Factor price equilisation argues that goods trade acts as substitute for factor; ? The increasing demand for capital intensive commodity increase the
Factor Price Equalisation Theorem ? Factor Prices under Autarky: ? In figure 1, ? is contract curve for country I and ? ? is contract curve
This paper extends the technique of integrated equilibrium analysis to con sider a trading world with unemployment due to a wage floor Unlike previous
This paper examines the status of factor price equalization (FPE) as a The formal proof of FPE is based on a neoclassical production structure with two
This paper examines the status of factor price equalization (FPE) as a scienrific hypothesis Every college :etu&nt af inlemational economics is exposed to
factor price equalization theorem was the first rigorous proof that trade trading entities would equalize factor prices has never been open to
In view of constant returns assumption, Ram Singh: (DSE) Factor Price Equalization Lecture 13 2 / 16 Page 3 International Trade: Basic Set-up II the
FULL OR PARTIAL FACTOR PRICE EQUALISATION? The present paper is concerned primarily with one aspect of this theorem-namely, the assertion that, while free
theorem, (2) to expand upon its intuitive demonstration, (3) to 1 "International Trade and the Equalisation of Factor Prices," EcoNoMIc JoURNAL, Vol
The Factor Price Equalization Theorem states that under the assumptions, free trade will make factor prices equal in the participating countries Since the
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Factor Price Equalization and Stolper-Samuelson
Theorem
Ram Singh
Microeconomic Theory
Lecture 13
Ram Singh: (DSE)Factor Price EqualizationLecture 13 1 / 16
International Trade: Basic Set-upI
Optional Readings: MWG, Stolper and Samuelson, (1941), Review of Economic Studies; and Samuelson, P. A. (1948), Economic JournalConsider a 'small" open economy
Two goods are produced; food and cloth/car,fandcTwo FOPs are used; labour and capital,landtProduction technology; constant returns to scale (?)
Production functions; strictly quasi-concave (?)
Food:yf=yf(zfl;zft)
Car/cloth:yc=yc(zcl;zct)
In view of constant returns assumption,
Ram Singh: (DSE)Factor Price EqualizationLecture 13 2 / 16
International Trade: Basic Set-upII
the optimum mix of inputs (cost minimizing combination of FOPs) does
not depend on the level of operation.Therefore, to search for optimum mix of FOPs, we can take output level
to be one:That is, we can focus on the following optimization:
Given vector of factor prices(w;r),
minfw^aj l+r^aj tg(1) y j(^aj l;^aj t) =1; wherej=f;c. In view of the assumption onyj, (1) has a unique solution. Leta fl;aftsolve (1) for food sectora cl;actsolve (1) for car/cloth sectorRam Singh: (DSE)Factor Price EqualizationLecture 13 3 / 16
International Trade: Basic Set-upIII
That is,
1=yf(afl;aft)
1=yc(acl;act)
Clearly, forj=f;cwe have
a fl=zfl(w=r) a ft=zft(w=r) a cl=zcl(w=r) a ct=zct(w=r)Ram Singh: (DSE)Factor Price EqualizationLecture 13 4 / 16
International Trade: Basic Set-upIV
Now, the production process is characterized by:
a fl=zfl(w=r)(2) a ft=zft(w=r)(3) a cl=zcl(w=r)(4) a ct=zct(w=r)(5) l=yfafl+ycacl=yfzfl(w=r) +yczcl(w=r)(6) t=yfaft+ycact=yfzft(w=r) +yczct(w=r)(7) p f=wafl+raft=wzfl(w=r) +rzft(w=r)(8) p c=wacl+ract=wzcl(w=r) +rzct(w=r)(9)Ram Singh: (DSE)Factor Price EqualizationLecture 13 5 / 16
Factor Intensity
Definition
Food sector is labour intensive if,
(8(w;r)>>(0;0))afla ft>acla ctAssumption Suppose for all possible pair of input prices we have a fla ft>acla ctorafla ft
>(0;0))afla ft>acla ct ;i:e:;(actafl aftacl)>0Ram Singh: (DSE)Factor Price EqualizationLecture 13 6 / 16 Factor Prices Across CountriesI
AssumeThere is flow of factors within an economy
No trade in factors between economies
Production technology is the same across countries There is free flow of goods across countries
So, the output prices are the same across countries then,Free trade is a substitute for free flow of FOP. Ram Singh: (DSE)Factor Price EqualizationLecture 13 7 / 16 Factor Prices Across CountriesII
Theorem
Factor Price Equalization Theorem. Suppose, the factor intensity assumption holds. For any given output price vector and technology, the factor prices will be the same across countries.Let,s=wr . So, p=pfp c=wafl+raftwa cl+ract = safl+aftsa cl+act(10) p=g(s)(11) Sign of
dpds =sign of(actafl aftacl)>0:Ram Singh: (DSE)Factor Price EqualizationLecture 13 8 / 16 Factor Prices Across CountriesIII
Thereforeg0(s)>0. Lets=h(p), where
h() =g 1(:) Clearly,h0()>0Question
What is theceteris paribuseffect of change in factor endowments on output levels?What is theceteris paribuseffect of change in output prices on factor prices? Ram Singh: (DSE)Factor Price EqualizationLecture 13 9 / 16 Stolper-Samuelson TheoremI
Theorem
Stolper-Samuelson Theorem. Given the factor intensity assumption, an increase in relative price of c leads to increase in relative price of t, and vice-versa.Let fl=waf lp f, the share of labour in food sector ft=raf tp f, the share of capital in food sector cl=wac lp c, the share of labour in cloth sector ct=rac tp c, the share of capital in cloth sectorRam Singh: (DSE)Factor Price EqualizationLecture 13 10 / 16 Stolper-Samuelson TheoremII
Clearly,
p fyf(=1) =wafl+raft y f(=1) =waflp f+raftp f fl+ft=1 andcl+ct=1. Recall(actafl aftacl)>0. So, we have
w:rp f:pc(actafl aftacl) =w:aflp fr:actp c w:aclp cr:aftp f =flct ftct =fl(1 cl) (1 fl)cl =fl cl>0:(12)Ram Singh: (DSE)Factor Price EqualizationLecture 13 11 / 16 Stolper-Samuelson TheoremIII
That is, the share oflis higher inlintensive sector, and vice-versa. The least cost condition gives us wda j l+rdaj t=0;i:e:;(13) wa j ldaj la j l+raj ldaj ta j l=0;i:e:;(14) il^ail+it^ait=0;(15) where ^ail=dai la il, etc. Differentiating (8) and (9) we get
dp f=afldw+aftdr+wdafl+rdaft(16) dp c=acldw+actdr+wdacl+rdact(17) In view of (13), we get
Ram Singh: (DSE)Factor Price EqualizationLecture 13 12 / 16 Stolper-Samuelson TheoremIV
dp f=afldw+aftdr dp c=acldw+actdr:That is, dp fp f=afldwp f+aftdrp f=aflwp fdww +aftrp fdrr dp cp c=acldwp c+actdrp c=aclwp cdww +actrp cdrr : That is,
^ pf=fl^w+ft^r ^ pc=cl^w+ct^r:Ram Singh: (DSE)Factor Price EqualizationLecture 13 13 / 16 Stolper-Samuelson TheoremV
That is,
^ pc ^pf= (fl cl)(^r ^w)(18) That is,
^ r ^w=1 (^pc ^pf)(19) where=fl cl<1.Theorem Given the factor intensity assumption, an increase in relative price of good c leads to more than proportionate increase in relative price of t, and vice-versa. Ram Singh: (DSE)Factor Price EqualizationLecture 13 14 / 16 Effect of Labour SupplyI
Differentiating (6) and (7) we get
d l=afldyf+acldyc(20) d t=aftdyf+actdyc(21) Note, a fldyf l=dyfy fa flyf l = ^yffl; wherefl=af lyf l. So, ^ l=dl l=^yffl+^yccl(22) ^ t=dt t=^yfft+^ycct(23)Ram Singh: (DSE)Factor Price EqualizationLecture 13 15 / 16 Effect of Labour SupplyII
Clearly,
fl+cl=1 ft+ct=1 Now, (22) and (23) will give us
^ yf ^yc=1 (^l ^t) where=fl ft>0. So, an increase in labour force leads torelative increase in food production relative decrease in food price relative decrease in relative price of labour (wage) Ram Singh: (DSE)Factor Price EqualizationLecture 13 16 / 16