ABSTRACT
Extensive cultivation models When the demand for agricultural goods increases, the extension of cultivation on ODQGVRIWKHVDPHJUDGHVHWVQRVLJQL¿FDQWHFRQRPLFSUREOHPWKHVDPHPDUJLQDO PHWKRGVDUHXVHGDQGQRFKDQJHVLQSULFHVZDJHVRUUHQWVRFFXU$OLPLWLVUHDFKHG ZKHQWKHFRUUHVSRQGLQJODQGEHFRPHVVFDUFH7KHQWKHSULFHVRIWKHDJULFXOWXUDO SURGXFWV ULVHDQGFXOWLYDWLRQ LVH[WHQGHG WRDQHZODQGRUDOWHUQDWLYHO\PRUH LQWHQVLYHPHWKRGVDUHVXEVWLWXWHGIRUWKHSUHVHQWRQHVRQWKHVDPHODQG7RLVRODWH H[WHQVLYHFXOWLYDWLRQSURSHUZHDVVXPHDXQLTXHPHWKRGRIFXOWLYDWLRQRQHDFK W\SHRIODQGEHFDXVHRIWKDWRQHWRRQHFRUUHVSRQGHQFHLWLVLQGLIIHUHQWWRUHIHU WR D ODQG RU DQ DJULFXOWXUDO PHWKRG 6UDIID DUJXHG WKDW WKH RUGHU RI FXOWLYDWLRQ LVQRW DQDWXUDOSKHQRPHQRQDQGPD\FKDQJHZLWK WKH H[RJHQRXV GLVWULEXWLRQYDULDEOH/HWWKHUDWHRISUR¿WEHJLYHQ3RVW6UDI¿DQVWXGLHVKDYH VKRZQ WKDW WKH H[WHQVLRQ RI FXOWLYDWLRQ IROORZV D VLPSOH UXOH WKH ODQGV DUH FXOWLYDWHGLQWKHRUGHURIWKHGHFUHDVLQJUHDOZDJHVWKH\\LHOGIRUD]HURUHQW6LQFH WKDWRUGHU LVZHOO GH¿QHG WKHUH H[LVWV DXQLTXH HTXLOLEULXP IRU HDFKGHPDQG EDVNHWÀXNHVDSDUW7KHHTXLOLEULXPLVFKDUDFWHUL]HGRQWKHSK\VLFDOVLGHE\D XQLTXHVHWRIFXOWLYDWHGODQGVDQGRQWKHYDOXHVLGHE\DXQLTXHDVVRFLDWHGVHWRI SULFHVZDJHVDQGUHQWV 7KH VWDQGDUG WKHRU\ RI H[WHQVLYH FXOWLYDWLRQ VXPPDUL]HG DERYH DGPLWV
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A generic equality &RQVLGHUIRUDZKLOHDPXOWLVHFWRUPRGHOZLWKnDJULFXOWXUDORULQGXVWULDOFRP PRGLWLHV7KHPRGHOLVRIWKHH[WHQVLYHW\SHZKHQDXQLTXHPHWKRGRIFXOWLYDWLRQ LVDYDLODEOHRQHDFKW\SHRIODQG7KH¿QDOGHPDQGYHFWRUd admits n degrees of IUHHGRP)OXNHVDSDUWVOLJKWFKDQJHVLQGHPDQGDUHPHWE\VOLJKWFKDQJHVLQWKH DFWLYLW\OHYHOVRIWKHRSHUDWHGWHFKQLTXHVEHWKH\PDUJLQDODJULFXOWXUDOPHWKRGV RULQGXVWULDOPHWKRGV/HWn'EHWKHWRWDOQXPEHURIPDUJLQDOODQGVDQGRSHUDWHG LQGXVWULDOPHWKRGV7KHSK\VLFDODGDSWDWLRQRIWKHQHWSURGXFWWRGHPDQGUHTXLUHV that n'EHDWOHDVWHTXDOWRn&RQYHUVHO\VLQFHDSULFHHTXDWLRQZLWKD]HURUHQWLV DVVRFLDWHG ZLWK HDFKPDUJLQDO PHWKRG DQG HDFK RSHUDWHG LQGXVWULDO PHWKRG n' does not exceed nLQRUGHUWRDYRLGDQRYHUGHWHUPLQDWLRQRISULFHV7KHUHIRUH WKHHTXDOLW\
QXPEHURIPDUJLQDOODQGVRSHUDWHGLQGXVWULDOPHWKRGV QXPEHURIJRRGV
KROGVJHQHULFDOO\IRUORQJWHUPHTXLOLEULD
Possibility of multiple Ricardian equilibria :HFRQVLGHUPRUHVSHFL¿FDOO\ELVHFWRUPRGHOVn ZLWKDQDJULFXOWXUDOVHFWRU SURGXFLQJFRUQFRPSOHPHQWHGHLWKHUE\DQLQGXVWULDOVHFWRUSURGXFLQJLURQRUD VHFRQGDJULFXOWXUDOVHFWRUSURGXFLQJULFH6HYHUDOW\SHVRIODQGVH[LVWEXWHDFK W\SHRIODQGDGPLWVDXQLTXHPHWKRGRIFXOWLYDWLRQLQSDUWLFXODUWKHFRUQODQGV GLIIHUIURPWKHULFHODQGVLIDQ\$VLJQL¿FDQWGLIIHUHQFHEHWZHHQWKHWZRIDPLOLHV RIPRGHOVLV WKDW LQDORQJWHUPHTXLOLEULXPULFHFDQEHSURGXFHGE\VHYHUDO PHWKRGVVLPXOWDQHRXVO\ ZLWKKRZHYHUDXQLTXHPDUJLQDO ULFHPHWKRG7KH VHFRQGIDPLO\RIPRGHOVLVWKHUHIRUHPRUHFRPSOH[,QERWKFDVHVRXUUHFRXUVH WRIRUPDOL]DWLRQLVPLQLPXPRQO\WKHVLJQRIWKHSRWHQWLDOUHQWPDWWHUVLILWLV SRVLWLYHWKHFRUUHVSRQGLQJODQGLVWRWDOO\FXOWLYDWHGLILWLVQHJDWLYHWKDWODQGLV QRWFXOWLYDWHGDWDOOLWLV]HURRQWKHPDUJLQDOODQGVDQGWKHVWDQGDUGSURSHUWLHV RIVLQJOHSURGXFWV\VWHPVZLWKRXWODQGVVXI¿FHWRFRQFOXGH ,QWKLVFKDSWHUWKHUDWHRISUR¿WLVJLYHQSRVLWLYHDQGVPDOOHQRXJKWRHQVXUH
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Property 1
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Proof
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Property 2
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Proof
/HWWKHLURQPHWKRGEHVSHFL¿HG%\3URSHUW\DPDUJLQDOFRUQODQGi associated ZLWK LW GH¿QHV D SULFHDQGZDJH YHFWRU $QRWKHU ODQG j LV XOWUDPDUJLQDO DQGWKHUHIRUHLVFXOWLYDWHGDIWHUODQGiZKHQGHPDQGLQFUHDVHVLIPHWKRGj is PRUHFRVWO\WKDQPHWKRGi7KHWKHRU\RIFKRLFHRIPHWKRGVHODERUDWHGE\6UDIID IRULQGXVWULDOPHWKRGVDSSOLHVWKHUHDOZDJHDVVRFLDWHGZLWKWKHXVHRIPHWKRGi LV KLJKHU WKDQ WKDW DVVRFLDWHG ZLWK PHWKRG j +HQFH WKH UXOH RQ WKH RUGHU RIFXOWLYDWLRQ
Property 3
7KHRUGHURIFXOWLYDWLRQRIODQGVPD\FKDQJHZLWKWKHRSHUDWHGLURQPHWKRG
Proof
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WKDW WKH FRUQPHWKRG LV FKHDSHU WKDQPHWKRGƍZKDWHYHU WKH LURQPHWKRG %\FRQWUDVWWKHUHODWLYHFKHDSQHVVRIWKHLURQPHWKRGVDQGƍGHSHQGVRQWKH PDUJLQDOFRUQODQG
Example 1
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First solution
0HWKRGTUFRUQWLURQODERXUDFUHVODQGĺTU corn
0HWKRGTUFRUQWLURQODERXUĺWLURQ 7KLVVROXWLRQLVVXVWDLQHGE\WKHSULFHYHFWRU corn ironp p p w 0HWKRGVƍ and 2ƍGHVFULEHGEHORZSD\H[WUDFRVWVDW WKHVHSULFHVDQGDUHQRW RSHUDWHG
Second solution
0HWKRGTUFRUQWLURQODERXUDFUHVODQGĺTU corn
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IDPLO\RIPRGHOVZHFRQVLGHUZLWKWZRDJULFXOWXUDOJRRGVLWVXI¿FHVWRSURFHHG WRDQRPLQDOFKDQJHRIµLURQ¶LQWRµULFH¶WRLQWURGXFHGDWDUHODWLYHWRWKHDUHDVRI ULFHODQGVSHUTXDUWHUSURGXFHGDQGWRFKRRVHWKHDYDLODEOHDUHDVRIODQGVLQRUGHU WKDWLQHDFKRIERWKHTXLOLEULDQRULFHODQGLVIXOO\FXOWLYDWHGVRWKDWWKHUHQWVRQ WKHVHODQGVDUH]HUR $V DQ DVLGH RI WKDW VWXG\ LW WXUQV RXW WKDW WKH V\PPHWU\ LQ WKH FRQGLWLRQV
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The notion of an external equilibrium 7KH HTXLOLEULD VWXGLHG LQ WKH SUHYLRXV VHFWLRQ LQYROYH RQH PDUJLQDO FRUQ method DQGHLWKHURQHLQGXVWULDOPHWKRGRURQHPDUJLQDOULFHPHWKRGWKHVHDUH µQRUPDO¶RUµ5LFDUGLDQ¶HTXLOLEULD)RUn JRRGVWKHHTXDOLW\LVWKHQ UHDGDV %XWRQHPD\QRWLFHWKDWIRUn HTXDOLW\DOORZVIRU DQRWKHU FRPELQDWLRQZLWK QRPDUJLQDO ODQG DQG WKH FRH[LVWHQFH RI WZR LURQ PHWKRGV 2/HWXV H[SODLQZKHQDQGZK\ WKLV W\SHRI HTXLOLEULXP RFFXUV
Example 2
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HTXLOLEULXPHDFKIHDVLEOH OHYHORIGHPDQG LVPHW LQDXQLTXHZD\%XW OHWXV PRGLI\WKHH[DPSOHDQGUHSODFHPHWKRGƍE\DQRWKHUƍƍVXFKWKDWWKHDERYH PHQWLRQHG YDOXH FRQGLWLRQV IRU H[WHUQDO UHQW DUH VWLOO PHW EXW WKH SK\VLFDO FRQGLWLRQVDUHUHYHUVHGZHVXSSRVHQRZWKDWPHWKRGƍƍLVlessHI¿FLHQWWKDQIRU WKHWUDQVIRUPDWLRQRIFRUQLQWRLURQ7KHVHFRQGLWLRQVZKLFKGH¿QHWKHFDVHRI µUHJUHVVLYHH[WHUQDOUHQW¶JHQHUDWHDPXOWLSOLFLW\RIHTXLOLEULDD¿UVWHTXLOLEULXP RIWKH5LFDUGLDQW\SHLVREWDLQHGE\FXOWLYDWLQJODQGSDUWO\DQGXVLQJWKHWKHQ FKHDSHUPHWKRG WR SURGXFH LURQ D VHFRQG HTXLOLEULXPRI WKH H[WHUQDO W\SH UHVXOWVIURPµRYHUÀRZLQJ¶ODQGLVWRWDOO\FXOWLYDWHGEXWWKHVXUSOXVRIFRUQLV SDUWO\VSRLOWEHFDXVHLWLVWUDQVIRUPHGLQWRLURQSDUWO\E\PHDQVRIPHWKRGDQG SDUWO\E\PHDQVRIWKHOHVVHI¿FLHQWPHWKRGƍƍ$QXPHULFDOH[DPSOHZLWKRQH FRUQODQGDQGWZRLURQPHWKRGVDQGƍƍLV
Example 3
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First solution (Ricardian equilibrium)
0HWKRGTUFRUQWLURQODERXUDFUHVODQGĺTUFRUQ 0HWKRGTUFRUQWLURQODERXUĺWLURQ 7KHSULFHVDUH p w $WWKHVHSULFHVPHWKRGƍƍGH¿QHGEHORZLV PRUHFRVWO\WKDQPHWKRG
Second solution (regressive external equilibrium)
0HWKRGTUFRUQWLURQODERXUDFUHVODQGĺTUFRUQ 0HWKRGTUFRUQWLURQODERXUĺWLURQ 0HWKRGƍƍTUFRUQODERXUĺWLURQ 3RVLWLYHSULFHVpƍ DUHGHWHUPLQHGE\WKHWZRLURQPHWKRGV$WWKHVHSULFHVWKHFRUQODQG\LHOGVDSRVLWLYHUHQWDQGLVIXOO\FXOWLYDWHG7KHUDWHRIWUDQVIRUPRI FRUQLQWRLURQIRUPHWKRGƍƍTUFRUQoWLURQLVVPDOOHUWKDQIRUPHWKRG TUFRUQoWLURQ
Algebraic characterization of external rent ,QWKLVPRUHWHFKQLFDOVHFWLRQZHSURYLGHDQDOJHEUDLFFKDUDFWHUL]DWLRQRIH[WHUQDO UHQWLQDELVHFWRUFRUQ±LURQPRGHOZLWKRQHPHWKRGRIFXOWLYDWLRQIRUFRUQDQG WZRLQGXVWULDOPHWKRGVIRU LURQ ,W LV WKHUHIRUHDJHQHUDOL]DWLRQRIH[DPSOHV H[WHUQDOSURJUHVVLYHHTXLOLEULXPDQGH[WHUQDOUHJUHVVLYHHTXLOLEULXP /HW i i ia b l EHWKHFRUQLURQDQGODERXUFRHI¿FLHQWVRIPHWKRGii ƍ)
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comes IURP WKH LQVHUWLRQ RI D QHZPHWKRGZKLFK WXUQV RXW WR EH LQHI¿FLHQW (Bidard, 2010). The similarity suggests a research programme on more general land models.
