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Unformatted text preview: ,..4uq.:,,;./ ..,.,_.< ‘L W “Ricardian Model: I and II” (1 F301“, 2 Goods, constant unit labor requirements) _
. FREE~TRADE EQUIUBRIUM ' ,_ ’ \
U I ‘ ‘tA‘ [60' ‘r id rom,(a);a r00 Ihs
P‘el’u e 5‘1“" Hum 0’ ome IS 5 0W" 7P0“? m P trade gre illustrated by the slope ol ho b i A' ' the lower diagram (b). Equilibrium lerms o . 
:56 vdvgshEd ”rig for eOCb counlry. The home country produces of E end consumes at B, flue for let Each country gains from trade. eign country produces at E ' and consumes a (D) (a) Food
S L096 0? _ ~  Flue nam
P‘sca: ‘5 —.. .. 3
\ X
n Notice that: II F (1) X; M (Exports of Food by Foreign = Imports of Food by Home) (2) X C = M c (Exports of Clothing by Home = Imports 05 Clothing by Foreign) and since the consumption points in each country are on the free trade pn'ce line that also
includes their production point we have: Forﬂome:
Pc'qc+Pr‘qr=Pc'Dc+pr‘DF
or
pc°(qc—Dc) =pF(DFqP)
01' pc . Xc = pr . Mr Balanced dec: Value of X=Value of M
1
Wm;
. s . D. +P . D‘ or 1— 11— ;_ ,_ nun ,
_ _ _ _ _ _ _ _ _  l_ 1 1— /4 11W (1 Factor, 2 Goods, ()0th unitlabor requirements} . Comparative Advantage
 start with an example from scratch and lets walk Our way through it trying to pick Up stuff at every step  Suppose our information looks like the following Wheat (hours of labor per unit) Tile (hours of labor per unit) The total labor endowment in each country is (ohours. o is to draw the production possibilities frontiers for each country s The ﬁrst thing we want to d
PF from both countries it has the form: 0 the easiest way to do that is by taking the equation for a linear P l (Ecuador)
aurQT + new Qw = L (Argentina) and “1.7 Q‘r + a‘Lw .Q“. 5 L‘ e if we just rearrange these equations. into slope intercept form we get the following equation for Ecuador
(put Tile on the Yaxis) Step 1: Write down the equation for the PPF in slopeintercept form (for both countries)
QT =  (auv/ an) Qw + U 8LT am! (2‘7 =' (a‘LWI 3‘15) Q*w + UV 5‘1; (3‘LW/ a‘u) ‘ so the slope of the PPF is just given by  (aLw/ an) or .
o if we plus the values into this equation we get
and OH = — (2/5) Qv + 20/5 QT= (5/4)Q\. + 20/4 Argentina Q‘LT=' (2/5)Qv + 4 Step 2: Graph The PPFs Tile Tile .
PPF PPF ' / 4 Wheat 10 Wheat Ecuador Argentina (*) Step 3: Opportunity Costs 0 what is the slope of the PPF? What does it represent?  so the slope of the PPF is just given by  (aLW/ an.) = 514 or _ (ath/ 3*“) = 4/5 0 What is the opportunity cost of wheat? 4: Determine comparative advantage Step
‘ Speciﬁcally, since we have the opportunity costs. advantage in Wheat (Argentina)  ’1‘:..’) I 17,...wlm\ we can determine which country has the comparative S_tgp_5_: Community Indifference Curves
Tile . How do we ﬁnd the point of maximum utility in a problem such as >
this? (ﬁnd the tangency to a budget line) ' 3 Wheat 0 We’re going to do the same thing in the context of international trade. Except, instead of making the
community indifference curve tangent to a budget line. ﬁrst we putt
together with the PPF. ‘ Step 5: Autarky relative price ratio and Equilibrium . V a We know that in autarky if (say) Ecuador is consuming both Tile and Wheat that the relative price line
(the GNP line) that it is facing is the same line as the PPF ' a that is to say that the GNP line of the PPF is also Pw / PT . o So in Ecuador, Pw / P1— = 5/4 ‘ So in Argentina, P*w / P*1— = 2/5 Step 6: Introduce Free Trade: Determine production points &CPF .
a given a new world price ratio such as Pw / PT = l. which country will produce each good?  Since Argentina has a comparative advantage in Wheat they will produce only Wheat
' Since Ecuador has a comparative advantage in Tile they will produce only Tile ' They will trade to a point on the world price ratio (the Consumption Possibilities Frontier) Tile Tile CPF 10 / 10 Wheat Argentina (*) a What is the CPF? What does it represent? v What is the CPF when we have autarky? (CPF=PPF)
 What is the CPF when we have free trade? Step 8: Determine export ﬂows and welfare changes
 if Ecuador wants to consume both goods. it must trade some (exports) Tile for (imports) Wheat 0 if Argentina wants to consume both goods, it must trade some (exports) Wheat for (imports) Tile 0 Are the countries better off? Since they can be on a higher indifference curve (more stuff) we say yes Real Wages:
 there are four real wages in each state of the world (autarky and free trade) that we need to worry about 0 Remember the proﬁt maximization rule MPL  P = w, so w/p = MPL Autarky
Ecuador » Argentina
W/szMPLw: 1/5 W*/P*W:MPL*W:1/2
\V/PT:MPLT= 1/4 . W*/P*T:MPL*T: 1/5 0 Remember the proﬁt maximization rule MPL . P : w, so w/p = MPL but this is only for the sector that
actually produces in free trade (Ecuador: Tile, Argentina: Wheat) Free Trade
Ecuador I ALB—"QB
W/Pw:Mp{:w=W/Pw(PT/PT) W*/I) \V=1VIPIJ*W:1/2
=W/P1 (PT [PW ) =(l/4)(l) : 1/4
W/PT = MPer = 1/ 4 W*/P 1 : MPH: = W*/PT (Pw IPw ) =W*/Pw (Pw le) = (l/2)(l) : 1/2 Remark: W/Pw =—M—Pl:w means that because wheat is not produced in Ecuador under free trade , the real wage in
terms of wheat in Ecuador (i.e. W/PW ) is not equal to the Marginal Productivity of labor m the Wheat sector (i.e., MPLW ). . W*/PT =MPE’ET means that because tiles are not produced in Argentina under free trade , the real wage in
) is not equal to the Marginal Productivity of labor m the Tlle sector terms of tile in Argentina (i.e. W*/PT
(i.e., MPL""T ). ' MARK’S RECIPE FOR RICARDO ‘ lSt INFO: ._ unit labor coefﬁcients for home and foreign country (ax, a,, a*,, a*,)
' ' labor supply (L, L*) 1) Using this info you can calculate the milemployment conditions for each country.
These are the equations that say that labor supply=labor demand. Labor supply is'L,
and total labor demand is how much labor is used in each sector. This equation looks
like: L= ai*X+ ay*Y . l 2) From this equation we can draw the PPF. The Y—intercept will be L/ay and the X
intercept will be L/ax. The slope will be a,./ay , which will determine comparative
advantage (CA). How? a) alt/ay is the opportunity cost of producing good X (it equals the number of
_ units of good Y you give up to produce a unit of X)
b) ax/ay IS also equal to px/py (recall that px=A C=w_a,r when a good is produced in
equilibrium). So CA in a good gives that country the lowest relative price of
that good in autarky. ' 3) Comparative advantage determines the pattern of trade. In free trade, countn'es will
export the good in which they have a CA, and import the other one. What price ratio
will they trade? Some pn'ce that is between the autarky relative prices, determined by
the total world demand and total World supply of each good Since we can’t know
what that price is exactly without looking at preferences (which 13 complicated!) We
in Econ 364 usually assume it is some nice number that lets us solve the problem easily. 2'"I INFO: Free Trade Price (p,}/p,.)Fr .4) Suppose we want to calculate by how much a co'untry gains from trade? Then we . need to know how its real wages change. In autarky, we know that real wages, (W/P,
or the amount of real “stuﬁ” we can buy, in temis of either good X or good Y) are
determined by productivity. In particular, whenever a good is produced, W/P=MPL,
so: " ' 3" : MPLx 17‘ because both goods are‘ produced in autarky
1 = MP1,, Pr Notice that here all prices are the aurarky prices. However, in free trade, the import good is no longer produced. So wecan’t use this condition. We need a new condition for the real wage in terms of the import good. But ' we can use the real wage for the export good and the free trade price equation'andcross—
multiply (assume we export X and import Y): ' P: ['7'
—W— =1 £2; because Y is NOT produced in this country
py px py I I ’ the ﬁrst equation is the usual condition that says workers can buy back exactly what they
produced. What does this second equation Say? That the amount workers can buy of
good Y is edual to the amount of good X they get as income (W/px) times the amount that
they can get for good X in terms of good Y on the world market, (p/pp” . 5) Finally, suppose we want to show that, through the mysterious workings of
'_ comparative advantage, countries that trade will always produceone good more
cheaply than the other (that is, even if your technology totally sucks, there will always
be something that you can produce more cheaply than everyone'else—pretty cool
huh?). Anyway, we know that AC=wa, and we know all the a’s, so all we will need
to know is‘what w is in each country. i . Unfortunately, w is a nominal value, and we have no Scale on which to judge nominal
values. All prices are ratios—rates at which goods trade, just as if we had a barter system
with no money—so thereis no such thing as an independent price. But if we set one
price (the numeraire), we. can ﬁgure out all the others through the ratios. 80 we need some new info:
3"1 INFO: Numeraire: px=1 This means that w/p,=w/1=w.  > . But we know w/p, from the step above. So the nominal wage w is equal to whatever we
found that 'w/p', was equal to before. Now wecan plug this wage in for 99th sectors,.to
'ﬁnd average cost. When a Country produces a good, since we know that w=pMPL, will see that
AC=wa =p(MPL)a = p(1/a)a é p. ' That is, price equals average cost. When a country does not produce a good, we will see
that it is because AC>p, so the country can import the good more cheaply than it can produce it itself. _ ~ w ‘ .
_. [£113ler }because X Lsstrll produced under ﬁee trade I Notice that hereall the prices are I]: e Fret Trade prices, although they are not explicitl
' written as FT prices everywhere.) ...
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 Spring '08
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