Heckscher-Ohlin Model (focus on 3 diagrams, magnification effect following increase in rel wages, autarky to trade diags, FPE diag (production choice+endowments parallelogram + cone) Flashcards
So what does HO theory say trade occurs due to
Differences in relative factor endowments.
I.e produce goods in which are intensive in the FoP the country is in abundance of.
Factor price equalisation theorem
Trade equalises the real return (wages and rents) across countries.
(Convergence of factor prices)
Stolper-Samuelson theorem
Trade increases the real return (wage or rent) to a country’s relatively abundant factor
But reduces real return to the scarce factor
(Since labour abundant country exports labour-intensive goods. Trade will increase demand for these goods, increasing demand for labour and correspondly wage)
Rybczynski
An increase in a country‘s endowments of one factor will increase output of the good which uses that factor intensively, and reduce output of the other good
(e.g an increase in labour=produce more labour-intensive goods)
(Used in outsourcing in a small country. Explains why wages rise for the domestic country low skill labour. Because outsourcing means there is now more low skill labour available (acts as an increased endowment of lowskill workers) and so sector that uses low-skill labour expands, and increases output.
Assumptions for the HO Model:
2 countries
2 goods
2 factors of production
Production functions identical and CRTS
Factors are mobile between industries (not countries
Factors are homogenous
2 other main key assumptions
Goods differ in factor requirements with no factor intensity reversals (i.e one is capital intensive, one is labour intensive)
Countries differ in relative factor endowments
Production functions
B) We assume marginal product of factors are positive, (adding an additional FOP increases output) … this means what?
X = X (Kx , Lx)
Y = Y (Ky, Ly)
I.e X requires capital K and labour L
B) since MP>0 (positive), means diminishing returns exist.
E.g if capital increases, K/L ratio increases and there is more capital per worker, so dismissing returns to the capital)
VMP (value of marginal product expression)
B) The ratio of marginal products (XL/XK) of labour to capital is equal to what?
C) What is this equation?)
Px x XL = w
Px x XK = r
(Price of product x Marginal product) = VMP
B) The wage to rental rate!
XL/XK = w/r
C) This is the MRTS = XL/Xk = -w/r (isoquant slope=isocost slope) where efficent production (cost minimisation) takes place
Isocost equation
wL + rk = C
Rearrange to make k subject
k = C/r + w/r L
Isocost slope is w/r
Imp:
Condition for efficient factor allocation
B) how to draw efficient production graph pg14 figure 9, with NO FACTOR INTENSITY REVERSALS
w/r = XL/XK = Yl/Yk
Isocost slope = isoquant slope of X = isoquant slope of Y
B) with no FIR
- only one factor intensity line for each good ,
- only one isocost line for both goods
How to draw efficient production WITH FACTOR INTENSITY REVERSALS
With FIR, each good changes their factor intensity i.e X becomes more labour intensive, Y more k intensive.
Also means more than 1 isocost.
General equilibrium 6 equations
2 production functions
X = X(Kx, Lx)
Y = Y(Ky, Ly)
2 full employment conditions
Kbar = Kx + Ky
Lbar = Lx + Ly
2 factor price conditions (factor prices = VMP)
w = XL = PYl
r = Xk = PYk
PYl
PYk are VMPs
Assume we
choose good X as numeraire so Px = 1 Py = P
kx>ky
Cost min diagram pg 14 figure 9
(Tip: draw both factor intensity lines lower down, draw them further apart for the FPE/parallelogram production decisions)
Kx>Ky so Y’s factor intensity line is lower/flatter
Imp: What if we increase RELATIVE wages.
Explain the effect to both cost minimisation diagrams on previous slide
Cost minimisation for X diagram:
Isocost: gets steeper (so isocost can produce less L as more expensive, but also sees an increase in K since capital is relatively cheaper so isocost extends on Y axis)
Factor intensity line: steeper (since using K/L, K increases; since relatively cheaper now). (NO NEW ISOCOST CURVE, JUST MAKE SURE NEW ISOQUANT IS TANGENT TO THE SAME ISOCOST)
Cost minimisation for Y diagram: since Y was labour-intensive, we produce less of it! so
Unlike X, we get a new isoquant tangent to new isocost, to represent less output of Y is now produced
So since relative wages has reduced output of Y (the relatively labour-intensive good) , what happens to the price of Y and why
Price of Y increases (since producing less)
(So good Y uses increases its capital intensity, but also reduces its output since it is still relatively more labour intensive)
Imp: Key result we found of an increase in relative factor prices
(e.g relative wage increase in this instance)
B) key consideration
An increase in the relative factor price will increase the COMMODITY PRICE of the good that uses that factor price intensively
THUS COMMODITY/FACTOR PRICE: POSITIVE REL
B) factor price changes must change by a larger amount than commodity price to maintain equilibirum - Magnification effect later!
Recall condition for efficent factor allocation
w/r = Xl/Xk = Yl/Yk
Wage-rental ratio (isocost slope) = slope of X’s isoquant = slope of Y’s isoquant
(pg 11 figure 6 diagram
Imp: How is there a magnification effect in addition following an increase in relative wages?
Using efficient factor allocaiton equation, as relative wages rise (w/r) , the ratio of marginal products also rise Xl/Xk = Yl/Yk.
P = W/XL (MPL) and so if XL increases, wage must increase by more to maintain equilibrium
Imp:
What happens to rental rates during this upon a increase in relative wages.
see pg 20 to see it
Rental rates fall!
As to consume previous amount X, a’ units of capital is needed. (Now need more of K, which shows a fall in marginal product!!!)
Px = r/MPK (Xk) so if MPK (Xk) falls, r mustve fallen too!
Final magnification effect expression
b) what does this prove
w^>Py^>P^x>r
++ > + > 0 > -
P^x is unchanged following an increase in relative wages
b) Proves Stolper Samuelson holds!
Effect on consumption
b) show final magnification effect diagram pg 20
can consume more of both
(despite price of y increasing, remember factor price w increases by more and so can get more of either good)
b) to represent increase consumption at the new wage/rent ratio, draw parallel line outwards and draw new IC
In autarky , what is the autarky equilibrium equation.
b) draw autarky diagram pg 22
(hint: no longer axis’ K and L, now good X and Y)
px/py = MRS = MRT
Price ratio = marginal rate of sub (indifference curve slope) = marginal rate of transformation (PPF slope)
b) we need a
PPF: shows combinations of good X/Y produced with given resources.
Price ratio: -px/py
Community indifferene curves
(equilibrium is where the indifference curve and PPF are tangent)
Important: Given Ka>Kb, what would this mean for PPFs in the autarky equilibrium?
B) draw it (pg 24)
PPFs would be biased
B)
Autarky equilibirum with 2 countries pg 25
Hint (In this relative prices differ: what do we need for the diagram then)
B) how do relative prices differ? Intuition
As relative prices differ we need 2 price slopes.
B) For each country, the price of the good that requires the relatively abundant factor in that country will be cheaper. ]
(Ka>Kb: country A is capital abundant, thus good X (Px) is cheaper!
Hence, price ratio (-Px/Py) is flatter since Px lower.
Country B’s price ratio is steeper for same intuition (price of good Y is cheaper)
That was autarky. Now look at free trade.
What will residents of country A and B think and respond?
Country A residents see that good Y is cheaper in country B (since Ka>Kb)
Country B see good X is cheaper in country A (since Ka>Kb)
Thus A imports good Y, and B imports good X, until prices are equalised. Each country will produce good that uses their relatively abundant factor (specialisation - not fully tho)
Free trade diagram pg 27 and 28
How does it change from autarky equilibrium
Since prices equalise. Price ratios must have the same gradient/slope!
Name them both Pw (since world price)
PPFs same as autarky (PPFb can produce more Y, PPFa can produce more X)
Indifference curves: draw them in the middle of the price ratios (figure 21 pg 28)
Add imports and exports flows between each country (pg 28 figure 22)
(This is the final HO diagram!!!)
make sure the connecting point is the point of tangency between indifference curve and each price ratio (Pw)
final HO diagram as it shows countries export the good that requires the relatively abundant factor and import the one that is made relatively cheaper by the other country.
When does HO fail to hold (3)
If countries have a strong bias towards the good produced using its relatively abundant factor (consume domestically and not export)
if there is factor intensity reversal
if there is different technology for one of the goods
Explain how different technology for one of the goods can violate HO
A country with superior technology for a good may specialise in that good regardless of its relative factor endowment (even if not abundant in the factor)
Explanation for first violation of HO:
When a country’s has a strong bias towards the good requiring the relatively abundant factor (that they should export in theory, but don’t!)
They import the good they have a comparative advantage in!
Country A (capital abundant) so SHOULD export good X……..
however it has a strong preference towards good X too, which means domestic consumption for good X is strong, and may not export good X. Further if demand for good X exceeds their domestic supply, contrary to HO, they will also import good X (not Y as in the theorem).
Bias preference diagram pg 31
Hint: this is the one with only one Pw (autarky to FT had 2 Parallel Pw’s for each PPF
Y axis is Y
X axis is X
Indifference curve of B: high up
since B wants to consume a lot of Y (which is also what they have a comparative advantage in and produce
Indifference curve of A: far across
since consume a lot of X (same explanation)
Factor price equalisation theorem - factor prices converge so long as what…
AS LONG AS both countries produce both goods (they produce both if endowment is in cone of diversification)
Imp: Illustrating FPE
Draw Efficient production diagram pg 33 (hint: draw factor intensity lines further apart)
b) add country endowments pg34
c) draw inefficieint production
X more capital intensive. Y more labour
b) since A is capital abundant, endowment line is biased towards capital, vice versa for B’s endowment line.
c) they produce at Ea and Eb
for X: produce efficiently (along Kx) until no capital endowment left. We see there is still idle labour to use reach across to Ea
for Y: produce efficiently (along Ky) until no labour endowment left. We see there is still idle capital to use reach across to Eb
d) they dont want to have to do this… efficient production should mean they switch goods to produce (paralellogram…)
Imp: Production decision in country A (pg 35)
What 2 options do they get? (Just do Ea for now)
b) what result/shape do we get? and identify how much of X and Y is produced in country A (pg 36 is good)
See diagram: they produce X, but realise they dont have enough capital per labour to continue producing X, so switch producion to Y. (using Ky K/L technique and thus should be parellel to Ky!)
OR
they produce Y and realise they dont have enough labour per capital to continue producing Y, so switch productionn to good X. (using Kx K/L technique so should be parallel to Kx)
b) we get a parallelogram - country A produces relatively more X. draw 2 isoquants through point where production changed for each side.
Imp: Same intuition for Country B’s production decision.
Starts producing Y, then doesnt have enough labour per capital so switches to produce X!
Or
Starts producing X, then not enough capital per labour so switches to Y.
Overall: produces relatively more Y (since endowed with labour)
Now can draw the combined production for A and B pg 39
Parallelograms overlap
Both countries produce X and Y, country A produces relatively more X, country B produces relatively more Y
Imp: Pg 40 just repeats diagram of inefficient production. When is that
(Note the diagram is just for A)
For country A: When you go up fully to Kx, and then use idle labour to keep producing X.
For country B: When you go as far as you can up to Ky, but no more labour so have to use idle capital to continue producing Y.
(We’ve seen previously, for efficient production you should switch production to the other good)
Cone of diversification pg 32. Where is the cone up to
And what does it mean/prove FPE
It is up to the top of Kx and Ky:
If endowment points lie within the cone of diversification, Ky and Ky will be the most efficient techniques (both countries produce both goods by switching production when they run out of producing one good efficiently) meaning factor prices equalise!!
So how does cone of diversification prove factor prices equalise
Because if endowment points lie within the cone, it means Kx and Ky are most efficient techniques, so both countries produce both goods (switching occurs once not enough capital per labour etc) allowing factor prices to equalise.
What if endowments fall ON Kx and Ky, what does result in, and does FPE still hold?
B) diagram pg 42
Full specialisation and FPE still holds
B) A only produces X, B only produces Y
Dotted line to show new wage/rental rate
When does FPE not hold (3)
Very diverse relative factor endowments (outside of cone)
Factor intensity reversals
Assumptions of model break e.g if identical CRS production functions is broken, transport costs
What if endowent is outside of the cone pg 44
Still full specialisation? FPE hold?
It means different technique is required. Still full specialisation, but FPE doesn’t hold: we can see (w/r)₂ has different slope
Ea in this example is more biased towards capital! It requires a more capital intensive technique, Kx₂!!
So FPE doesn’t hold if we have FIR.
What does this look like in diagram
Multicone equilibria - if endowments lie in different cones FPE doesnt hold, i.e we get different w/r slopes
Rybczynski: increased endowment of one factor increases output of the good that uses this factor intensly. (And also reduce output of the other good)
Assume an increase in capital
How can we depict this (pg 51 and 52)
B)
What happens to output of each good
Edgeworth box - extend the box up to show more K, but keep K/L ratios constant to show constant prices (parallel)
B) We see total output of X is higher (as expected as capital has increased, and X uses capital intensly), so new higher isoquant
And less output of Y. (Lower isoquant)
Gains from trade how under HO
Allows higher consumption on a higher CIC. (Since factor price changes more than price changes, allowing for more consumption of both goods. Even though Py increased, the change in wage was higher! W^>P^y)
Where do gains arise from
Consumption (gains from exchange)
Key: even if remains in autarky production equilibirum, It can gain from importing and exporting at world prices (FT diagram that shows residents seeing price cheaper in other countries so A export X and import Y, vice versa for B)
Production (gains from specialisation)
An additional gain when a country moves to optimal production at world prices
Criticism of HO
Predictions not accurate at higher dimiensions than 2x2
If G<=F (goods<=factors)
If GF
If G<=F production and trade is determinate, hence goods content of trade is determinate
If G>F production and trade is indeterminate, but net factor content of trade is determinate (complies with HO)
Leontief against HO
Saw US was capital abundant, and so exports should be capital intensive accordign to HO
But exports were labour intenisve
Explanations for this adverse result (4)
US was actually labour abundnat
Could’ve been a bad year
Shouldve incuded more factors (F) in his model
HO is just not realistic e.g assumptions of identical CRTS prod functions, no transport costs, identifcal tech etc
