The Role of Uncertainty in a Simple Temporary Equilibrium Model of International Trade with Quantity Rationing under Fixed Exchange Rates

Schi ko, Ul ich K.; Eckwe , B. A icle The Role o Unce ain y in a Simple Tempo a y Equilib ium Model o In e na ional T ade wi h Quan i y Ra ioning unde Fixed Exchange Ra es Zei sch i ü Wi scha s- und Sozialwissenscha en (ZWS) - Vie eljah essch i de Gesellscha ü Wi scha s- und Sozialwissenscha en, Ve ein ü Socialpoli ik P o ided in Coope a ion wi h: Duncke & Humblo , Be lin Sugges ed Ci a ion: Schi ko, Ul ich K.; Eckwe , B. (1983) : The Role o Unce ain y in a Simple Tempo a y Equilib ium Model o In e na ional T ade wi h Quan i y Ra ioning unde Fixed Exchange Ra es, Zei sch i ü Wi scha s- und Sozialwissenscha en (ZWS) - Vie eljah essch i de Gesellscha ü Wi scha s- und Sozialwissenscha en, Ve ein ü Socialpoli ik, ISSN 0342-1783, Duncke & Humblo , Be lin, Vol. 103, Iss. 5, pp. 461-483, h ps://doi.o g/10.3790/schm.103.5.461 This Ve sion is a ailable a : h ps://hdl.handle.ne /10419/291559 S anda d-Nu zungsbedingungen: Die Dokumen e au EconS o dü en zu eigenen wissenscha lichen Zwecken und zum P i a geb auch gespeiche und kopie we den. Sie dü en die Dokumen e nich ü ö en liche ode komme zielle Zwecke e iel äl igen, ö en lich auss ellen, ö en lich zugänglich machen, e eiben ode ande wei ig nu zen. So e n die Ve asse die Dokumen e un e Open-Con en -Lizenzen (insbesonde e CC-Lizenzen) zu Ve ügung ges ell haben soll en, gel en abweichend on diesen Nu zungsbedingungen die in de do genann en Lizenz gewäh en Nu zungs ech e. Te ms o use: Documen s in EconS o may be sa ed and copied o you pe sonal and schola ly pu poses. You a e no o copy documen s o public o comme cial pu poses, o exhibi he documen s publicly, o make hem publicly a ailable on he in e ne , o o dis ibu e o o he wise use he documen s in public. I he documen s ha e been made a ailable unde an Open Con en Licence (especially C ea i e Commons Licences), you may exe cise u he usage igh s as speci ied in he indica ed licence. h ps://c ea i ecommons.o g/licenses/by/4.0/ The Role o Unce ain y in a Simple Tempo a y Equilib ium Model o In e na ional T ade wi h Quan i y Ra ioning unde Fixed Exchange Ra es* By Ul ich K. Schi ko and B. Eckwe A wo-pe iod model o empo a y equilib ium wi h a ioning and in e - na ional ade unde ixed exchange a es is p esen ed, emphasizing he im- po ance o agen 's expec a ions o u u e p ices and cons ain s. I is shown ha se e al adi ional compa a i e s a ics esul s a e only compa ible wi h a speci ic expec a ional s uc u e. Especially his is he case o he eac ion o he ade balance o exogeneous pa ame e changes. 1. In oduc ion The ailu e o he p ice sys em o adjus immedia ely o i s Wal asian equilib ium alue ga e ise o he o mula ion o empo a y equilib ium models wi h quan i y a ioning, s a ing e.g. wi h J. P. Benassy (1975), E. Malin aud (1977), W. and K. Hildenb and (1978), and culmina ing in he wo k o V. Böhm (1980). I he planning ho izon o he economic agen s is no con ined o one pe iod, hen he u u e o e shadows he p esen in he sense ha he agen s ha e o decide now wi hou know- ing he p ices and wages o omo ow no he quan i y cons ain s hey will ha e o ace when he u u e un olds. The ollowing model o a small open economy ies o ake his si ua ion as a s a ing poin in a o mula ion o a simple model wi h p ice expec a ions (depending on he cu en p ices and wages) and unce ain y conce ning u u e quan i y cons ain s. The eby we can complemen A. Dixi 's model (1978) in se e al espec s. Fi s ou model con ains an explici in e empo al o mula ion o he consume s' and p oduce s' op imizing beha iou , especially allow- ing in en o y decisions. Secondly we examine he in luence o a speci ied expec a ional pa - e n conce ning u u e p ices and wages as well as possible andom * Financial suppo o he Deu sche Fo schungsgemeinscha is g a e ully acknowledged. OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.103.5.461 | Gene a ed on 2023-04-04 12:02:50 462 Ul ich K. Schi ko and B. Eckwe es ic ions in he labou ma ke on he op imizing beha iou and he compa a i e s a ics p ope ies o he whole model. The chosen o mula ion conce ning p ice and quan i y cons ain ex- pec a ions is su icien ly gene al o cap u e he main in luences o hese phenomena. Ou esul s a e qui e obus agains mo e sophis i- ca ed expec a ional o mula ions. Wi h ega d o p ice expec a ions we use a one-poin -dis ibu ion, meaning ha u u e p ices a e expec ed wi h p obabili y one. Indi iduals ha e no a ional expec a ion, so ha expec ional e o s a e possible. Quan i y expec a ions a e s ochas ic and modelled by a disc e e p obabili y dis ibu ion. A gene aliza ion o he assumed expec a ional pa e n is no likely o al e ou esul s in a cen al way. These enla gemen s p oduce se e al new insigh s conce ning he in- luence o unce ain y on he p ope ies o he possible sho - un equilib ia. Mos o he indi idual decisions depend essen ially on he expec a ional pa ame e s. The en ep eneu ial beha iou is dicho o- mized in he sense ha he sales- and in en o y-decisions a e sensi i e wi h espec o expec a ions, while he p oduc ions- and labou demand decisions a e no . This is no a consequence o ou speci ic expec a ional pa e n and will be in e p e ed economically. Ou use o he small coun y assump ion es ic s as usual he powe o he model, o i excludes some in e es ing disequilib ium si ua ions, which show up in a wo-coun y se ing (compa e Schi ko and Eckwe (1981, 82, 83)). To s udy he in insic dynamics would be oo leng hy and is le o a subsequen pape (1982). 2. The basic model Ou economy is a small coun y which p oduces i s na ional p oduc by means o he single non adable ac o labou , whose p ice is ixed in he sho un. Fo he p oduced good he wo ld p oduc p ice is gi en o he small coun y, bu he e a e no quan i y cons ain s es ic ing he goods ma ke decisions o he coun y. I can e y well happen, ha he domes ic goods ma ke is in disequilib ium, so ha he o eign ade abso bs he excess supply o demand. We ha e hen p = n p = 1,2, so ha p ices o he ou pu s a e ansla ed by means o he exchange a e om o eign cu ency o home cu ency uni s. We assume coun y speci ic ou pu s o be comple ely subs i u able in consump ion, so ha we ha e in ac a single adable good. Ou model is a wo-pe iod one, OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.103.5.461 | Gene a ed on 2023-04-04 12:02:50 Simple Tempo a y Equilib ium Model o In e na ional T ade 463 in which he economic agen s base hei beha iou in pe iod = 1 on he ma ke da es o he p esen and on hei subjec i ely ce ain poin expec a ions conce ning p ices and wages in pe iod = 2 and hei andom expec a ions conce ning he cons ain le els on he labou ma ke in he u u e. The use o a wo pe iod model does no mean ha he economy ends a e pe iod 2 bu a he , ha he agen s o mula e plans only one pe iod ahead in o he u u e. The home coun y has i s own money, which is he only asse se ing as a s o e o alue. Consump ion and p oduc ion decisions a e desc ibed by means o ep esen a i e decision uni s, he ep esen a i e consume and he ep esen a i e p oduce . 2.1. Consume beha iou Le us begin wi h he beha iou o he consump ion side. The con- sume decisions a e he ou come o he maximiza ion o a single, spec- i ied u ili y unc ion which is de ined on he p esen and u u e con- sump ion possibili ies comp ising home and impo ed goods, i.e. (1) u (<cl9 Ml c2, M2) = u (xly = xx-x2 , whe e x : = c + M , = 1, 2, deno es he consump ion o he p oduced good a ime , which consis s o consump ion o he home p oduced good c and he impo ed good M . We could ha e chosen ano he u ili y unc ion, say yj {u (xi, xg)) = = log xi + log X2, p a s ic ly mono one ans o ma ion. This u ili y unc ion has he special, bu impo an p ope y, ha he ma ginal u ili y o consump ion in pe iod 2 becomes e y la ge, when he amoun o consump ion becomes smalle and smalle . This u ili y unc ion has an A ow-P a -measu e o isk-a e sion o one, so ha we ha e isk- neu ali y. Conce ning he u u e ma ke da es he consume has he ollowing poin expec a ions { P2 = Wl (Pi) = lPl w2 = >2 (w ) = bw1 , whe e p is he p ice le el and W he wage a e bo h in pe iod , = 1, 2. The linea unc ions y>i, i = 1, 2, show he way p ice expec a- ions a e o med. I a> 1, hen he p ice expec a ions o he consume a e called in la iona y; i a — 1, hen hey a e called s a ic expec a ions, and i a < 1, hen we ha e de la iona y expec a ions. Depending on he OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.103.5.461 | Gene a ed on 2023-04-04 12:02:50 464 Ul ich K. Schi ko and B. Eckwe labou ma ke si ua ion in he p esen , he ep esen a i e indi idual expec s a a ioning on he labou ma ke in he u u e (pe iod wo) wi h di e en subjec i e p obabili ies. Tha amoun s o ha he e- p esen a i e consume expec s wi h a ce ain p obabili y no be a- ioned, espec i ely o be a ioned a a ce ain le el h. I , = 1,2, deno es he ixed labou supply o he consume . The si ua ion can be summa ized in he ollowing ma ix, whe e R1 deno es a labou ma ke a ioning in pe iod and N* ha he consume is no a ioned on he labou ma ke in pe iod , = 1,2. R2 JV2 m 1-Q2 q2 m 1-Ql Qi qi deno es he co esponding subjec i e p obabili ies. Le us s a o de i e he op imal consump ion decisions. I he consume is no a ioned on he labou ma ke in pe iod one, he employmen in pe iod wo, L2, is a disc e e andom a iable whose p obabili y dis ibu ion is gi en by wi h p obabili y q (3) I* = ' " { U wi _ k Wi wi h p obabili y 1 — q Le X21 deno e he ac ion o he consume , i he is no a ioned on he labou ma ked in pe iod wo, and he ac ion he chooses, i he is a ioned in ha pe iod. Then a andom a iable X2 can be de ined as ^ __ L2 = I i L2 *22 > i L2 X2 is a disc e e andom a iable wi h p obabili y dis ibu ion qu (1 — qi). Le us now de ine a ans o ma ion by means o (5) X2 ; — X2~*21 *22 — x2l which posesses a binomial dis ibu ion acco ding o (6) x'2 —• B (1, q j) L2 = l2. F om (5) we ob ain , O , i H..« (7) = X2 (X22 — ^l) + *21 OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.103.5.461 | Gene a ed on 2023-04-04 12:02:50 Simple Tempo a y Equilib ium Model o In e na ional T ade 465 As X2 is a andom a iable, he expec ed alue o he u ili y unc ion (1) is a ele an op imali y c i e ion, i.e. ou consume (in case o non- a ioning in pe iod one) has o maximize (8) max {xx • [x2l + (x^ - x21) Eq1 (X2)]} XV x2i' ^ s. . (i) x ¡> 0, x2i ^ 0, mi ¡> 0, i = l,2 (ii) Pi Xx -!- 77lj TTZ Q -j- W^ (iii) P2 x2i = m1 + w212 (i ) p2x& = + w2'l2 . To ind a solu ion o p oblem (8) we use a s anda d me hod o dynamic p og amming, i.e. we i s maximize wi h espec o he second pe iod's decision a iables o e he cons ain se o pe iod wo (gi en an a bi a y bu ixed decision in pe iod one). So we ha e o sol e he ollowing maximiza ion p oblem in case o non- a ioning in pe iod one (9) max E (u (xh X2)) = max E (u (xl X2(x^ — x21) + x21) = X2V X22 x2i* X22 max u (x , x2i + (x22 - x2i) Eq (X2)) = X21,X22 max {x1 [x21 + {xm - x21) Eq (X2)]} x2i,x22 s. . (iii), (i ) and he non-nega i i y condi ions o he decision a iables. As a solu ion we ind m1 + l2w2 (10) *21 = x22 = P2 m1 + ¿2 V2 As in ou simpli ied se up he labou supply is ixed, he op imal solu ion (10) can be de i ed di ec ly om (8) (iii) and (8) (i ).1 We ha e desc ibed he p ocedu e o sol ing (8) in de ail o p epa e o he mo e complica ed decision p oblem o he p oduc ion sec o . We ecall, ha gi en he (*i, mi)-decision x^i deno es he op imal decision in pe iod wo, i he consume is no a ioned in his pe iod. O he wise he op imal decision would be x^. I we subs i u e he 1 This was poin ed ou by he e e ee. OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.103.5.461 | Gene a ed on 2023-04-04 12:02:50 466 Ul ich K. Schi ko and B. Eckwe op imal solu ion o pe iod wo in o (8), we ob ain an indi ec u ili y unc ion. / mi - bw u (11) V (xh ml pl wl l2, ¿2, ql a, b) = q x — —j + / TTli + bWi U The indi ec u ili y unc ion (11) has now o be op imized wi h espec o xi, mi, subjec o he ollowing pe iod-one es ic ions (12) XX > 0, TTIi > 0 (13) m^ + w1li = p1x1 mi . We assume ha mi > 0, which holds, i (14) q{ bw1l2 + (1 - gx) bw1 l2<mii + w1ll . By making his assump ion, which says ha he weal h o pe iod one is g ea e han he expec ed labou income o pe iod wo, we exclude bounda y solu ions. Fo he op imal decisions we hen ob ain (15) 1 [7720 + w l 4- <?1 bwx l2 + (1 - <Zj) bw y 2 Pl = [wio.+ Ii - Q± (bw l2) - (1 - Qi) (bw^h*)] • The pa ial de i a i es o he op imal decisions wi h espec o he exogeneous a iables a e 3 *J/3 = (1 - bi^/2 Pi > 0 , (16) 3 JC /3 777o = 1/2 pj > 0 , bWi z Pi The las inequali y e.g. shows, ha he eac ion o he op imal con- sump ion decision in pe iod one due o a change in he subjec i e p obabili y o be ully employed in pe iod wo, is p opo ional o he expec ed unemploymen in ha pe iod. Fu he mo e we deduce 3 xJ/3 a = 0 3 *J/3 b = —J— w (q1 Iq + (1 - <?i)l2) > 0 A Pi OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.103.5.461 | Gene a ed on 2023-04-04 12:02:50 Simple Tempo a y Equilib ium Model o In e na ional T ade 467 (17) 3xJ/3Pi = - (1/Pi)*|<0 q1 (Zi + bl2) + (1 - q ) (h + bl2) >0 . 3 w 2 Pi In (17) only he i s pa ial de i a i e is su p ising. In e empo al subs i u ion as a consequence o changes in p ice expec a ions does no occu because o ou chosen u ili y unc ion. The sign eac ion o m can be deduced om he budge condi ion o pe iod one, gi en he sign eac ions o x . In case o a ioning in pe iod one we calcula e by a simila p ocedu e he op imal decisions o pe iod one as i a simila condi ion as be o e in (14) ensu es he posi i i y o m . The sign eac ion o pa ame e changes can be in e ed om (18) like be o e. I is e iden , ha he sign eac ions a e quali a i ely simila o he p e ious ones in case o non- a ioning in pe iod one, because also in ha case h is no a decision a iable. Le us now desc ibe he p oduc ion decision o ou economy. We assume ha he p o i s o pe iod a e axed ully by he go e nmen . The e o e he ep esen a i e i m has no ini ial money balances, bu has an endowmen a)o o he consump ion good, which has been s o ed om he las pe iod. The i m plans o sell y uni s o he good and o buy z uni s o labou ( = 1,2). Wi h a p oduc ion unc ion his inpu is ans o med in o ou pu co , = 1,2, which is ins an aneously a ailable, i.e. (19) co = (z ) = hzQ i 0 < q < 1, h > 0, = 1,2 . The p oduc is s o able, and simila o he consump ion sec o he p oduce s an icipa e he u u e ma ke da es by subjec i e expec a ions. Conce ning u u e p ices and wages we assume ha hei expec a ions a e iden ical o hose o he consump ion side. I he p oduce is no a ioned in pe iod one on he labou ma ke , he expec s no o be a ioned in pe iod wo wi h p obabili y (so ha his no ional demand would be ul illed) and o be a ioned wi h p obabili y (1 — qo) a he (18) x* = — [TOQ + w1l1 + q2 bw! u + (1 - q2) bwi U] ¿p ! - 1 m = [mo + Wi - qQ bwy l2 - (1 - q2) bw112) — , 2.2. P oduce beha iou OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.103.5.461 | Gene a ed on 2023-04-04 12:02:50 468 Ul ich K. Schi ko and B. Eckwe ull employmen le el. Tha means Z2 is a andom a iable wi h he ollowing dis ibu ion: , w2) wi h p ob. q3 ( z2 (P2» 1 (20) Z2 1 ' wi h p ob. (1 — q 3) In case he p oduce is a ioned in he i s pe iod, his expec a ion conce ning he u u e labou ma ke si ua ion is gi en by { Zo (p9, w2) wi h p ob. q4 l2 wi h p ob. (1 — <?4) . The p oduce maximizes his expec ed p o i o e he planning ho izon. To calcula e he expec ed alue o he p o i unc ion o he case o non- a ioning in pe iod one, we ans o m he andom a iables Z2 by means o z« - L (22) Z9: = 2 ' Z2 (p2, W2) - l2 which is dis ibu ed acco ding o B {1, <?q), so ha we ha e 1 , i Z2 = z2 (p2, w2) (23) Z2 = [o , i Z2 = i2 . F om (22) we ob ain (24) Z2 = Z2 (z2 (p2, w2) - l2) + l2 . We know om he p oduc ion unc ion, ha co21 = hz% , i Z2 = z2 [œ22 = hlQ2 i Z2 = Z2, Q2 = hZ =< so ha Q2 is also andom. As an accoun ing es ic ion we ha e o conside + — 2/1 = h (pe iod one) (25) + h = (pe iod wo) , ii deno ing he s o age ac i i y in pe iod one. The u u e sales a e also andom, depending on Z2. This andom a iable Y2 can be ans o med by Y2 - (hl% + i,) (26) 2 -hzl OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.103.5.461 | Gene a ed on 2023-04-04 12:02:50 Simple Tempo a y Equilib ium Model o In e na ional T ade 475 wi h Zi deno ing he labou demand cons ain . I is easy o show he exis ence and local s abili y o hese wo disequilib ia. Le us now gi e an e ec i e classi ica ion o he equilib ia o he model in (pi, w{) — space. This classi ica ion is impo an , because i enables us o assign ce ain pa ame e cons ella ions o he di e en ypes o disequilib ia. Fu he mo e he classi ica ion inc eases ou in- ui i e unde s anding o he model. We s a o de i e he slope o he labou ma ke equilib ium cu e in (pi, i^i) — space. An equilib ium in he labou ma ke is desc ibed by (62) zA (pl w ) = I wi V " 1 PiQh ) The slope o his cu e is gi en by 3 w< (63) 3 Pi Zi (pl wx) = Zi Pi The e o e we can illus a e he equilib ium locus as in ig. 1. The ade balance in case o unemploymen ( he e ec i e ade balance) in pe iod one is de ined as Pi Pi - - (64) HB = y (Pi Jil wly co0> a, b) x (p? ny w iq , <j2, b; l U, l2) — 71 71 Pi Pi Pi (i - g) , , ( wi (g"= ) , i 7 9~ 7T [ 2 (w ,b) +n[ Vloh ) +a>0~ 2Pl w ( 1 ) • [77-io + ^ j 9 +q>2 (^1 bl2) + (1 - q2.) (1^1 bi2)] - g . F om (64) we calcula e 30* OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.103.5.461 | Gene a ed on 2023-04-04 12:02:50 476 Ul ich K. Schi ko and B. Eckwe (65) and (66) 3 HB 3 Pi Pi (1 - a) ( W1 ( H)( h(o- 2) V + Pl e h ) 2 (<? - 1) ) (wl b) (+) 3 3 HB 3 w, (Pi)2 (1 - a) ^ (2 {w b))2 (—) b (<£> h + (1 - + Pi£ 2 - e h I 2Pl(Q-l) ) 2 Pi q2) k). (+) The i s e m in (65) and (66) ep esen s he s o age e ec s o he pa ame e a ia ion, while he second e m in (65), espec i ely, he second and hi d e m in (66) ep esen he e ec s on he excess goods supply in ou economy. ^ ^ (1_a) (p^U-a)-^- No ice i s , ha he s o age e ec s?^ - and — ^ 6 (wl b) (2 (wl b))2 o (65) and (66) a e always o opposi e signs. The slope o he HB = 0- cu e in (w , pi)-space, gi en by dwi dp! HB = 0 3 HB/3 Pj 3 HB/3 w. , is he e- o e posi i e, i we ei he assume bo h s o age e ec s o be dominan o weak. So we can speci y (67) 3 Pi 3 w1 U HB = 0 >0 in he unemploymen egion no mally. No e ha o special alues o he expec a ional pa ame e s he slope o he HB = 0-cu e in he unemploymen egion could also be nega i e. This can be summa ized in he ollowing pic u e ( ig. 2). ig. 2 OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.103.5.461 | Gene a ed on 2023-04-04 12:02:50 Simple Tempo a y Equilib ium Model o In e na ional T ade 477 When he economy aces o e employmen he ade balance is gi en by Pi Pi (68) HB (2/1 (Pi , wl <o0, a, b; IJ) -x (pj n, wh n^, q b L2, Z2) 71 El 71 + (1 - q ) (bw l2)) - g Fo he pa ial de i a i es we de i e (69) (70) 3 HB 3 Pi 3 HB 3 w1 1 71 EL 71 2 Pi (-) (+) P! (1 — a) 3 /3 2( (u71>b))2 (+) - (Zi + Qi bl2 + (1 - Qi) bZ2) I we assume he s o age e ec s in (69) and (70) bo h o be ei he dominan o nondominan , we ge opposi e signs o (69) and o (70). We can conclude, ha (71) 3 w1 3 Pi 3 HB/3 pi >0 , HB = 0 3 HB/3 w which is illus a ed in ig. 3. No e ha o special alues o he expec a ional pa ame e s he slope o he ade balance equilib ium cu e in he egion o o e employmen can be nega i e as illus a ed by he b oken line in ig. 3. ig. 3 OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.103.5.461 | Gene a ed on 2023-04-04 12:02:50 478 Ul ich K. Schi ko and B. Eckwe 4. Compa a i e S a ics 4.1. Unemploymen equilib ium Fi s we s udy he in luence o pa ame e changes on he endogeneous a iables Zi and HB, when he economy is no ully employed. The equa ion sys em is gi en by (72) Ki : = L z1 (71 V1 , U>l) = 0 K2 : = V*[y (p*n, VJ1, a> k) - xl wl> e b'y h> h> h) - -g] -HB = 0 The implici unc ion heo em gi es us he e ec s o a pa ame e change on he endogeneous a iables h, HB in a neighbou hood o he equilib ium solu ion. // deno es a special pa ame e o in e es : (73) dl 3 11 dHB whe eby D : 3 Ki 3 K« 3 K< 3 K2 • = - 1 < 0 dl dHB dHB dl Fo a change in go e nmen expendi u es we de i e by means o (73) (74) 3^/30 = 0; dHBJdg = -pj<0 . In a sys em o ixed exchange a es a change o go e nmen expendi- u es has no in luence on he employmen le el. Since he goods ma ke is always equilib a ed, he e exis s no ansmission mechanism om he goods ma ke o he labou ma ke . The nega i e eac ion o he ade balance o an inc ease o g is ob ious. Wage a e policy esul s in (75) and (76) 3 HB/3 w = 3 3 w-^ — 3 z^J3 i^! •< 0 3 x 3 zj P* I 3 2/j 3 xx 3Zi 3 w1 3 z j + 71 2 Pi 3 w1 (-) 71 3 w1 3 y ( dV 3*i 3 w 3 w J (+) 3 w1 3 x (+) OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.103.5.461 | Gene a ed on 2023-04-04 12:02:50 Simple Tempo a y Equilib ium Model o In e na ional T ade 479 In (76) we ha e 3 yi/d w < 0 o high p ice expec a ions. I he goods ma ke e ec s a e dominan , we end up wi h a nega i e sign. A a ia- ion o he ixed labou supply leads o The employmen le el Zi is independen o he agg ega e labou supply Zi. Since unemploymen can be measu ed by we can de i e he e ec o labou supply a ia ions on he excess labou supply as dU/dh = 1. As is in ui i ely clea , a educ ion o he agg ega e labou supply causes a educ ion o unemploymen . The ade balance eac ion is a i s sigh su p ising, since he employmen le el in pe iod one is de e mined by he demand side. Bu no e ha a educ- ion o he labou supply educes he expec ed income o pe iod wo, because he consume expec s wi h p obabili y q<% no o be a ioned in ha pe iod. So he expec ed loss o income in he u u e has a con- sump ion demand e ec in pe iod one. We u he deduce he e ec s o an exchange a e policy (79) 3 yd = 3 z J3 n > 0 . A de alua ion has posi i e labou ma ke e ec s. The ade balance eac ion depends on wo eal and a kind o mone a y e ec . 1. The eal consump ion demand inc eases (labou ma ke e ec ). 2. The eal goods supply inc eases. 3. The consump ion demand in o eign cu ency dec eases nominally. The ade balance eac s posi- i ely i he labou ma ke induced consump ion e ec is domina ed by he wo emaining e ec s. Depending on he p ice expec a ions an op- posi e sign speci ica ion o (80) could be easonable. Finally we examine he in luence o changes o he expec a ional pa ame e s a, b on he unemploymen equilib ium o ou model. (81) 3 yd a = 0 , 3 yd b = 0 , 3 yd q2 = 3 yd q3 = 0 (77) 3 l /d li = 0 , 3 HB Id h= - —< 0 . (78) U: = h-h , (80) (82) OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.103.5.461 | Gene a ed on 2023-04-04 12:02:50 480 Ul ich K. Schi ko and B. Eckwe 3 HB pi 3 ¡/i 1 (83) = V^b 2V lq*wi ^ + (1 ~ ^ h) __ 1 p 2 (l - a) 3 /3 b _ ~ ~~ 2 n 2 (+) ^— (Q2 w2 h + -<?2) ^ 0 (-) (81) ells us ha expec a ional a ia ions do no a ec he employmen le el o ou economy. In ou ega ded disequilib ium he employmen le el is acco ding o (72) demand de e mined. The labou demand howe e does no depend on expec a ions. Inc eases in p ice expec a- ions lowe cu en sales plans und wo sen he eby he ade balance (compa e (82). Highe wage expec a ions inc ease s o age cos s and he eby cu en sales plans as well as o al cu en consump ion. I he posi i e s o age e ec is domina ed by he consump ion e ec , hen we ha e a nega i e sign in (83). (84) 3 HB/3 q<> = - —— bw (Zg - Zg) < 0 , 3 HB/3q 3 = 0 . 2 71 The expec a ional pa ame e s ha e no in luence on he en ep e- neu ial labou demand decisions, so ha he le el o employmen does no a y when expec a ions change. This is due o he ac ha in ou model p oduc ion does no ake ime. The ade balance howe e depends sensi i ely on he p ice-, wage-, and cons ain expec a ions. 4.2. O e employmen equilib ium In his ype o equilib ium which is desc ibed by (85) he employmen le el is gi en by he ixed labou supply l . (85) K,: = - l + l = 0 K4: =p* [y1 (p* n, wl o)0, a, b; l ) - x (p n, wl9 m<,, q b ll l2, l2) - - g] - HB = 0 . As endogeneous a iables we ha e Zi and HB. The compa a i e s a ics p ope ies can be ob ained like be o e and a e summa ized as ollows. OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.103.5.461 | Gene a ed on 2023-04-04 12:02:50 Simple Tempo a y Equilib ium Model o In e na ional T ade 481 Fo a change in go e nmen demand we ha e (86) 3 zi/3 Q = 0 , 3 HB/3 g = - p* < 0 . Wage a e policy esul s in 3 Zj/3 w1 =0 (87) 3 HB/3 w = - + + W " «1) Pi 2 (1 - a) 3 /3 ^ /I - ^ - 1 — W1 + 91W2 + a- 2 7*2 (+) (-) du^ KPiQh ) np*Qh(o - 1) Dl deno ing excess labou demand. dDL / w Q - (88) —?- = [ — <0, H a Pi&h ) These mul iplie s lend hemsel es o a comple ely analogous in e - p e a ion as he p eceeding ones. A change in Zi gi es 3 V (89) 3 Z^ h = l ; 3 HB/3 Zx = p* dl 1 2 71 [w± (1 + q bw )] ^ o . An exogenous inc ease in he labou supply s imula es sales plans as well as consump ion demand. The ne e ec depends on he ela i e s eng h as shown in (89). Exchange a e policy leads o 3 V pi (90) 3 Z^S ¡7T = 0 ; 3 HB/3 n = pj ^ + ^ 0 whe e he sign o he ade balance eac ion depends on he p ice ex- pec a ion. The highe he p ice expec a ion, he mo e likely a nega i e ade balance eac ion will ollow. This a ypical esul unde lines he impo - ance o expec a ions. OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.103.5.461 | Gene a ed on 2023-04-04 12:02:50 482 (91) Ul ich K. Schi ko and B. Eckwe 1 3 DL! 3 n : 3 n aplçh Q - 1 - h >0 . Fo he in luence o a change in he expec a ional pa ame e s we cal- cula e (92) (93) (94) (95) 3 l J3 a = 3 l /d b = 3 l /d q = 0 3 HB/3 a = pj ^ < 0 3HB 3 b Pi db db) = PÎ — n pi (1 — a) 3 /3 b 3 ^ 3b~ 2 2 3 HB dq 2 ZZ7| b (¿2 - Z2) < 0 . We ecognize ha he eac ion o he ade balance essen ially depends on he expec a ional pa ame e s, while he labou ma ke si ua ion is no in luenced by expec a ions. In a model wi h an explici empo al p oduc ion s uc u e, which we will p esen in he u u e, o cou se, his conclusion does no hold. 5. Concluding Rema ks Though ou model has a d ama ically simpli ied s uc u e, i became e iden ha expec a ions play a signi ican ole in classi ying he e ec- i e equilib ia and o he esul s o compa a i e s a ics. As a conse- quence o ou speci ica ion o he p oduc ion p ocess mainly p ice expec- a ions a e esponsible o he quali a i ely di e en esul s. Since he p oduc ion and labou demand decisions do no depend on expec a ional pa ame e s in ou model, he in luence o hese pa ame e s shows up in he ade balance only ia he goods demand decisions. E en e y adi ional esul s conce ning he e ec i eness o a de alua ion can be upse by ou simple expec a ional s uc u e. Wage expec a ions would become mo e decisi e, i he p oduc ion p ocess is speci ied di e en ly. We saw ha con a y o Dixi s* esul s e en in he case o ixed ex- change a es he ade balance shows di e en eac ions depending on he kind o expec a ions. The expec a ions conce ning he labou ma ke cons ain s would also play a mo e dis inc i e ole, i we would admi goods ma ke a ioning. On his ques ion wo k is in p og ess. OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.103.5.461 | Gene a ed on 2023-04-04 12:02:50 Simple Tempo a y Equilib ium Model o In e na ional T ade 483 Summa y In a wo pe iod model o empo a y equilib ium wi h quan i y a ioning and in e na ional ade unde ixed exchange a es expec a ions conce ning u u e p ices and cons ain s play a signi ican ole in classi ying he e ec- i e equilib ia and o he esul s o compa a i e s a ics. I he p oduc ion sec o can hold in en o ies (as in ou model), he expec a ional s uc u e in- luences signi ican ly he sales bu no he p oduc ion and labo demand decisions. This su p ising esul depends on he way he p oduc ion p ocess is modelled, e ealing he ole o an a empo ally o mula ed p oduc ion s uc u e. Zusammen assung In einem empo ä en Gleichgewich smodell eine o enen Volkswi scha mi Mengen a ionie ung (bei es en Wechselku sen) spielen E wa ungen be- züglich zukün ige P eise und Mengensch anken bei de E ek i klassi ika- ion de Gleichgewich e und ü die Resul a e de kompa a i en S a ik eine wich ige Rolle. Wenn ü den P oduk ionssek o Lage hal ung zugelassen wi d (wie in unse em Modell), beein luß die E wa ungss uk u signi ikan die Ve kau s- abe nich die P oduk ions- und A bei snach ageen schei- dung. Dieses übe aschende Resul a häng on de A de Modellie ung des P oduk ionsp ozesses ab und o enba die Rolle eine a empo al o mu- lie en P oduk ionss uk u . Re e ences Benassy, J. P. (1975), Neo-Keynesian Disequilib ium Theo y in a Mone a y Economy. Re iew o Economic S udies 42, 503 - 523. Böhm, V. (1980), P eise, Löhne und Beschä igung. Tübingen. Dixi , A. (1978), The Balance o T ade in a Model o Tempo a y Equilib ium wi h Ra ioning. Re iew o Economic S udies 45, 393 - 404. Hildenb and, K. and W. Hildenb and (1978), On Keynesian Equilib ia wi h Unemploymen and Quan i y Ra ioning. Jou nal o Economic Theo y 18, 255 - 277. Malin aud, E. (1977), The Theo y o Unemploymen Reconside ed, Ox o d. Schi ko, U. K. (1981), Zu mik oökonomischen Fundie ung de mak oöko- nomischen Theo ie — ein empo ä es Außenhandelsgleichgewich smodell mi Mengen a ionie ung. Jah buch ü Sozialwissenscha en 32, 241 - 278. — and B. Eckwe (1981), A Two-Coun y Tempo a y Equilib ium Model wi h Quan i y Ra ioning. Diskussionspapie 50, Uni e si ä Augsbu g. —/— (1982), Dynamic Aspec s in a Tempo a y Equilib ium Model o In e - na ional T ade wi h Quan i y Ra ioning. Diskussionspapie 53, Uni e si ä Augsbu g. —/— (1983 b), Local S abili y and Dynamic Aspec s in a Two-Coun y Model wi h Fixed and Flexible Exchange Ra es. Diskussionspapie , Uni e si ä Augsbu g. OPEN ACCESS | Licensed unde CC BY 4.0 | h ps://c ea i ecommons.o g/abou /cclicenses/ DOI h ps://doi.o g/10.3790/schm.103.5.461 | Gene a ed on 2023-04-04 12:02:50