 Co gin n vep 0, hng ho thay th. Mt t l co gin cho cao c ngha nhng hng ha c kh nng thay thcho nhau cao( v d: c ph v tr c th thay th cho nhau)2. Nu e pX < 0, l hng ha b sung. (v d: Nhng my thu c m thanh trung thc v nhng a CD). 3. Nu e pX = 0, cc hng ha c lp vi nhau.CO GIN CA CU THEO THU NHPCo gin ca cu theo thu nhp l s thay i ca lng cu tng ng vi s thay i ca thu nhp, vi iu kin cc yu t khc khng i, c tnh nh sau://YXdQ Q dQ YedY Y dY Q %Q thay i%Y thay iNu e Y > 0, sn phm l hng ha thng thng hoc hng ha cao cp c cu thay i ngay khi thu nhp thay i, vi gi nh gi khng i. Mt lng ln hng tiu dng l hng cao cp.Nu e Y < 0, hng ha l hng th cp. Cu gim khi thu nhp c nhn tng ln, do ngi dn chuyn sang tiu th cc hng ha xa x khi c mc thu nhp cao hn. V d v hng ha th cp:u rang, lp xe t v li, v hng ha lu bn CO GIN CA CU THEO QUNG CO co gin ca cu theo qung co l t l phn trm thay i trong sn lng bn ra (hoc th phn) tng ng vi t l phn trm thay i trong chi tiu qung co ca mt sn phm//AXdQ Q dQ AedA A dA Q %Q thay i%A thay iN dng o s hiu qu ca qung co trong ngn hn. Co gin ny c th b nh hng bi mt s cc yu t nh giai on pht trin th trng cho mt sn phm, mc 41/142 phn ng ca cc i th cnh tranh i vi qung co ca hng, hoc i vi nhng n lc xc tin hoc qung co c tng ln, tm quan trng ca cc yu t marketing khc (v d nh gi, thu nhp, th hiu), s lng v cht lng ca qung co hin ti v trc y ca hng.S CO GIN CA TH PHNL phn trm thay i trong th phn ca mt cng ty c c t mt phn trm thay i trong gi CO GIN KHNG IMi quan h c th th 2 v cu c dng m cho bit s co gin lin tc. C th tm thy dng thc ny trong dng hm m:Mt v d lQ = aPbAcYd(1)Trong P = gi, A l qung co, v Y = thu nhpTheo nh ngha,pQ PeP Q %Q thay i%P thay i(2)Vi phn biu thc (1) theo gi (P), ta c:1 b c dQabP A YPDo , e p = abPb-1AcYd.(P/Q)(3)Thay Q trong (3) bi (1) c:e p = abPb-1AcYd.(P/ aPbAcYd) (4)Bin i biu thc, ta c:Xb c dabP A YPe bpb c dPaP A Y Nh vy, co gin cu theo gi bng b (thng mang du m), bin gi c biu din trong hm cu dng m nh trong biu thc (1). Do , co gin khng phi l mt hm ca t l gi/lng (P/Q) v v vy l khng i. Tng t, c th chng minh c rng (1) co gin theo thu nhp l c, v (2) co gin qung co l d. CH 42/142Dng hm m c th chuyn sang dng log tuyn tnh dng logarit v tnh bng phng php bnh phng nh nht. Biu thc (1) tng ng vi: log Q = log a + b log P + c log Y + d log AC c s co gin khng i l rt hu ch, v n c ngha l s thay i ca mt trong cc bin c lp, nh thu nhp s dn n s thay i tng ng trong lng cu. Ch rng s co gin ca mt hm tuyn tnh thay i trn ton b ng cuV D 5Cho hm cu c dng m sau:Q = 2077P-0.144PX0.097A0.314Co gin theo gi lun lun l -0.144, c ngha l gi gim (tng) 1% s dn ti cu tng (gim) 0.14%CHNH SCH NH GI TI U V CO GIN GICh rng, nu khng c php o hm ton hc, th mi quan h gia co gin im ca cu theo gi, doanh thu cn bin v gi l:

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+ peP MR11(ch : ep l s m)iu ny suy ra trc tip t nh ngha ton hc ca MR. Dng thc ny rt hu ch trong thit lp chin lc nh gi ca mt hng. T iu kin ti a ha li nhun MR=MC, chng ta rt ra c cng thc xc nh mc gi ti a ha li nhun, c biu din nh sau:MC = MR

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+ peP MC11Tm c P* l mc gi ti u hay ti a ha li nhun:peMCP11*+V D 6Mt ngi qun l ca ca hng chi thy rng khi gim gi 1% cho mi con bp b Bamboo s lm tng 2,5% doanh s bn hng tun. Tng chi ph bn bun cho mi bp b, cng vi chi ph trng by v marketing l $30 mi con. Co gin cu theo gi trong trng hp ny l:43/1422.52.51Pe %Q thay i%P thay iMc gi ti a ha li nhun lP = $30/(1 +1/-2.5) = $50Gi thit rng ngi qun l, thng qua lng hng ha mua, c th gim chi ph cn bin cho mi ch bp b l $3 cn li 27$. Mc gi ti u mi l:P = $27/(1 +1/-2.5) = $45Nh vy, mc gi ti a ha li nhun gim xung $5 sau khi chi ph cn bin mi sn phm gim $3.HM CUNGCho n phn ny, chng ta tp trung nghin cu kha cnh cung ca th trng ng vai tr l na ngun lc xc nh mc gi trn th trng. Mt na ngun lc c tnh quyt nh khc l cung th trng. L thuyt kinh t cho chng ta bit rng cung i vi mi sn phm ph phuc vo gi bn ca n, v d nh:Qs = f(P)L thuyt kinh t cn cho bit cung cn chu nh hng ca cc yu t khc ngoi gi: Qs = f (P, PX, W,...)Trong P = gi bn ca sn phm , PX = gi ca hng ha c lin quan n nhau v mt k thut, W = gi tr ca cc bin khc nh hng n cung, nh cng ngh hin c hay thi tit. Hm cung l mi quan h ton hc cho bit lng cung ca mt hng ha hay dch v thay i nh th no khi cc yu t ny thay i (xem hnh 6). Mt hng cnh tranh s sn xut mc sn lng m ti chi ph cn bin bng doanh thu cn bin (gi bn). Nh vy, mt s thay i trong gi u vo nh hng ln chi ph cn bin v lng cung ra.Cc yu t phi gi gi l yu t lm dch chuyn cung. nh hng ca mi yu t phi gi ln lng cung c th c lng thng k theo thi gian v d liu cho.S DCH CHUYN CUNGS thay i ca bt k mt yu t phi gi no u lm cho cung ca mt sn phm dch chuyn. Trn th, s dch chuyn cung c minh ha bng mt ng song song vi ng cung. Mt s dch chuyn sang phi (tri), hoc l mt s tng ln (hay gim) trong cung cho bit sn phm c cung ra nhiu (t) hn trc khi gi tng ln (gim xung). Cc nhn t lm dch chuyn cung gm (1) gi u vo, (2) cng ngh, (3) s lng cc hng sn xut, (4) hng ha thay th trong sn xut, v (5) thu mn bi.44/142HNH 6HM CUNG V CC NHN T DCH CHUYN CUNGCN BNG TH TRNGCn bng th trng (market equilibrium) trong mt th trng cnh tranh c xc nh l giao im ca ng cung v cu th trng. Gi cn bng l mc gi ca mt sn phm (hng ha v dch v) m mt th trng cnh tranh hng ti, khi , mc gi ny khng thay i. l mc gi m ti th trng n nh ngha l mc gi c xc nh bng im giao nhau ca ng cung v cu (Hnh 7). Lng cn bng l sn lng tng ng vi gi cn bng. N l mc u ra m ti th trng n nhQd = Qs45/142HNH 7CN BNG TH TRNGV D 7Cc phng trnh sau y m t cc hm cung v cu hng thng i vi cc dch v git kh mt a phng:Qd =50 - 2P(cu)Qs = -20 +5P (cung)Kt hp gi - u ra cn bng c xc nh nh sau:Ti im cn bng, Qd = Qs50 - 2P = -20 + 5P-7P = -70; P = $10 tm lng cn bng, chng ta ch cn thay mc gi ny vo hm cung hoc cu. V d, dng hm cu, tm c Qs = -20 +5P= -20 +5(10) = 30 n v.CU HI1. Phn tch v l thuyt cu gm nhng vn g? Lit k tc dng ca n trong xc nh doanh thu ca mt hng.2. Cc nhn t dch chuyn cu l g? Cho v d.3. nh ngha tng doanh thu, doanh thu bnh qun, v doanh thu cn bin. Gii thch mi quan h gia chng.4. Cc yu t lin quan n co gin cu? 5. Phn bit co gin on v co gin im.6. im c bit ca ng cu tuyn tnh trong mi lin h vi co gin gi l g? 7. M t mi quan h gia co gin ca cu theo gi v tng doanh thu.8. Cho 2 v d gii thch co gin gi c s dng trong ra quyt nh marketing9. Bn hiu khi no th mt sn phm l hng ha thng thng, khi no l mt hng ha th cp?10. Cc dng hm s cho bit s co gin lin tc ca cu?11. M t mi quan h gia co gin im ca cu theo gi, doanh thu cn bin, v gi.BI TP1. Mt nh sn xut van cn nhc xem c nn tng gi bn van t mc gi bnh qun hin ti l $2,000 mi chic. Hin nay, mi thng nh sn xut bn c 600 chic, nhng ang c gng gim doanh s xung mc nhiu nht l 500 chic mi thng. Nu co gin cu theo gi ca hng l -2 trong khong t $2,000 46/142n $2,500 mi van, nn xc nh mc gi mi no sn xut mc nng sut ny?2. Cng ty lin doanh Lilex Watch ang xem xt gim gi bn ng h eo tay t mc gi bn hin nay l $80 xung $70 mi chic. Cng ty bn c 2,000 mi thng. Nu co gin cu theo gi ca ng h l -2, lng bn mi l bao nhiu?3. Cng ty lin doanh Sunhee Bags c lng hm cu i vi ti ng cao cp khu vc vnh San Francisco nh sau: P = 600 - 0.3Qa. Xc nh hm MR v TR.b. Xc nh mc gi ti Sunhee Bags khng bn c mt chic ti ng no c?c. Sn lng ti a m Sunhee Bags c th bn c?d. Hng c th t c doanh thu ti a l bao nhiu?e. Vi mt lng phn trm thay i trong gi cho trc, phn trm thay i trong lng cu l bao nhiu mc sn lng u ra Q = 700?f. Co gin on ca cu theo gi i vi s lng t 700-800 ti ng?4. Cho ng cu sau:Q = 250 - 0.5PXc nh hm tng doanh thu (TR), doanh thu cn bin (MR), v hm doanh thu cn bin (AR) tng ng.5. Cho ng cu sau:P = 400 - 3QXc nh hm tng doanh thu (TR), doanh thu cn bin (MR), v hm doanh thu cn bin (AR) tng ng6. Phng marketing ca mt cng ty sn xut phn cng t c hm cu i vi sn phm t ca h nh sau:Q = 150,000 -52P + 80PC + 0.3A + 0.5YTrong Q = s lng t hng bn c mi tunP = Gi bn t ca hngPC = Mc gi bn t ca i th cnh tranh trc tipA = Chi ph qung co hng tunY = thu nhp dnh cho tiu dng bnh qun ca mi gia nha. Nu P = $12,000, PC = $10,000, A = $310,000, v Y = $25,000, tm hm cu v xc nh co gin ca cu theo gi.47/142b. Nhn xt v co gin gi tm c trong phn (a). Nu hng tng gi, iu g s xy ra vi tng doanh thu?c. Vi gi tr tm c trong (a), tnh co gin ca cu theo thu nhp. Gii thch.d. Xc nh co gin cho ca cu gia hai loi t cnh tranh. Gii thch7. Cu i vi sn phm ca cng ty bn c tnh l QA = 8,500 - 4PA - 2PB +PC - 0.1Y, trong P = gi v Y = thu nhp. Gi tng ng v s liu v thu nhp nh sau: PA = 10, PB = 50, PC = 50, v Y = 40,000.a. u l hng ha thay th cho sn phm A? u l hng ha b sung?b. A l hng ha thng thng hay th cp ?c. Lng sn phm A bn ra s l bao nhiu? 8. a. Bin i cng thc:b. Gii thch mi quan h gia MR v co gin cu theo gi (ep)9. Ngi qun l ca mt ca hng chi thy rng c gim 1% gi bn bp b th doanh s hng tun tng ln 2%. Tng chi ph bn bun cng vi chi ph trng by v marketing l $15 mi con bp b.a. Co gin im ca cu theo gi ca ca hng?b. Tnh gi bn ti u c. Gi s nh qun l thng qua lng hng mua vo c th gim $1 chi ph cn bin xung cn $14 mi ch bp b. Tnh mc gi ti u mi?10. Sn phm lng thc ca cng ty bn c co gin cu theo gi l -0.8. Nu gi bn lng thc tng ln 5%, lng cu i vi lng thc v tng doanh thu thay i nh th no?11. Cc phng trnh sau m t hm cung v cu hng thng i vi dch v git kh mt a phng 48/142 1 MR = P1 + ---- ep Qd = 40,000 - 4,000P (cu)Qs = -10,000 + 10,000P (cung)a. Ti mc gi bnh qun no, cu bng 0?b. Ti mc gi bnh qun no, cung bng 0?c. Tm kt hp gi- u ra cn bng?TR LI1. Phn tch cu bao gm: Lng ha nhu cu c tha. Tnh ton h s co gin ca cu b. c lng cc hm s ca nhu cuc. D bo doanh sd. Quyt nh gi2. Nhng nhn t dch chuyn cu lm tng hoc gim cu bng cch thay i mt nhn t phi gi bt k. Nhng nhn t ny bao gm: (1) Thu nhp ca ngi tiu dng, (2) Gi ca hng ha thay th hoc hng ha b sung, (3) Th hiu ca ngi tiu dng. Xt trn s , s dch chuyn ca mt ng cu c biu din bng mt ng cu khc song song vi n.3. Tng doanh thu (TR) ca mt cng ty lin quan trc tip n cu i vi hng ha v dch v ca cng ty . Doanh thu bnh qun (AR) l tng doanh thu trn mi n v u ra, bng tng doanh thu chia cho tng u ra, tc l AR = TR/Q. Doanh thu cn bin (MR) l t l thay i ca tng doanh thu theo lng cu, tc l MR = dTR/dQ.Tng doanh thu c ti a ho khi MR bng 0.4. Cc yu t chnh tc ng n co gin cu l:1. Gi c ca hng ha (trong trng hp co gin theo gi) 2. Gi c ca hng ha thay th (trong trng hp cu c co gin cho) 3. Thu nhp (trong trng hp co gin theo thu nhp) 4. Qung co (trong trng hp co gin theo qung co)5. Co gin on ca cu l thay i ca lng cu bnh qun khi c s thay i ca gi gia 2 gi tr khc nhau, trong khi co gin im c tnh ti mt im xc nh.6. Trng hp hm cu tuyn tnh, trong khi dc ca ng cu c dng ng thng l bng nhau ti mi im, th co gin ca ng ny thay i t mt im ti im tip theo.7. Cc nh kinh t xy dng c mi quan h gia co gin gi (ep) v tng doanh thu (TR), c th gip cho hng xc nh gi bn.49/142Gi ep > 1 ep = 1 ep < 1Tng TR gim Khng i TR tngGim TR tng Khng i TR gim8. Co gin gi c th dng tr li cc dng cu hi sau: (a) nh hng ca 5% gi tng ln tc ng g n doanh s? (b) cn gim gi bao nhiu nng doanh thu ln 20%? 9. Nu co gin thu nhp (eY) ln hn 0, sn phm l hng ha thng thng hay hng ha cao cp c cu thay i trc tip khi thu nhp thay i, gi nh gi khng i. Nu e Y < 0, sn phm l hng ha th cp.10. Dng m cho bit co gin lin tc. Mt v d l: Q = aPbAcYd.11. Mi quan h gia co gin im ca cu theo gi, doanh thu cn bin, v gi l:

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+ peP MR11GI TR LI:1.2 / ) /( ) (2 / ) /( ) (] 2 / ) /[( ) (] 2 / ) /[( ) (1 2 1 21 2 1 21 2 1 21 2 1 2P P P PQ Q Q QP P P PQ Q Q Qep+ + + + -2 =[(500 - 600)/(P2 - 2000)][(P2 + 2000)/(500 + 600)]=-100(P2 + 2000)/1100/(P2 - 2000)-2(11P2 - 22000) = -P2 - 2000-22P2+ 44000 = -P2 - 2000-21P2 = -46000P2 = $2190.48 2.-2 = [(Q2 - 2000)/( 70 - 80)][(70 + 80)/(Q2 + 2000)]-2 = 150(Q2 - 2000)/-10(Q2 + 2000)-2(-10Q2 - 20000) = 150Q2 - 30000020Q2 + 40000 = 150Q2 - 300000-130Q2 =-340000Q2 = 2615.383.50/142a. Cho P = 600 - 0.3Q:TR = PQ = (600 - 0.3Q)Q = 600Q - 0.3Q2MR = dTR/dQ = 600 - 0.6Qb. Ti P = $600, Q = 0 v P = 600 - 0.3(0) = $600.c. P= 600 - 0.3Q, v vy Q = 2,000 - 10/3PTi mc gi bng0, Q = 2,000 - 10/3(0) = 2,000 ti ngd. TR ti a ha khi MR = 0. MR = dTR/dQ = 600 - 0.6Q = 0; Q = 1,000 ti ngTi Q = 1,000 ti ng, TR = 600Q - 0.3Q2 = 600(1,000) - 0.3(1,000)2 = $300,000e.//PXdQ Q dQ PedP P dP Q %Q thay i%P thay iTh nht,3 / 10 DPdQTh, ti Q = 700, P = 390e p = -(10/3) x (390/700) = -1.86. Co gin im ca cu l -1.86, v vy phn trm thay i trong lng cu l -1.86 nhn vi phn trm thay i trong gi.(f) V P= 600 - 0.3Q, Ti Q = 700, P= 600 - 0.3(700) = $390Ti Q = 800, P= 600 - 0.3(800) = $360V vy, co gin on ca cu67 . 1) 700 800 () 390 360 () 390 360 () 700 800 () () () () (1 21 21 21 2 ++++XQ QP PXP PQ Q4.Q = 250 - 0.5P ---->0.5P = 250 - Q ----> P = 500 - 2QTR = P x Q = (500 - 2Q)Q = 500Q - 2Q2MR = dTR/dQ = 500 -4QAR = TR/Q = 500 - 2Q51/1425.TR = P x Q = (400 - 3Q)Q = 400Q - 3Q2MR = dTR/dQ = 400 -6QAR = TR/Q = 400 - 3Q6.a. Hm cu l:Q =150,000 -52P + 80PC + 0.3A + 0.5Y =150,000 -52P + 80(10,000) + 0.3(310,000) + 0.5(25,000) = 1,055.500 -52PV vy, Q = 1,055,500 - 52P = 1,055,500 -52(12,000) = 431,500b. Co gin ca cu theo gi l .52(12, 000/ 431, 500) 1.45 1.45 1PQ PeP Q >%Q thay i%P thay iCu i vi t co gin v v vy, nu gi tng ln, tng doanh thu s gim xung nhanh chngc. co gin ca cu theo thu nhp l.0.5(25, 000/ 431, 500) 0.029 1YQ YeY Q c%Q thay i%P thay iV co gin cho ln hn 0 nn hai loi xe ny l hng ha thay th.7.a. C l hng ha thay th, trong khi B l hng ha b sung cho A.b. A l hng ha th cp c th hin qua bin thu nhp mang gi tr m52/142c. QA = 8,500 - 4PA - 2PB +PC - 0.1Y = 8,500 -4(10) - 2(15) + (50) - 0.1(40,000) = 4,4808.a. Theo nh ngha,MR = dTR/dQ = d(P x Q)/dQ = d[f(Q)x Q)]/dQ =f(Q) + f(Q) Q = P + Q (dP/dQ)b. Ta thyMR > 0 khi ep > 1MR = 0 khiep = 1MR < 0 khi ep < 19.a.221Pe %Q thay i%P thay ib. Mc gi ti a ha li nhun l:P = $15/(1 +1/-2) = $30c. Mc gi ti u mi l:P = $14/(1 +1/-2) = $28V vy, mc gi ti a ha li nhun gim $2 khi chi ph cn bin ca ca hng gim $1 mi con bp b.10.0.8Pe %Q thay i %Q thay i%P thay i 5%53/142 Q dP1 = P 1 +------= P 1 +----- P dQ eP % Q thay i Q = -0.8(5) = -4%. Cu i vi lng thc gim 4% nu gi tng 5%. V co gin gi b hn 1, cu khng co gin. V vy, gi tng ln s dn n tng doanh thu tng ln11.a. t Qd = 0v tm P Qd = 40,000 - 4,000P = 0; P = $10.b. t Qs = 0 v tm P Qs = -10,000 + 10,000P = 0; P = $1c.Ti cn bng th trng, Qd = Qs.40,000 - 4,000P = -10,000 + 10,000P50,000 = 14,000P; P = $3.57, Thay P = $3.57 vo c hm cung v cu, c: Qd = 40,000 - 4,000P = 40,000 - 4,000($3.57) = 25,720 n v.54/142CHNG 4 - PHN TCH CU NH LNGMC TIU HC TP:Sau khi hc chng ny bn c th:1. Thit k bn iu tra ngi tiu dng2. Thc hin v tho lun v th nghim th trng3. Tho lun v ch ra vn nhn dng4. Gii thch phn tch hi quy5. Tnh ton v cho v d v hi quy tuyn tnh6. nh ngha v tnh ton hi quy n 7. Gii thch phng php bnh phng nh nht8. Hiu v gii thch c phng php hi quy bi9. Tnh ton sai s chun ca h s hi quy 10. Biu din v tnh ton sai s chun ca c lng 11. Minh ha v gii thch h s xc nhTrong chng trc, chng ta nghin cu l thuyt v nhu cu; khi nim co gin ca cu. Trong chng ny, chng ta nghin cu quy trnh dng trong c lnghm cu theo kinh nghim. Vi c lng cu, c th tnh ton nh lng cc co gin v xc nh nh hng ca mt s thay i trong cc nhn t nh gi, thu nhp hay qung co i vi lng cu. V c bn, c 2 phng php c lng cu chnh: Trc tip v thng k. Phng php c lng cu trc tip gm iu tra ngi tiu dng v th nghim th trng. Mt mu d liu th trng thu c ti mt thi im l mt vn i hi s tham gia ca nhiu ban ngnh. c lng thng k ca hm cu ch yu da trn kinh t lng v phn tch hi quy.IU TRA NGI TIU DNG (CONSUMER SURVEYS)iu tra ngi tiu dng v phn ng ca h ti nhng yu t nh mc nhy cm i vi s thay i gi, s sn sng mua, hoc s quan tm n cc chin dch qung co. Bng vic x l cc d liu thu thp c, hng c th nhn thc tt hn cc yu t chnh trong hm cu. Mt u im l trong d on doanh s ngn hn, thng tin ch quan v quan im v mong mun ca ngi tiu dng, ch c th c c bng phng php phng vn, cho thy khong cch r rng gia mt c lng chnh xc v mt c lng khng chnh xc. Phng php ny cng c mt s nhc im. Mt trong s l ngi tiu dng thng khng th, hoc i khi khng sn lng cung cp cu tr li chnh xc cho nhng cu hi c tnh gi thuyt v phn ng ca h i vi s thay i trong cc yu t bin i chnh ca cu.55/142TH NGHIM TH TRNG (MARKET EXPERIMENTS)Th nghim th trng kim tra cch m ngi tiu dng phn ng trong nhng tnh hung th trng thc t. Mt hng thay i gi, qung co v cc yu t c thkimsot khctronghmcutheothi gianvgiaccth trng, t quan st nh hng ca chng ln lng cu. u im ca phng php ny l v ngi th nghim c th kim sot c cc bin quan trng trong hm cu nh gi v qung co, hng sn xut c th c c hiu bit su sc v nhng nh hng trong ngn hn. C th nhn thy c s co gin gi hoc co gin cho ca cu i vi mt sn phm. Cc hn ch chnh l: a. Khi iu tra trn din rng, nhng thc nghim ny thng c chi ph t . b. V chi ph cao v hm cha ri ro, thi gian thc nghim ngn nn nhng ngi thc hin th nghim phi min cng kim tra d liu ngn hn v phi c ko di thi gian. c. Nhng thay i c th xy ra trong cc iu kin kinh t ngoi vi hoc hnh vi ca i th trong sut cuc th nghim th trng c th bp mo kt qu. CH :Mi phng php c lng cu u c nhng u im v hn ch quan trng. Cc hng phi t la chn phng php c lng cu cho mnh, hoc l s kt hp ph hp gia 2phng n, da trn c im ca mi phng php c lng. VN XC NH (IDENTIFICATION PROBLEM)Chng ta thng gp phi kh khn trong c lng thng k cc tham s ca mt hm nh hm cu khi c nhiu quan h ng thi tn ti. Khi 2 bin ni sinh xut hin cng mt lc trong t nht 2 biu thc khc nhau ca mt m hnh ng thi, th vn xc nh xem l mi quan h no c th c lng c phi da trn c s d liu, bi v tt c cc bin thay i ng thi. V d, c ng cu v ng cung u c th c xc nh vi lng nh l bin ph thuc, v gi l bin gii thch. Cc quan st sn c trn thc t u nh nhau, gi l giao im ca cung v cu. Khng th phn bit ng cu t ng cung thc t hay bt c ng no khc i qua giao im (Xem hnh 1). C s phn b cc im ny v c ng cu v ng cung u dch chuyn (kh c th quan st c) phn bit c 2 biu thc, i hi phi hiu c s dch chuyn thc t ca cu hay cung do s thay i trong cc yu t nh hng ln ch mt trong hai ng. Khi vn tr nn phc tp hn v khng hiu c nguyn nhn dn n s dch chuyn , c th dng iu tra ngi tiu dng v th nghim th trng c c nhng thng tin quan trng v cu.56/142HNH 1VN XC NH: CUNG V CUKINH T LNG V PHN TCH HI QUYMt cng vic c bn da trn kinh nghim c thc hin trong phm vi ca mn kinh t lng. Kinh t lng cp n l thuyt kim nh kinh t hc s dng nhiu phng php c lng trong c phn tch hi quy. Phng php hi quy c th c nhiu ngi bit n v thng c s dng trong c lng hm cu. PHN TCH HI QUYPhn tch hi quy (Regression analysis) l quy trnh thng k dng c lng ton hc mi quan h trung bnh gia (cc) bin c lp v bin ph thuc. Hi quy n ch c mt bin c lp trong hm cu, gi hoc qung co, trong khi hi quy bi c t 2 bin tr ln, ngha l ng thi c c gi v qung coPHNG PHP BNH PHNG NH NHTPhng php bnh phng nh nht (The least-squares method) c dng rng ri trong phn tch hi quy c lng gi tr tham s trong biu thc hi quy. Phng php hi quy bao gm cc d liu c c t quan st v c gng tm ra mt phng trnh ph hp nht. tm ra ng ny dng phng php bnh phng nh nht. u tin xem xt mi quan h tuyn tnh: Y = + X + e, trong v l tham s tng th tht s (nhng khng c bit) ca phng trnh hi quy v 57/142e= sai s. Trong thc t, chng ta cn tm c lng ca vt mt mu s liu. V vy, cn tm Y' = a + bX, trong a v b ln lt l c lng ca v , v Y l gi tr tnh c ca Y vi mt gi tr c th X v mi quan h c lng cho trc. Khi :Y = a + bX + uTrong u l sai s cho mi quan h c c lng v l c lng ca e sai s tng th. Do vy, u = Y - Y'Tiu chun bnh phng nh nht i hi phng trnh ph hp nht phi l tng bnh phng cc sai s (hay l khong cch tung t im quan st ti phng trnh trn hnh 2) l b nht, tc l:B nht: u2 = (Y a - bX)2Dng vi phn ring c c t biu thc sau, gi l biu thc thng: Y = na + b X XY = a X + b X2Gii phng trnh tm b v a b = 2 2X) ( X nY) X)( ( - XY na =X b Y Trong Y= nY vX = nX58/142V D 1Cng ty du la DHG quan st mi quan h gi lng qua 6 giai on nh sau: Giai on Gi (X) Lng cu (Y)1 1.20 2502 1.21 2453 1.25 2004 1.17 3105 1.15 3756 1.19 2807.17 1660 minh ha qu trnh tnh ton b v a, chng ta s chuyn v d liu trong bng 1. Tt c php tnh c thc hin trong bng di yBNG 1 BNG TNH TONGiai on Gi (X) Lng cu (Y) XY X2Y21 1.20 250 300.00 1.4400 62,5002 1.21 245 296.45 1.4641 60,0253 1.25 200 250.00 1.5625 40,0004 1.17 310 362.70 1.3689 96,10059/142HNH 2 TH PHN B: Y V Y5 1.15 375 431.25 1.3225 140,6256 1.19 280 333.20 1.4161 78,4007.17 1660 1973.60 8.5741 477,650T bng trn: X = 7.17; Y = 1660; XY = 1973.60; X2 = 8.5741X = X/n = 7.17/6 = 1.20; Y = Y/n = 1660/6 = 276.67Thay nhng gi tr ny vo cng thc tnh b:48 . 16970.035760.60 -) 17 . 7 ( ) 5741 . 8 )( 6 () 1660 )( 17 . 7 ( ) 60 . 1973 )( 6 () () )( (2 2 2 X X nY X XY nba =Y - bX=276.67 - (-1697.48)(1.20))= 2305.15Do Y' = 2305.15 1697.48 XCh rng y khng dng Y2 m tnh ton cho (r2).Ch : Mc ch ca biu tham s l biu din cc mi tng quan. Mi quan st c biu din bng mt im trn th tng ng vi mt gi tr c th ca X (bin c lp) v Y (bin ph thuc).V D 2Gi thit chi ph cho qung co nm ti l $1.10, doanh thu d tnh nm ti c tnh nh sau:60/14201 0 02 0 03 0 04 0 00 . 9 0 1 . 0 0 1 . 1 0 1 . 2 0 1 . 3 0P r i c eQuantity demandedHNH 3BIU THAM SY' = 2305.15 1697.48 X = 2305.15 1697.48(1.10) = $437.92PHN TCH HI QUYPhn tch hi quy l mt phng php thng k. Do , phn tch hi quy dng nhiu thng k ni v tnh chnh xc v tin cy ca kt qu hi quy. 1. H s tng quan (r) v h s xc nh (r2)2. lch chun ca ng hi quy v khong tin cy ca c lng bin ph thuc3. lch chun v khon tin cy ca cc h s hi quy (Sb) 4. Thng k t Mi phn tch c ni r di y.1. H s tng quan (correlation coefficient ) (r) v h s xc nh (coefficient of determination ) (r2)H s tng quan r o lng mi tng quan gia Y v X. H s ny nhn gi tr t -1 n +1. Tuy nhin, h s xc nh c dng rng ri hn, k hiu l r2 (c l r-bnh phng). r2 cho bit ph hp ca biu thc hi quy dng c lng. Ni cch khc, n l cng c o ph hp trong hi quy. V vy, r2 cng cao, biu thc dng c lng cng ng tin cy. CH :Mt r2 thp l ch s cho bit m hnh khng tin cy gii thch bin Y. Cc nguyn nhn chung gy nn vn ny l:1. Dng sai dng hm.2. X c t s la chn nh l mt yu t d on.3. B st mt bin hoc cc bin quan trng no t m hnhV D 3Nhn nh Doanh thu l mt hm ca gi vi r2 = 70 %, c th hiu l 70% s thay i ca doanh thu c gii thch bng biu thc hi quy v s thay i trong gi v 30% cn li l do cc yu t phi gi, nh thu nhp v qung co.Nh trong hnh 4, tng thay i ca bin ph thuc Y vY(Y trung bnh) c th tch lm 2 phn.(Y -Y )= (Y - Y') +(Y' -Y )(Tng lch)( lch khng c gii thch)( lch c gii thch)o lng s ph hp ca phng trnh hi quy, thng qua h s xc nh (r2), c c t vic so snh (Y' -Y )2, l tng cc bnh phng c gii thch, vi tng cc bnh phng.Vy th, 61/142Thay i c gii thchr22) ' () ' (Y YY Y---------------------------------Do , h s xc nh cho bit t l ca tng thay i trong Y v c ni r trong biu thc hi quy. H s ny nhn gi tr trong khong t 0 n 1.CH :Tng bnh phng ca thay i c gii thch cngvi tng cc bnh phng thay i khng c gii thch bng tng cc bnh phng.HNH 4CNG C C BN O S SAI LCHTuy nhin, trong trng hp hi quy n, c mt cng thc rt gn: ] Y) ( - ][ X) ( [Y)] X)( ( - [2 2 2 222Y n X nXY nrSo snh m hnh ny vi m hnh theo b, thy rng nhng thng tin cn thm vo tnh ton r2 l Y2.V D 4Chuyn sang d liu trong bng 1 minh ha cc php tnh ca phn tch hi quy. S dng phng php rt gn cho r2, ) 110300 )( 0375 . 0 () 60 . 60 (] ) 1660 ( ) 477650 )( 6 ][( ) 17 . 7 ( ) 5741 . 8 )( 6 [(] 0) (7.17)(166 - 1973.60) ( [(6)22 222 r

62/142Tng thay i % 26 . 93 9326 . 071 . 393736 . 3672 iu ny c ngha rng c khong 93.26% tng thay i trong doanh thu c th gii thch bng gi v 6.74% cn li vn khng th gii thch c. Mt r2 cao tng i cho bit hm cu c c lng l kh tin cy v gi l mt yu t quyt nh nhiu n cu.2. lch chun ca ng hi quy v khong tin cy ca c lng bin ph thucSai s chun ca c lng, k hiu l Se, c nh ngha l s thay i chun ca hi quy, c tnh ton nh sau: Se = 2 - n) Y' - Y (2 = 2 - n XY b - Y a - Y2 C th dng phn tch ny bit c chnh xc ca d on. V D 5Tr li s liu trong v d trn, Se c tnh nh sau:Gi s bn mun c mt d bo v mt gi tr Y no - nh d bo v doanh s khi gi l $1.10. Thng th chng ta mun phng php o mc tin cy no trong d bo a ra, v mt trong nhng phng php l khong tin cy (hay d bo) tnh Y.Khong tin cy i vi Y c d bo, vi mt gi tr X cho trc, c th tnh theo cch sau:Y' t Se + +nX) (- XX) (X n11222pTrong :Y' = gi tr c d bo ca Y theo X; Xp = gi tr ca bin c lp dng lm c s cho d bo;Ch :t l gi tr ti hn cho mc ngha c dng. V d, vi mc ngha 0.025 (tng ng vi tin cy 95% trong kim nh 2 pha), gi tr ti hn ca t cho 4 mc t do l 2.776 (xem bng 5 trong phn ph lc)CH : Bc t do (df) l s quan st tr i s ti thiu cn thit tnh mt thng k hoc phng trnh hi quy cho trc. V d, tnh mt s hng khng i, a, cn t nht mt quan st, tnh a v b cn t nht 2 quan st V D 6Nu mun c d bo c khong tin cy l 95%, vi mc gi$1.10, khong d bo nm t $356.93 n $518.91, c xc nh nh sau. (Ch rng tv d 2, c Y' = 2305.15 - 1697.X = 2305.15 - 1697.48($1.10) = $437.92). 63/142V vy, khong tin cy c thit lp nh sau:C ngha l vi chi ph qung co cho trc l $1.10, th khong d bo l t $356.62 n $518.21. Ch rng $356.93 = $437.92 80.30 v $518.91 =$437.92 + 80.30.CH :Nhiu ti liu kinh t qun l s dng Y' t Se cho khong tin cy, b qua yu t iu chnh. Trong v d 6, khong tin cy l $437.92 (2.776)(17.66).3. lch chun v khon tin cy ca cc h s hi quy (Sb) Sai s chun ca h s hi quy, k hiu l Sb, v phn tch - t c mi lin h cht ch. Sb c tnh nh sau:Sb = 2e) X - X (SHoc dng rt gn:Sb = ) X X - XS2eSb cho bit c lng ca mt khong trong h s thc s thc s ri vo . Trc y dng Se xc nh khong tin cy cho d bo, Sb c lng khong tin cy gi tr thc ca h s hi quy vi cc mc tin cy. Cc khong tin cy l:b +t Sb4. Thng k tThng k t (hay gi tr t) l cng c o mc ngha thng k ca bin c lp X trong gii thch bin ph thuc Y. N c xc nh bng:bb - t=S kim nh gi thuyt = 0, th = 0 vo cng thc ny, ngha l chia h s hi quy c c lng cho lch chun Sb. Sau so snh gi tr ny vi bng gi tr-t xc nh xem gi thuyt bng 0 l ng hay khng.Ch : Thng k t c bn dng o sai s chun ca h s xung quanh 064/142 1(1.10 - 1.195)2 $437.92 (2.776)(17.66) 1 + + 68.5741 -(7.17)2/6 = $437.92 (2.776)(17.66) (1.638) = $437.92 80.30 Gi tr t cng cao, tin cy ca h s cng ln nh l mt d on.Gi tr t thp l ch s cho bit tin cy ca lc d onca h s thpV D 7Sb trong v d ca chng ta l:15 . 2310764 . 066 . 1717 .) 7 )( 195 . 1 ( 5741 . 866 . 17 bSV vy, thng k34 . 715 . 23148 . 1697 0 bsbtV t = 7.34(gi tr tuyt i ca 7.34) > 2.776 (t bng gi tr - t), kt lun rng gi thuyt bng 0 l sai v do h s b c ngha thng k.CH :1. Trong hi quy bi c nhiu gi tr thng k t2. r2 cho bit ton b phng trnh hi quy tt nh th no trong khi thng k t cho bit tt ca tng bin c lp.Bng gi tr t, dng tm tt, da vo bc t do v mt mc ngha, c dng:a. Thit lp khong tin cy gii hn trn v gii hn di cho gi tr d on ca bin ph thuc. b. c lng khong tin cy trong gi tr thc ca h s hi quy ri vo .3. Gi tr gii hn cho kim nh tS DNG EXCEL CHO HI QUYCc chng bng tnh nh Excel c chui hi quy c th s dng m khng gp kh khn. Bn c th truy cp vo cng c hi quy theo cc bc sau:1. Chn th Tools2. Chn Data Analysis3. Chn RegressionSau khi chn lnh Regression, hp thoi Regression xut hin cc la chn Y-Range, X-Range, v Output Range. Sau khi la chn, click chn OK v Excel s tnh cc gi tr bnh phng nh nht cho cc tham s a v b (cng vi cc thng k tm tt khc) c biu din di y TM TT U RAThng k hi quy65/142R bi 0.96572R SquareR20.93261H s xc nh iu chnh R20.91577Sai s chun17.5983Quan st 6ANOVAdf SS MS F tin cy FHi quy 1 17144.54 17144.54 55.35873 0.001742641S d4 1238.796 309.6989Tng 5 18383.33H s Sai s chunThng k tGi tr PThp hn 95%Cao hn 95%B chn 2305.15 272.7282 8.452204 0.001073 1547.937731 3062.37Bin X1 -1697.48 228.1452 -7.44035 0.001743 -2330.912925 -1064.05CH :Ch t kt qu hi quy ca Excela. b = -1697.48 v a = 2305.15; do , hm cu c c lng l Y = 2305.15 1697.48Xb. r2 = 0.93261c. Se = 17.5983d. Sb = 228.1452e. t i vi h s hi quy = -7.44035Con s tnh ton t my tnh khc vi tnh ton c c t cc lch c lm trn. Cc con s ca my chnh xc hn v my tnh tnh ton trn nhng con s thp phn CU HI1. Ti sao trong c lng cu, vn xc nh thng phc tp?2. Tiu chun no cn c tha mn nu phn tch da trn hi quy cung cp mt c lng chnh xc v cc mi quan h ca cu?66/1423. iu tra ngi tiu dng l g? Nhng vn no thng pht sinh khi s dng iu tra ngi tiu dng c lng cu i vi sn phm ca mt hng?4. Gii thch thc nghim th trng: l g? Dng nh th no? C nhng hn ch no?5. Phn bit hi quy n v hi quy bi. Mi loi cho mt v d. 6. H s r2 cho bit iu g? Cc nguyn nhn dn n iu ?7. Tc dng ca bng gi tr - t c c da trn mt bc t do v mt mc ngha cho trc? 8. Tc dng chung ca sai s chun?BI TP1. Sau y l s liu v doanh thu v qung co ca tp on Jupiter qua 8 thng Qung co Doanh thu(nghn n v)(nghn n v) 320 $2,600200 1,500230 2,150240 2,250720 4,700560 3,700470 3,300750 4,750a. Xy dng biu thc cu s dng phng php bnh phng nh nht. b. Tnhh s xc nh. c. Nhn xt v s la chn ca qung co trong doanh thu d tnh. Qung co c phi l mt ch s d on tt? 2. Mt nh kinh t ca chnh ph mun thit lp mi quan h gia thu nhp X v tit kim Y h gia nh hng nm. Chn mt mu gm 100 h gia nh v c c cc tnh ton sau (n v ca X v Y l nghn la):X = $1,239 Y = $79 XY = $1,613X2 = $17,322 Y2 = $293a. Xc nh phng trnh ca ng hi quy c c lng67/142b. ngha ca trn b v gi tr chn ac. Tnh h s xc nh r2d. Tnh sai s chun ca c lng see. Vit biu thc khong d on ca Y (Dng bng gi tr t = 1.98 vi 98 mc t do v mc tin cy 5%).3. c lng hm cu i vi xng. S liu v u ra hi quy t Excel cho trc. Thi k Gi (P) lng cu (Q)1 1.20 3002 1.30 2953 1.25 2984 1.33 2755 1.27 2666 0.99 3607 1.15 3258 1.36 2669 1.19 31110 1.22 32512.26 302168/142U RA TM TT a. Vit hm cu c lng b. Con s r2 cho bit iu g?c. Tnh ton co gin im ca cu khi gi l $1. Cu ca sn phm ny c co gin theo gi khng?d. Xc nh khong tin cy ca bin (bng gi tr t vi mc tin cy 5% v 8 bc t do (10-2) l 2.306)e. Gi tr t no ng vi h s hi quy? N cho bit iu g? f. C th xy dng mi quan h c c lng hay khng? Cho kin?69/142 VARIABLEORIGINAL COEFF. VARIABLE VALUECOEFF.SENS. X 1 20250 Note:X1 = 20 X 2 15400X2 = 15 CONSTRAINT ORIGINALSLACK ORSHADOW NUMBERRHSSURPLUS PRICE 1 100 08.75 Note:u1 = $8.75 190 02.50u2 = $2.50 OBJECTIVE FUNCTION VALUE:1100Note: Z = $1,100 SENSITIVITY ANALYSIS OBJECTIVE FUNCTION COEFFICIENTS LOWER ORIGINALUPPER VARIABLELIMITCOEFFICIENTLIMIT X 120 25 60 X 216.6740 50 RIGHT HAND SIDE CONSTRAINT LOWER ORIGINAL UPPER NUMBER LIMITVALUE LIMIT 160100 180 250 90 150 TR LI Vn xc nh xut hin khi cc yu t nh hng n cu sn phm cng nh hng cung sn phm. Khi 2 mi quan h kinh t, nh hm cung v hm cu, quan h cht ch vi nhau lm cho c lng l thuyt ca cc mi quan h l khng th, chng ta ni rng khng th xc nh c cc hm ring.M hnh hi quy hon ton c th xc nh. Ni cch khc, cc yu t nh hng n cu phi hon ton c xc nh v phi s dng ng dng hm. Nhiu thng k nh r2 v kim nh t dng chc chn nhng iu kin ny c c tha mn hay khng? 1. Khch hng tim nng v khch hng hin thc c phng vn v cc yu t nh hng n cu ca h i vi sn phm ca mt hng. Hai vn l: (a) ngi tiu dng c th khng tr li chnh xc cc cu hi c th nh s thay i gi c nu, v (b) nhng iu tra nh vy c th kh tn km. 2. Mt th nghim th trng c xy dng bi cc yu t nh hng c ch ch v b kim sot n cu, nh gi v qung co. Thc nghim th trng c th tn km v cha ri ro. N c th pht sinh mt lng ln cc quan st c c nhng c lng cu tin cy. 3. Hi quy n c mt bin c lp, gi hoc qung co trong hm cu, trong khi hi quy bi c 2 hoc nhiu hn 2 bin, ngha l ng thi c c gi v qung co. 4. Mt r2 thp l ch s cho bit m hnh khng gii thch bin Y. Cc nguyn nhn chung ca vn ny l: (a) dng sai dng hm, (b) t s la chn bin X nh l yu t d on, v/hoc (c) b qua mt hoc cc bin quan trng no t m hnh. 5. Bng gi tr t dng (a) xy dng khong d on gii hn trn hoc di xy dng cng vi mt mc tin cy c th (v d 95%) - cho gi tr c d on ca bin c lp, (b) xy dng khong tin cy cho cc h s hi quy, v (c) nh l mt gi tr b loi cho kim nh t.6. Sai s chun ca c lng, Se, dng xy dng khong d on cho gi tr ph thuc vi cc mc tin cy, trong khi sai s chun ca h s hi quy, Sb, cho bit mt c lng ca khong m h s thc s thc s gim.GI TR LI 1.a. Da vo phng php bnh phng nh nht, ta c:70/142Qung co Doanh thuXYXY X 2

Y 2

320 $2,600 832,000 102,400 6,760,000200 1,500 300,000 40,000 2,250,000230 2,150 494,500 52,900 4,622,500240 2,250 540,000 57,600 5,062,500720 4,700 3,384,000 518,400 22,090,000560 3,700 2,072,000 313,600 13,690,000470 3,300 1,551,000 220,900 10,890,0007504,7503,562,500562,50022,562,500 3,49024,95012,736,0001,868,30087,927,500 T bng:n = 8X = 3,490Y = 24,950 XY = 12,736,000X2 = 1,868,300Th cc gi tr ny vo cng thc tm b trc:35 . 5 $) 490 , 3 ( ) 300 , 868 , 1 )( 8 () 950 , 24 )( 490 , 3 ( ) 000 , 763 , 12 )( 8 () () )( (2 2 2 X X nY X XY nba = (Y/n) - b (X/n) = 24,950/8 - (5.35)(3,490/8) = 3,119 - 2,334 = $785V vy, m hnh hi quy l $785 + $5.35 Xb.% 01 . 98 9801 . 0(24,950) - 27,500) ][(8)(87,9 (3,490) - ,300) [(8)(1,868,950)] (3,490)(24 - 6,000) [(8)(12,732 222 rQung co l s la chn thch hp trong gii thch s thay i ca doanh thu v r2 cao cho bit 98.01% ca tng thay i trong doanh thu c gii thch bi mt mnh qung co. Ch 1.99% l do ngu nhin. 2.a.(100)(1, 613) (1, 239)(79) 63, 4190.3218(100)(17, 322) (1, 293)(1, 293) 197, 079b 79 1, 239( 0.3218) 3.1971100 100a V vy, mi quan h c c lng gia thu nhp v tit kim hng nm l -$3.1971 + $0.3218 mi la ca thu nhp hng nm71/142b. b) Gi tr b, $0.3218, ngha l trung bnh, mi h gia nh tit kim khong $0.32 trong mi mt la h kim c hng nm. Gi tr chn a (-3.1971) ngha l trung bnh mi h gia nh c khon n hng nm l $3,197.10.c.2 2(63, 419) (63, 419)20.885(197, 079)[(100)(293)-(79)(79)] (197, 079)( 23, 059)r d. e.Y' (1.98)( (0.52) + +nX) (- XX) (X n11222p

3.a. Q = 616.13 256.15Pb. r2 = 83.33%, ngha l tng thay i trong lng cu c gii thch ch bi mi mnh gi. 16.67% cn li vn c th gii thch c. c. Ti P = $1, Q = 616.13 256.15P = 616.13 256.15($1) = 359.98.( 256.15)(1/ 359.98) 0.71 1pcdQ PedP Q AP; ngc li khi MP25, khng phi l kt hp u vo c chi ph t nht v u ra mi la chi ph thm vo ca nc ln hn ca phn bn.HNH 5NG NG LNG, NG NG PH V NG M RNGHIU QU THEO QUY MHiu qu theo quy m (The returns to scale)ca mt h thng sn xut cho bit s tng thm ca u ra khi tng thm tng ng tt c cc yu t u vo, phn nh s thay i ca u ra khi tt c u vo u tng cng mt bi s. C 3 kh nng xy ra: Hiu qu theo quy m tng, khng i v gim xung. Nu u ra tng ln vi mt t l ln hn so vi u vo th hiu qu theo quy m tng ln. Trong di hn, mt hng c hiu qu tng ln khi c tit kim theo quy m. Tit kim theo quy m v lng ph theo quy m nh hng n chi ph ca hng. Khi hng t c tit kim theo quy m, chi ph trung bnh di hn ca mt hng s gim xung. Lng ph theo quy m xut hin khi chi ph bnh qun di hn tng ln. Khng p dng quy lut tit kim v lng ph theo quy m cho thi k ngn hn bi v rt nhiu chi ph c c nh. Trong di hn, tt c cc chi ph u bin i. Nu u ra tng ln vi cng mt t l, hiu qukhng i theo quy m xut hin. Cui cng, nu u ra tng ln vi mt t l nh hn, hiu qu gim xung theo quy m xut 112/142hin. Cc hiu qu theo quy m ng mt vai tr quan trng trong ra quyt nh kinh t. Chng nh hng ti quy m ti u, hay quy m nh xng ca mt hng v cc thit b sn xut. Chng cng nh hng ti bn cht ca cnh tranh trong mt ngnh v do ng vai tr quan trng trong xc nh kh nng sinh li trong mt ngnh c th ca nn kinh t. Hiu qu theo quy m iu kinHiu qu tng theo quy m Phn trm tng trong u ra > phn trm tng trong u voHiu qu khng i theo quy m Phn trm tng trong u ra = phn trm tng trong u vo Hiu qu gim theo quy m Phn trm tng trong u ra < phn trm tng trong u voC th xc nh hiu qu theo quy m bng nhiu cch, trong c:1.So snh phn trm u ra tng ln vi phn trm u vo tng ln cho trc.1.S dng mt phng php i s ni chung.V D 8Vi mt hm sn xut cho trc: Q = 10L + 15K + 20KLa. Nu L=K=100, thQ1 = 10(100) + 15(100) + 20(100)(100) = 202,500Tng mi n v ln 1% th:Q2= 10(101) + 15(101) + 20(101)(101) = 206,545 dn n 2% tng ln trong u ra (Q2/ Q1 = 1.02), v do , hm biu din hiu qu tng theo quy m. b. Tng t, vi mt k phn trm thay i trong tt c u vo (trong k>1) chng ta c:Q1 = 10L + 15K + 20KLQ2 = 10L + 15K + 20KL = 10(kL) + 15(kK) + 20(kL)(kK) = k (10L + 15K + 20kKL). V k > 1, Q2 > Q1. Nn hm biu din hiu qu tng theo quy m. CO GIN U RA V LI NHUN THEO QUY MCo gin u ra (output elasticity) o tnh nhy cm ca u ra i vi mt s thay i trong mt u vo c s dng, c tnh nh sau:113/142QQ XeX X Q %Q thay i%thay iTrong X l tt c u vo (vn, nhn cng,...). Cng c th dng co gin ny c lng hiu qu theo quy m, da theo cc tiu chun sau:CU HI1. Cho vi v d khc nhau v hm sn xut2. Hm Cobb-Douglas khc cc hm khc nh th no?3. Th no l sn phm doanh thu cn bin (MRP)? ngha ca n trong ti a ho li nhun?4. M t tm tt 3 giai on sn xut. 5. Th no l co gin u ra? Cch tnh ton?6. M t mi quan h th gia sn phm cn bin v sn phm bnh qun.7. Ch r iu kin kt hp cc u vo c chi ph nh nht (ti u).8. Cho 2 v d v thay th hon ton. 9. Nu cc u ra khng thay th c cho nhau th khng ra c quyt nh no v kt hp u vo. Nhn xt.BI TP 1. Cng ty Anaheim, sn xut phim, c hm sn xut sau:Q = 0.5K2 + 0.3KL + 0.4L2Gi nh rng t l s dng hng tun l L = 100 gi lao ng v K = 30 l chi ph sn xut (a) Tng sn phm mi tun.a. Sn phm cn bin ca lao ng.b. Sn phm cn bin ca vn.2. Cng ty Lin doanh knh thuc John-Jay Opticals, mt nh sn xut knh thuc c hm sn xut c tnh sau:Q = 20L0.75K0.30Trong Q =s gng nha c sn xut mi ca lao ng (gm 8 gi), L = s nhn cng, K = s vn c s dng.114/142Co gin u ra Hiu qu theo quy meQ > 1 Tng lneQ = 1 Khng ieQ < 1 Gim xunga. Tnh s gng nha hon thnh mi ca khi L = 10 v K = 100.b. Tnh sn phm cn bin ca lao ng khi L = 10 v K = 100.3. Lin doanh Nng phm Ding-Dong l mt nh sn xut cam. Cng ty c tnh rng s lng cam sn xut ra s tng 1,500 qu mi thng khi h thng ti tng thm 1,000 gallon nc mi thng. Hoc l, sn lng cam s tng 900 qu khi tng thm 2 tn phn bn mi thng. Gi nh rng chi ph ca nc l $0.06 mi gallon v ca phn bn l $25 mi tn. Hng c ang s dng kt hp ti u ca nc v phn bn hay khng? Ti sao?4. Lin doanh Nng phm Agasi l nh sn xut l. Cng ty c tnh rng sn lng l s tng 1,200 qu mi thng khi h thng ti tng thm 1,000 gallon nc mi thng. Hoc l, sn lng l s tng 1000 qu khi tng thm 2 tn phn bn mi thng. Gi nh rng chi ph ca nc l $0.06 mi gallon v ca phn bn l $25 mi tn. Hng c ang s dng kt hp ti u ca nc v phn bn hay khng? Ti sao?5. Cng ty ABC c hm sn xut:Q = 12KL + 0.7KL2 - 1/30KL3Xc nh:a. u ra ti a c th sn xut c khi K = 5.b. Mc s dng ca L khi sn phm bnh qun ca lao ng (APL) t cc i.c. Mc u ra xut hin hiu qu gim dn theo L.6. Cng ty Khai thc m ng Bc c hm sn xut i vi u ra than sau:Q = 250L0.5K0.6a. Xc nh hiu qu theo quy m v nhn xt.b. Xc nh hiu qu theo quy m i vi mi yu t u vo.7. Cng tykhai thc m Nova c hm sn xut i vi u ra than sau:Q = 300L0.5K0.5Trong Q = Sn lng than sn xut c (nghn tn), L = Lao ng (trm cng nhn), v K = Vn (trm triu la).Ti im sn xut cc i, cng ty cn 10,000 cng nhn v $900 triu tin vn chi ph. Sn lng u ra than sn xut c bn ti mc gi ca th trng cnh tranh l $40 mi tn. a. Xc nh mc lng hng nm ln nht m cng ty sn sng tr thu ht 10,000 cng nhn.115/142b. Cng ty sn sng tuyn bao nhiu cng nhn khi mc lng hng nm m cng on lao ng yu cu l $20,000. 8. Tng sn phm ca lao ng (mi gi) ca mt cng ty cho di y:Q =30L - 0.5L2a. Xc nh sn phm cn bin ca lao ng.b. Cng ty nn s dng bao nhiu lao ng nu t l lng l $30 mi gi v sn phm doanh thu cn bin l $24?TR LI1. Cc v d l hm sn xut tuyn tnh, hm sn xut Leontief, v hm sn xut Cobb-Douglas2. Hm sn xut Cobb-Douglas nm gia cc tr ca hm sn xut tuyn tnh v hm sn xut Leontief. Khng ging hm tuyn tnh, mi quan h ca hm Cobb-Douglas gia u ra v u vo l khng tuyn tnh. Khng ging nh hm sn xut Leontief, khng cn s dng u vo vi cc t l xc nh. 3. Sn phm doanh thu cn bin l phn thu rng thm vo tng doanh thu c th quy cho s thm vo ca mt n v dch v sn xut a nng (variable productive service) v gi tr tnh theo la ca sn phm cn bin (MP) ca mt u vo. Sn phm doanh thu cn bin (MRP) ca mt u vo bng MP nhn vi MR ca hng ho. Mt hng ti a ho hiu qu s s dng mt dch v sn xut a nng cho n khi t ti im m MRP ca mt u vo bng ng vi gi bn ca u vo .4. Ba giai on sn xut in hnh c bit quan trng trong phn tch tnh hiu qu ca cc ngun lc u vo c s dng vi (xem hnh 4). Mt hm sn xut biu din s lng hiu qu tng ln, gim xung v m c th chia ra 3 phn. Phn 1 bao gm khong hiu qu tng theo u vo bin i tng ln v im ca hiu qu cn bin gim xung (DMR) t ti (im A) v vt qua, kt thc khi t ti im hiu qu trung bnh gim xung (DAR) (im B). Phn II gm phn m ti lng u ra tng ln vi mt t l gim xung, theo , sn phm cn bin (MP) ca u ra bin i l gim xung, mc d vn nhn gi tr dng. Phn III trng vi khong u vo m vic dng cc u vo bin i thm vo tng ng vi s gim xung trong u ra nhng MP m.5. Co gin u ra o s nhy cm ca u ra i vi mt thay i trong mt u vo c s dng, c tnh nh sau:QQ XeX X Q %Q thay i%thay iTrong X l tt c u vo (vn, nhn cng,). Cng c th dng co gin ny c tnh hiu qu theo quy m.116/1426. (1) Vimt u vo tng ln, ban u MP tng ln (hiu qu cn bin tng ln) sau bt u gim (hiu qu cn bin gim dn), v cui cng v m (hiu qu cn bin m). (2) Min l MR tng, MP > AP; ngc li khi MP 18, l kt hp u vo c chi ph nh nht bi v u ra mi la thm vo tiu dng cho nc ln hn cho phn bn. 4. MPW = 1200 v MPF = 1000117/142PW = 1000 gallons mi thng x $0.06 mi gallon = $60 mi thngPF = 2 tn mi thng x $25 mi tn = $50 mi thngV vy,1200 10060 50C, 20 =20, l kt hp u vo c chi ph nh nht bi v u ra mi la thm vo tiu dng cho c nc v phn bn bng nhau.5.a. Q = 12KL + 0.7KL2 - 0.3KL3Ti K = 5, TPL = 12(5)L + 0.7(5)L2 - 1/30(5)L3 = 60L + 3.5L2 - 1/6L3t MPL bng 0 c:MPL = Q/L = 60 + 7L - 0.5L2 = 0;(-0.5L + 10)(L + 6) = 0V vy L = 20 (Loi L = -6) l gi tr cc i v2Q/L2 = 7 - L = 8 - 20 = -12 < 0.V vy u ra cc i l 1267 n v:Ti L = 20, TPL = 60L + 3.5L2 - 1/6L3 = 60(20) = 3.5(20)2 - 1/6(20)3 = 1267.b. TPL = 60L + 3.5L2 - 1/6L3APL = TPL/L= (60L + 3.5L2 - 1/6L3)/L = 60 + 3.5L - 1/6L2 tm APL ln nht, t APL=0 v tm L nh sau:dAPL/dL = 3.5 - 1/3L = 0; L = 10.5, l gi tr nh nht v d2APL/dL2 = -1/3 < 0.Sn lng u ra khi APL c ti a ha l 823 n v:TPL = 60L + 3.5(10.5)2 - 1/6(10.5)3 = 823.c. Hiu qu cn bin gim dn bt u khi MPL c ti a ho.MPL = Q/L = 60 + 7L - 0.5L2dMPL/dL = 7 - l = 0; L = 7, l gi tr cc i v d2MPL/dL2 = -1 < 0.Do ti L = 7, TPL = 60L + 3.5L2 - 1/6L3 = 60(7) + 3.5(7)2 - 1/6(7)3 = 534.Hiu qu cn bin gim dn theo u vo lao ng bt u khi u ra l 534 n v.118/1426.a. Q = 250L0.5K0.6 = 250(kL)0.5(kK)0.6 = k0.5k0.6 250L0.5K0.6 = k1.1 Q, tc l k1.1 > k, cho bit hm sn xut trn biu din hiu qu tng theo quy m.b. Hiu qu theo mi nhn t c th c xc nh bng cch da vo s thay i ca mi sn phm cn bin khi tng thm u vo.Hiu qu theo lao ng:MPL = Q/L =125L-0.5K0.6; d2MPL/dL2 = -62.5 L-1.5K0.6 < 0. V vy hiu qu theo lao ng gim. Hiu qu theo vn:MPK = Q/K =125L0.5K-0.4, d2MPL/dL2 = -50L0.5K-1.4 < 0. V vy hiu qu theo vn gim. 7.a. Dng quy tc nhn cng ti u:Gi ca mt u vo (Pi) = Sn phm doanh thu cn bin ca u vo (MRPi)i vi lao ng, Gi nhn cng = sn phm doanh thu cn bin ca lao ng, hayPL = MPL x MRQ=(150L-0.5K0.5)($40 x 1,000 tn)=[150(100)-0.5(9)0.5]($40 x 1,000 tn)= $1,800,000 mi trm lao ng hay $18,000.b. PL= MPL x MRQ$20,000 x 100 = (150L-0.5K0.5)($40 x 1,000 tons)$2,000,000 = [150L-0.5 (9)0.5]($40 x 1,000 tons)$2,000,000 = [150L-0.5 (9)0.5]($40 x 1,000 tons)$2,000,000/ $18,000,000 =150L-0.5

$2,000,000/ $18,000,000 =1/L0.5

L0.5 = 9L = 81 hay, 8,100 lao ng. Do vy, ti mc lng $20,000, hng ch sn sng thu 8,100 lao ng.119/1428.a. MPL = Q/L = 30 - Lb. S dng nguyn tc nhn cng ti uPL= MPL x MRQ$30 = (30 - L) x $24$30 = $720 - $24LL = 23Hng nn tuyn 23 cng nhn mi gi.120/142CHNG 7 - LP K HOCH A SN PHM V QUY HOCH TUYN TNH MC TIU HC TP:Sau khi hc chng ny bn c th:1. nh ngha quy hoch tuyn tnh (LP). 2. Hiu v tho lun hm mc tiu3. Cho v d v cc rng buc4. Minh ho cc rng buc khng m 5. nh ngha v cho v d v phng n kh thi.6. Tho lun v minh ho phng n kh thi c bn7. Tnh ton v nh ngha phng n ti u 8. Cho v d v cc bi ton i ngu.9. Gii thch v a ra nhng v d v gi m10. Gii thch bin lng11. Minh ho v tho lun cc rng buc ng12. Gii thch iu kin lng b sung13. Minh ho v gii thch tc dng ca phn tch hot ng. 14. Phc ha v gii thch tia qu trnh15. Minh ho ng ng phQuy hoch tuyn tnh (Linear programming - LP) l mt thut ton nhm tm ra phng n ti u (hoc k hoch ti u) t v s cc phng n quyt nh. Phng n ti u l phng n tha mn c cc mc tiu ra ca mt hng, ph thuc vo cc hn ch v cc rng buc. N cp n vn phn b ngun lc khan him gia cc hot ng cnh tranh trong mt phng thc ti u. Quyt nh ti u mang li hiu qu cao nht, li gp (Contribution Margin-CM) cao nht, hay doanh thu, hay chi ph thp nht. M hnh LP gm 2 thnh phn 1. Hm mc tiu: Hng phi xc nh mc tiu c th phi t ti2. Cc rng buc: Cc rng buc di dng cc hn ch v s sn c ca ngun lc hay tho mn cc yu cu ti thiu. Nh tn gi quy hoch tuyn tnh, c hm mc tiu v cc rng buc phi di dng tuyn tnh.121/142CH :Cc phng php tnh ton c in, nh l phng php nhn t Lagrangean,khng thch hp cho vic tm ra cc phng n cho cc bi ton km cc rng buc bt ng thc. M hnh LP gii quyt vn ti u ho b rng buc vi cc hm mc tiu tuyn tnh v cc rng buc bt ng thc tuyn tnh, trong khi php tnh vi phn v phng php nhn t Lagrange gii quyt cc vn bao gm cc hm mc tiu tuyn tnh v phi tuyn tnh v cc rng buc ng thc.V D 1Mt hng mun tm kt hp sn phm ti u. Kt hp ti u l kt hp ti a ho tng hiu qu hay li gp (CM) trong ngn sch c gii hn v cng sut sn xut. Hoc l hng c th mun xc nh kt hp nguyn liu u vo c chi ph nh nht trong khi vn p ng c cc i hi ca sn xut, tn dng cng sut sn xut v s dng nhn cng sn c. NG DNG CA LPLP c nhiu ng dng. Bao gm1. La chn kt hp u vo c chi ph thp nht cho sn phm sn xut ra2. Xc nh ngn sch ti u3. Quyt nh danh mc u t ti u (hay phn b ti sn)4. Phn b ngn sch qung co cho cc phng tin thng tin5. Ln k hoch s dng my mc6. Quyt nh phng thc vn chuyn c chi ph thp nht7. Ln k hoch cho cc chuyn bay8. Kt hp kh t9. Phn b nhn lc ti u10.La chn v tr t nh xng ph hp nhtCNG THC CA LP xy dng mt bi ton LP, theo cc bc sau.1. Xc nh cc bin quyt nh phi tm.2. Biu din hm mc tiu v cc rng buc theo cc bin quyt nh ny. Cc phng trnh phi c dng tuyn tnh. S dng phng php ny trong v d sau tm kt hp sn phm ti u. 122/142V D 2Cng ty sn xut ni tht Omni sn xut 2 sn phm: bn giy v bn n. C 2 sn phm cn thi gian c x l trong 2 b phn: B phn Lp rp v b phn Hon thin. D liu v hai sn phm ny nh sauSn phm Sn cX l Bn giy Bn n GiLp rp2 mi chic 4 100 giHon thin 3 2 90Hiu qu mi chic$25 $40Cng ty mun tm c cch kt hp 2 loi sn phm ny sao cho c li nht.Bc 1: Xc nh cc bin quyt nh nh sau:x1 = S lng bn giyx2 = S lng bn n Bc 2: Hm mc tiu ti a ho hiu qu (Z) c biu din di y:Z = 25x1 + 40x2Sau lp cng thc cc rng buc nh l cc bt ng thc: 2x1 + 4x2 < 100 (Rng buc lp rp) 3x1 + 2x2 0Ti u ho:Z =25x1 + 40x2Rng buc:2x1 + 4x2 < 1003x1 + 2x2 < 90x1, x2 > 0CC PHNG PHP TNH TONC nhiu phng php tnh ton LP bao gm: 1. Phng php n hnh 2. Phng php th123/142Phng php n hnh l phng php c s dng gii bi ton LP. N l mt thut ton, mt phng php tnh ton lp i lp li, t phng n ny ti phng n khc cho n khi t c li gii tt nht. CH :Phng php n hnh cp n cc bin s ph (k hiu l s1 v s2) chuyn t bt ng thc sang ng thc:2x1 + 4x2 < 100------------> 2x1 + 4x2+ s1 = 1003x1 + 2x2 < 90 -------------> 3x1 + 2x2 + s2=90Trong s1 v s2 phi khng m.Nu nh v tri ln hn v phi (>), thng l trng hp tm hm mc tiu, chng ta ni rng c mt s thng d. Khi chng ta cn -s1 v -s2 chuyn bt ng thc thnh ng thc.Phng php th d s dng hn nhng ch i vi cc trng hp LP c 2 (hoc 3) bin quyt nh. Phng php th gm cc bc sau y:Bc 1: a bt ng thc v dng ng thc.Bc 2: Minh ha bng th cc ng thc. minh ha:1. t mt bin bng 0 v tm gi tr bin cn li v ni 2 gi tr trn th,2. nh du cc im trn 2 trc v kt ni vi nhau thnh mt ng thng. Bc 3: Xc nh phn tha mn ca cc ng thc bng cch nh bng. Lp li cc bc t 1-3 i vi mi rng buc.Bc 4: Sau ht, xc nh tp phng n tc l nh du cc vng cha cc phng n tho mn tt c cc rng buc.Bc 5: Gii ng thi cc rng buc (th hin di dng cc ng thc) tm ra im cn bin.Bc 6: Xc nh hiu qu hoc li gp ti tt c cc nh trong min kh thi.CH :Tp phng n l nhng gi tr ca bin quyt nh tho mn ng thi cc rng buc. Chng c tm thy pha trn v bn trong min kh thi. Phng php th da vo 2 c im quan trng ca LP:1.Phng n ti u nm ng bin ca vng kh thi, c ngha l c th b qua cc im bn trong vng kh thi (rt nhiu im) khi tm kim phng n ti u.2.Phng n ti u nm 1 trong cc nh ca min ti u (cc phng n kh thi c bn) 124/142V D 3S dng cc d liu v m hnh LP v d 2, lm theo cc bc t 1 n 4. Ta c vng kh thi sau y (vng c nh bng).Bc 1: Chuyn cc bt ng thc v ng thc.2x1 + 4x2= 100 3x1 + 2x2 =90 Bc 2: Lp th. lp th, cho mt bin bng 0, tm gi tr bin cn li, nh du cc im trn 2 trc, v ni 2 im thnh mt ng thng.i vi ng thc 1: Nu x1=0, x2=25; nu x2=0, th x1=50, ni x2=25 v x1=50.i vi ng thc 2: Nu x1=0, x2=30; nu x2=0, th x1=45, ni x2=30 v x1=45.Bc 3: Xc nh cc gi tr ng ca cc bt ng thc ban u. Cc gi tr ng nm trn ng thng v min bn di ng thng cha cc rng buc dng nh hn hoc bng.Bc 4: Xc nh vng kh thi tc l min cha cc phng n kh thi. Min cha cc phng n kh thi l vng nhn i c minh ho bi vng c nh bng trong hnh 1.Bc 5: Gii ng thi cc rng buc (di dng cc ng thc) tm cc nh ca min kh thi.Bc 6: Xc nh hiu qu hoc li gp ti cc nh ca min kh thi.nh gi tt c cc nh nh sau:im nh Li nhunx 1x 2$25x 1 + $40x 2(a) 30 0 $25(30) + $40(0) = $750(b) 20 15 25(20) + 40(15) = 1,100(c) 0 25 25(0) + 40(25) = 1,000(d) 0 0 25(0) + 40(0) = 0im nh (b) (x1=20, x2 =15) cho bit kt hp c kh nng sinh li nht (Z*=$1,100). C th tm thy im ny bng cch gii ng thi hai biu thc cha n 2x1 + 4x2 = 100(1)3x1 + 2x2 = 90(2)Nhn biu thc th 2 vi 2 v ly (1) tr i biu thc th (2) mi tm c, ta c:125/1422x1 + 4x2= 100 (1) 6x 1 + 4x 2= 180 (2)- 4x1= -80x1= 20Th x1 = 20 vo (1) hoc (2) c x2 = 15.CH :C th dng phn mm vi tnh LP nh LINDO (Tng tc tuyn tnh v ti u ho ring r - Linear Interactive and Discrete Optimization)v Whats best nhanh chng gii mt bi ton LP.HNH 1TP PHNG N V CC PHNG N CN BINBI TON I NGU TRONG LPMi bi ton ti a ho LP c mt bi ton i ngu (dual problem) tng ng, l mt bi ton ti thiu ho v, ngc li, mi bi ton ti thiu ho LP li c mt bi ton i ngu tng ng, l bi ton ti a ho. Bi ton ny c cc c im sau:a. C bi ton i ngu v bi ton gc s cho gi tr ging nhau i vi cc bin quyt nh trong cc hm mc tiu ca bi ton chnh ti cc im phng n ti u.126/142b. Gi tr ti u ca bi ton gc bng vi gi tr ti u ca bi ton i ngu.c. Bi ton i ngu hu ch bi n c cc ngha kinh t quan trng. V d, phng n ti u ca bi ton i ngu cho bit gi tr c quy cho (hay gi m) hoc chi ph c hi ca mt hng i vi ngun lc khan him. Phn trnh by sau cho bit cc bc lp bi ton i ngu:Trong i = 1,2,...m v j =1,2,...nTrong trng hp 2 x 2: bt u, xc nh cc bin i ngu nh u1, u2. S lng cc bin i ngu bng vi s lng cc rng buc bi ton chnh. Tip tc theo cc quy tc sau:Bi ton chnh Bi ton i ngu1. Cc h strong hm mc tiu

Pha bn phi trong cc rng buc2. Pha bn phitrong cc rng buc

Cc h strong hm mc tiu3.Cc rng buc l Cc bin i ngu l 04.Cc bin ca bi ton chnh 0 Cc rng buc i ngu l 5. Ma trn ca h s cc rng buc Ma trn chuyn v127/142 a11a12 a11a21 a21a22 a12a22 V D 4T v d 2, ta c:Ti a ho:Z =25x1 + 40x2Rng buc:2x1 + 4x2 < 100 (i vi b phn lp rp)3x1 + 2x2 < 90 (i vi b phn hon thin)x1, x2 > 0 lp bi ton i ngu, u tin xc nh cc bin i ngu u1, u2. Bi ton ny ch c 2 bin v ch c hai rng buc trong bi ton chnh. Bi ton i ngu c thnh lp nh sau:Ti thiu hoV = 100u1 +90u2Rng buc2u1 + 3 u2 25(bn giy)4u1 + 2 u2 40(bn n)u1, u2 0V D 5:Gii bi ton i ngu theo s c c u1* = 8.75 v u2* = 2.50. Gi tr ti u V* = 1,100. Hnh 2 cho bit phng n ca bi ton chnh v bi ton i ngu gii bng phn mm my tnh.HNH 2D LIU RA CA MY TNH I VI LP

128/142 NGHA KINH T CA BI TON I NGUBi ton i ngu c nhiu ngha kinh t. l:1. u1, u2 biu th mt loi gi tr ca ngun lc trong ang c ni n. Gi tr ny khng phi l gi th trng; m ng hn l gi tr c quy cho ngun lc. V l do ny, gi tr ca cc bin i ngu c phn nh nh l gi m hay chi ph c hi cho ngun lc. Ni cch khc, gi m l mc gi cc i m hng sn sng tr cho mt n v thm vo ca ngun lc cho trc. Trong v d 4 v 5, mc gi cc i m hng sn sng tr cho mt gi lao ng lp rp tng thm l $8.75 trong khi mc gi sn sng tr cho mi gi lao ng hon thin ch l 2.50. Nu gi thc t ln hn gi m, hng s khng thm bt c mt n v no cho ngun lc .2. Chuyn sang rng buc trong bi ton i ngu. Kim tra rng buc u tin:2u1 + 3 u2 25. Con s 25 v phi cho bit li nhun mi n v hay li gp ca mt chic bn giy, trong khi 40 l li nhun ca mt chic bn n. V 2 gi biu th thi gian mt chic bn giy c x l trong b phn lp rp v 3 gi biu th thi gian ca khu hon thin nn v tri biu th tng chi ph c hi sn xut 129/142 VARIABLEORIGINAL COEFF. VARIABLE VALUECOEFF.SENS. X 1 20250 Note:X1 = 20 X 2 15400X2 = 15 CONSTRAINT ORIGINALSLACK ORSHADOW NUMBERRHSSURPLUS PRICE 1 100 08.75 Note:u1 = $8.75 190 02.50u2 = $2.50 OBJECTIVE FUNCTION VALUE:1100Note: Z = $1,100 SENSITIVITY ANALYSIS OBJECTIVE FUNCTION COEFFICIENTS LOWER ORIGINALUPPER VARIABLELIMITCOEFFICIENTLIMIT X 120 25 60 X 216.6740 50 RIGHT HAND SIDE CONSTRAINT LOWER ORIGINAL UPPER NUMBER LIMITVALUE LIMIT 160100 180 250 90 150 ra mt chic bn giy. Do vy ci m rng buc i hi l chi ph c hi khi sn xut mt chic bn c quy cho mc t nht l phi bng li nhun trn mi chic bn. 3. By gi chuyn sang hm mc tiu i ngu, V = 100u1 +90u2. V n gin ch l tng gi tr cquy (tng chi ph c hi) cho ca cc ngun lc. V vy s tng ng gia bi ton chnh v bi ton i ngu cho thy: Ti a ho tng li nhun bng cch tm ra mc sn lng u ra ti u tng ng vi vic ti thiu ho tng gi tr c quy cho hay chi ph c hi ca cc ngun lc ca hng, vi iu kin l chi ph c hi ca vic sn xut mi sn phm phi khng t hn li gp t sn phm . 4. Tuy nhin ch rng, nu chi ph c hi ca vic sn xut trn thc t vt qua li nhun th s phn b ngun lc chc chn khng ti u, bi v n gin l khi gim sn phm tng ng, cc ngun lc s c gii phng t v ngay lp tc c th c s dng cho cc li ch khc tt hn. Kim tra li iu 2u1 + 3 u2 25(bn giy)4u1 + 2 u2 40(bn n)Chng ta bit c phng n ti u l: u1* = 8.75 v u2* = 2.50. Lp cc con s ny vo cc rng buc c 2(8.75) + 3 (2.50)= 25 = 25 (bn giy)4(8.75) + 2 (2.50)= 40 = 40 (bn n)N cho bit vi mi sn phm, chi ph c hi bng li nhun, v vy phn b ngun lc tr nn ti u. Kt qu ny gi l iu kin lng b sung Mt cp cc phng n kh thi ca bi ton i ngu v bi ton chnh l ti u i vi cc bi ton ring r khi v ch khi iu kin lng trong mt bi ton l dng hon ton, bin cn li trong bi ton khc l khng dng tng ng. C th hn:1. Nu mt rng buc ca bi ton chnh l m (tc l, tn ti mt iu kin lng), th gi m ca rng buc bng 0. Nu mt rng buc l ng(v d, khng tn ti iu kin lng), gi m dng.2. Nu mt rng buc ca bi ton i ngu l m (tc l, chi ph c hi ln hn li nhun trn mi n v), th bin ca bi ton chnh bng 0. Nu mt rng buc l ng (tc l, chi ph c hi bng li nhun trn mi n v), th bin ca bi ton chnh dng. 62Cc rng buc i ngu Cc bin chnh2(8.75) + 3 (2.50)= 25 = 25 (i vi bn giy) -------->x1*=20>0130/1424(8.75) + 2 (2.50)= 40 = 40 (i vi bn giy) -------->x2*=15>0Cng vy,Cc bin i ngu Cc rng buc ca bi ton gcu1* = 8.75 > 0---------> 2(20) + 4(15) = 100 = 100u2* = 2.50 > 0---------> 3(20) + 2(15) = 90 = 90CH :1.Trong v d ny, cc rng buc ca bi ton chnh v bi ton i ngu u ng (khng tn ti iu kin ph hoc chi ph c hi ng bngli nhun trn mi n v). Do gi tr ti u ca bi ton chnh v bi ton i ngu l dng.2. Gi m bng 0 nu rng buc m bi v n khng tt m rng cng sut mt khu vc m bn ang khng s dng ht cng sut mbn c. 5. Cc gi tr phng n ti u cho bi ton chnh v bi ton i ngu l nh nhau. chng minh: Z* = 25(20) + 40(15) = 1,100 v V*= 100(8.75+ + 90(2.50) = 1,100, do Z*=V*=$1,100.PHN TCH HOT NG V SN PHM Nng dng ca LP trong sn xut cp phn trc quan tm n cc sn phm ng hnh (multiple products). Bi ton gii quyt vn xc nh kt hp ti u ca cc sn phm (tc l, kt hp sn phm ti u), cc hn ch cho trc ca ngun lc (cc u vo) dng trong qu trnh sn xut. Vic tp trung nghin cu u ra - nh li rng trc tung v honh ca th o cc s lng ca cc sn phm tng ng (cc u ra) v rng cc ngun lc (u vo) c biu din ch nh l mt chui cc ng rng buc trn u ra.Di y chng ta tho lun phn tch hot ng mt sn phm n (single product). N lin quan n vic la chn mt kt hp ti u ca mt qu trnh sn xut c dng sn xut mt s lng sn phm n ln nht, vi mt lng u vo c nh. Mi mt qu trnh c cp n l mt hot ng. Cng dng LP tm phng n ti u. Phn tch tp trung nghin cu vn u vo v cc phng n la chn qu trnh sn xut m trong u vo c th c s dng c c sn phm. LP tm kim mc ti u ca mi hot ng. C th dng l thuyt sn xut (tc l cc tia qu trnh, cc ng ng lng v cc ng ng ph) minh ho cho cc phng n la chn qu trnh sn xut v khi nim thay th u vo. u 131/142tin chng ta xy dng v gii bi ton ti a ho u ra. Bi ton ti a ho li nhun s c cp sau.DNG CA BI TON TI A HO U RA V d sau minh ha cch thc xy dng v gii bi ton ti a ho u ra V D 6Mt hng x l da s dng vn v nhn cng trong qu trnh nhum trng da cu. C th la chn mt trong 3 qu trnh sn xut khc nhau (A, B, v C). Mi qu trnh c mt kt hp nhn cng v vn khc nhau: Qu trnh A cn mt n v vn v bn n vnhn cng, qu trnh B cn 2 -2, qu trnh C cn 5-1. Nng sut ca hng l gii hn 5 n v vn v 8 n v mi ngy cho hot ng nhum.Gi QA, QB, v QC l lng da nhum c mi ngy tng ng trong quy trnh A, B v C. Bit rng mc tiu ca hng l ti a ho u ra ph thuc vo cc rng buc u vo (vn v nhn cng), bi ton c th xy dng nh mt bi ton LP nh sau:Ti a hoQ = QA + QB + QC.(hm mc tiu)Rng bucQA + 2QB + 5QC 5(rng buc vn)4QA+ 2QB + QC 8(rng buc nhn cng)QA, QB, QC 0(rng buc khng m)PHNG PHP TH VI BI TON TI A HO U RABi ton hot ng LP c th c minh ha v gii thng qua th, s dng cc tia hot ng biu din cc qu trnh sn xut, cc ng ng lng sn xut biu din hm mc tiu v mt min kh thi biu din cc rng buc.CC TIA QU TRNH (PROCESS RAYS)Mt qu trnh sn xut l qu trnh m trong u vo c kt hp theo mt t l xc nh c c u ra. Theo nh ngha ny, mt qu trnh sn xut c th c biu din trn th nh mt tia i qua gc 0 c dc bng t l cc u vo ca cc ngun lc tng ng cn sn xut mt n v u ra. Trong v d ny, 3 tia qu trnh sn xut c m t trong hnh 4.Trn theo tia A, cc u vo c kt hp trong t l ca 4 n v nhn cng v mt n v vn. Do , tia A c dc l 4. Tng t, trn theo tia B, cc u vo c kt hp trong mt t l gm 2 n v nhn cng v 2 n v vn. Tia qu trnh C, cho bit cc u vo c kt hp trong t l 1 v 5.Mi qu trnh sn xut biu din li nhun khng i theo quy m. iu ny c ngha l u ra dc theo mi tia tng theo mt t l tng ng vi mc tng 132/142trong u vo. V d D, G, J biu din cc u vo cn thit sn xut mt, hai, v ba n v u ra.CC NG NG LNG SN XUTMt ng ng lng sn xut (production isoquant) cho bit cc kt hp ca bt k 2 hay nhiu hn 2 u vo lm tng u ra cng mt mc. Cc ng ng lng c xy dng bng cch v cc ng thng ni cc im ca u ra bng nhau trn cc tia qu trnh lin nhau. Bn ng ng lng Q biu din cc mc u ra 1, 2, 3 v 4 tng ng trong hnh 3. Chng c cc on song song gia cc tia qu trnh lin nhau. V d, on DE song song vi GH, on EF song song vi HI. C c iu ny l v cc h s ca cc bin s Q trong hm rng buc ngun lc l cc hng s.CH :on thng ca mt ng ng lng nm gia hai tia qu trnh sn xut ng rng kt hp ca 2 qu trnh ang c dng sn xut mt mc u ra c th. Nh cp trn, cc im dc theo mi tia qu trnh biu din sn lng u ra c c nu hai u vo (nhn cng v vn) c kt hp trong mt t l ca mt lng tng ng cc n v ca mi ngun lc cn sn xut mt n v u ra cho trc. Tuy nhin, cc im nm trn ng ng lng gia 2 tia qu trnh gn nhau c mt ngha khc nhau khng ng k. Nhng im ny biu din mt kt hp u ra t mi qu trnh sn xut gn nhau. V d, im S trn ng ng lng "Q = 4" trong hnh 3 cho bit mt kt hp sn xut dng trong c qu trnh B v C. Sn lng u ra sn xut c trong mi qu trnh c th c c bng vic v mt hnh bnh hnh nh trong hnh 4. Mt ng v t im J song song vi tia qu trnh B, ct tia qu trnh C ti im L. Mt ng khc v t im S song song vi tia qu trnh B, ct tia qu trnh C ti im D. T hnh bnh hnh OESL, c th xc nh c sn lng u ra sn xut c bi mi qu trnh ln lng u vo tng ng dng cho mi qu trnh.133/142HNH 3CC TIA SN XUT V CC NG NG LNG SN XUTHng nn sn xut mt n v u ra s dng B, bi v im E nm trn ng ng lng "Q = 1", v 3 n v u ra s dng qu trnh C, v im L nm trn ng ng lng "Q = 3". Kt hp ny s cho ra 4 n v u ra. Ti im E hai n v vn v 2 n v nhn cng c dng trong qu trnh B, v ti im L 15 n v vn v 3 n v nhn cng c dng trong qu trnh C. Tng ngun vn v nhn cng dng sn xut 4 n v u ra l 17 vn v 5 nhn cng. Tt c cc im khc nm gia cc qu trnh c th c hiu tng t. TP PHNG NMin kh thi cha tt c cc kt hp u vo ca vn v nhn cng ng thi tho mn tt c cc rng buc ca bi ton LP. Hnh ch nht c nh bng 0TRW trong hnh 3 biu din min kh thi cho bi ton v d. V c ti a 5 n v vn sn sng mi ngy, nn ch cc kt hp u vo nm pha trn hoc nm v bn tri ca ng RW mi cho bit cc phng n kh thi cho bi ton LP. Tng t, do ch c ti a 8 n v vn sn sng mi ngy nn cc phng n kh thi phi nm trn hoc di ng TR. Cui cng, cc rng buc khng m gii hn cc kt hp u vo pha bn tri ng 0T v pha di ng 0W.PHNG N TI UKt hp cc qu trnh sn xut ti u ho u ra b rng buc vo ngun lc xut hin ti im trn bin ca vng kh thi nm trn ng ng lng sn xut cao nht. Hnh 4 ch ra rng phng n ti u xut hin ti im R. Ti R, c c 3 n v u ra khi s dng 5 n v vn v 8 n v nhn cng. V hnh bnh hnh 0DRH cho bit nn s dng qu trnh A sn xut mt n v u ra, (QA=1) v phn cn li, trong trng hp ny l 2 n v, s dng qu trnh B (QB=2).T phng n trn th chng ta cng c th thy rng u ra ti a ho khi QC=0, v vy th gi tr ny vo trong 2 biu thc rng buc, ta c134/142QA + 2QB =54QA+ 2QB =8V tr biu thc 1 cho biu thc 2, c -3QA=-3 hay QA=1. Sau tm c QB=2. Gi tr ny tng t vi kt qu tm c bng th.BI TON TI A HO LI NHUNBi ton sn xut c th c dng ging nh dng bi ton ti a ho li nhun.V D 7Trong v d 6, gi nh rng li nhun gp ca u ra sn xut bi cc qu trnh A, B v C tng ng l $6, $5, and $4 mi n v. Vi gi thit l hng mong mun ti a ho li nhun (Z) thay v ti a ho u ra (Q), hm mc tiu tr thnh:Maximize: Ti a ho: Z=6QA + 5QB + 4QCMt kt qu ti u i vi bi ton ti a ho li nhun LP c th c c v c minh ho bng cc ng ng li ch khng phi l cc ng ng ph.NG NG LI Mt ng ng li phn nh cc kt hp khc nhau ca cc sn phm m hng c th bn thu c mt mc li nhun cho trc. ng ny c xc nh bng cch v cc ng thng gia cc im nm trn cc tia qu trnh gn nhau c cc tng li nhun bng nhau. minh ho, xt ng ng lng "