A political-economic analysis of free-trade agreements: Comment

Transcription

1 A oltcal-economc analyss of free-trade agreements: Comment By ueeng u Abstract: n hs aer n the Amercan Economc Reve, evy (997) develos a oltcal economy model of free-trade agreements (s). He emhaszes that the homothetcty restrcton of the roducton functon assumed for the dfferentated roduct s crucal for hs model. Ths comment shos that ths homothetcty assumton s unnecessary and actually roblematc. t s roblematc n the sense that the model ends u not havng a ell-defned equlbrum. f ths roblem and reork the model usng a dfferent roducton functon th fed cost. Ths comment also onts out that the necessty of the homothetcty restrcton on the roducton functon of dfferentated goods s a common msunderstandng n trade lterature. (JE: F5) ntroducton Phl evy (997) develos a medan voter theory of free-trade agreements (s) and demonstrates that blateral s can undermne oltcal suort for further multlateral trade lberalzaton. Ths nfluental aer has been dely cted n the trade lterature. Hoever, there s a roblem arsng from the homothetcty of the roducton functon assumed for the dfferentated roduct n the model. f the roblem and reork the model usng a dfferent roducton functon. The Problem n evy (997) n hs model, evy assumes that countres dffer only n factor endoments (catal, and labor, ) and n the dstrbuton of factor onersh. Each agent ons one unt of labor and k unt of catal. Hence the total catal s k, and the ncome of agent s rk +, (, 2,...), here r s nterest rate and s age rate. Deartment of Economcs, Fnance and Quanttatve Analyss, Coles School of Busness, ennesa State nversty, 000 Chastan Rd., ennesa, GA E-mal address: lu6@kennesa.edu. thank Devashsh Mtra for hs gudance and encouragement. also thank the edtor, Rchard Rogerson, and to anonymous referees for helful comments. All remanng errors are my on.

2 There are to sectors of roducton. The homogeneous roduct Y (numerare good) s roduced under constant returns to scale th a roducton functon defned as y γ Y µ µ Y Y. The dfferentated roducts are roduced under ncreasng returns to scale (RS). For each varety of, evy assumes a homothetc roducton ( ) functon γ, here > s the ncreasng returns to scale (RS) arameter. Ths roduct functon, hoever, s ncorrect as t leads to ndetermnacy of the otmal roducton of. Gven ths roducton functon, e can obtan the cost functon of the dfferentated goods by solvng Mn C( ), ( ) + r, s.t. γ The resultng searable cost functon s: / C f, here f γ r Hence the average cost and margnal cost can be rtten as: AC( ) f and MC ( ) f (, r ) The roft mamzaton condton (MCMR) and the free-entry condton (AC) are β f and f resectvely. The above to condtons are dfferent only by some arameters and solvng them smultaneously yelds no soluton for. Grahcally e can sho that the to curves arallel to each other and never cross to gve a soluton. t s lkely that evy makes a mstake on the free-entry condton. f he mstakenly rtes the free-entry condton 2

3 as f, he ould end u th a soluton σ, as shon by evy β ( σ ) (997,. 55). The Corrected Poltcal Economy Model of s Assumng a fed cost s the tradton of the monoolstc cometton trade lterature. To correct the roblem n evy s model, assume a roducton functon for the dfferentated good as γ a, here a s the fed cost of roducton measured n the unt of. The cost functons can be easly derved from the roducton functons of and Y as C c r y and C c ( a), here Y Y ) + c Y s the unt cost of the goods Y and c s the margnal cost functon of. Both cost functons are searable. On the consumton sde, agents are assumed to have dentcal utlty functons as α α y, here s the sub-utlty functon for consumtons n, th a Dt- Sence-Stgltz tye CES functonal form. β n β D, β ( ), σ > σ here D s the consumton of varety by an agent; n s the number of varetes; and σ s the elastcty of substtuton beteen varetes. Follong a to-stage budgetng rocess, agent s otmal consumton of Y and are α y ( α ) and D, n here s the relatve rce of n terms of Y. Substtutng these otmal consumtons 3

4 nto the utlty functon for agent yelds α α σ α α α α /( ) ( ) n. Therefore, agent s utlty under relatve to autarky can be rtten as: n n CAE α VE α /( σ ) evy calls the frst to terms on the rght hand sde comaratve advantage effect (CAE) and the last term varety effect (VE). The magntude of the relatve utlty determnes the desrablty of an for the agent. The reduced forms of CAE and VE can be solved from the follong general equlbrum system. (). Producton sde: a). Free entry condton for Y and : [.e., AC( y); AC( ) ] µ µ µ µ (). cy γ Y r µ µ Y ac (2). + c, here c γ r b). Proft mamzaton condton for : [.e., MRMC] (3). β c (). Factor market: full emloyment condtons (4). cy c y + n (5). cy c y + n r r (). Demand sde: utlty mamzaton condtons n the frst stage budgetng (6). n α ( + r) 4

5 (7). y ( α )( + r) The free-entry condton (2) and roft mamzaton condton (3) unquely determne the otmal roducton for each varety of : a( σ ), hch s dfferent from evy s result as shon on age 55 n evy (997). n the follong, sho only the maor stes n solvng the model: (8). bk, r here [ µ + αβ ( µ )] b [ µ + αβ ( µ )] hch says that the rato of returns to labor and catal deends only on the overall catal-labor rato and some arameters. α (9). n f (.), here f (.) γ ( )[ b + b ] aσ hch says that the number of varetes s a functon of total and, the fed cost and some arameters. Hence the varety effect can be shon as: α α n σ (0). σ VE [( + λ ) ( + λ ) ] n here λ ; λ are the ercentage ncreases n and hen a country moves from autarky to an ntegrated economy resultng from an. Equaton (0) above s same as equaton (2) on age 55 n evy (997). (). ρ b + ϕ b + ρ 5

6 k / k / here ρ andϕ. ρ > ( ρ <) f agent s k / k / relatvely catal-rch (catal-oo under autarky. ϕ > (ϕ <) f artner country s more catal-abundant (labor-abundant). (2). ϕ (3). µ ϕ Combnng ()-(3) yelds the comaratve advantage effect as: (4). CAE α ρ b + ϕ ϕ b + ρ [ α + ( α ) µ ] [ µ + αβ ( µ )] here b s a functon of the arameters. Equaton (4) above s [ µ + αβ ( µ )] smlar to equaton (5) on age 56 n evy [997]. The arameters b and, hoever, are dfferent. Conclusons t s fortunate that the mstake evy makes on the free-entry condton hels hm go through the model. Otherse, th the homothetc roducton functon, the model ould not have a ell-defned equlbrum. Ths comment serves to correct the mstake and comlete ths dely cted oltcal economy model of s. t also shos that homothetcty assumton of the Cobb-Douglas roducton functon for dfferentated goods s unnecessary, and actually, roblematc. 6

7 Ths correcton onts out a common msunderstandng on the monoolstc cometton models n trade lterature. As emhaszed n footnote 3 on age 54 n evy (997), The results do not deend on the Cobb-Douglas form of the roducton functons. They do deend, hoever, on the assumton of homothetcty n roducton. evy (997) s not alone n ths regard. For eamle, even n the classc book by Dt and Norman (980), they note on age 285, Ths result [equaton (55)] deends crucally on homethetcty n roducton. Although ths concluson ll hold for certan forms of homothetc roducton functons, as shon by Dt and Norman (980, ), t can not carry over to the Cobb-Douglas roducton. Gven the oularty of evy s aer and the mortance of modelng dfferentated goods under monoolstc cometton, beleve that the correcton of ths roblem s nontrval. Reference Dt, Avnash. and Vctor D. Norman Theory of nternatonal Trade. Cambrdge nversty Press. evy, Phl A oltcal-economc analyss of free-trade agreements. Amercan Economc Reve 87 (4),