Hecksher-Ohlin and the Standard Model

ECES905205 meeting 4

Krisna Gupta

2023-09-01

Last time

• Ricardian: comparative advantage & specialization, everybody happy.

• Specific factor: comparative advantage, better in aggregate amid open possibilities / choices.

  • the gain are not shared equally.
  • this is the basis of political struggle among different factor owners.

Hecksher-Ohlin Model

Intro H-O Model

• Both Ricardian and Specific Factor model relies on difference in technologies in explaining why two countries trade.

• However, even some countries with the same tech still trade.

• In addition to difference in technologies, difference in relative abundance of resources can also drive trade.

• Here, we also show how different relative factor intensity drives trade.

Two Factor H-O model

• 2 countries: Home and foreign
• 2 mobile factor \(i\): kapital (K) and labor (L)
• 2 sectors \(j\): cloth (C) dan Food (F)
• Total K and L fixed, but different between countries.
• long run model: Capital is mobile.
  • All L got paid \(w\), all K got rent \(r\).

Technology

• \(a_{i,j}\) is the number of factor \(i\) used by industry \(j\) to make 1 unit of good \(j\).
  • e.g.: \(a_{KC}=\) capital used to make 1 meter of cloth.
• Tech still has a diminishing return.
  • There is a labour-capital substitution.
• Assumption: \(F\) is a capital intensive sector, while \(C\) is labour intensive.
  • in \(F\), to substitute 1 \(K\) requires lots of \(L\). \(C\) is the opposite.

Factor intensity

• Since capital can move freely this time, then the price of capital matter.
• Cuz \(C\) is relatively labor intensive, then:

\[ \frac{a_{LC}}{a_{KC}} > \frac{a_{LF}}{a_{KF}} \\ \frac{L_C}{K_C} > \frac{L_F}{K_F} \]

H-O model

• Production allocation is exactly the same as specific factor model.
• That is, production exists where the slope of PPF= \(-\frac{P_C}{P_F}\)
• The difference is in capital and labour prices.

Factor allocation

• Unlike specific factor, we have a substitution effect.
  • Each industry can replace labour with more capital.
• This leads to the importance of relative factor prices.
• If labour is relatively much cheaper than capital, then industries will use lots of labour and less capital.

Reminder micro

• Remember MRS=price ratio. Meaning, labour-capital demand

\[ \frac{\frac{\partial Q}{\partial K}}{\frac{\partial Q}{\partial L}}=\frac{r}{w} \rightarrow \frac{L}{K}=\omega \left(\frac{w}{r}\right) \]

\(\frac{MP_L}{MP_K} \propto \frac{L}{K} \propto \frac{w}{r} \propto \frac{P_C}{P_F}\)

Reminder micro

• Industry \(j\)’s unit cost:

\[ c_j=wa_{Lj}+ra_{Kj} \]

• the isocost function then:

\[ a_{Kj}=\left(\frac{c}{r}\right)-\left(\frac{w}{r}\right)a_{Lj} \]

• which, if holds, leads to the optimal allocation.

Factor and good prices

• In a competitive market, \(p=c\)

• F>0 which means:

\[ P_F=a_{LF}(.)w+ a_{KF}(.)r \\ P_C=a_{LC}(.)w+ a_{KC}(.)r \]

• Where \(a_{ij}(.)\) is the amount of labour and capital per good which is chosen optimally.

Factor and good prices

• Full employment means all capital and labour are exhausted to the two industries.

• meaning:

\[ L=a_{LF}(.)F+a_{LC}(.)C \\ K=a_{KF}(.)F+a_{KC}(.)C \]

Stolper-Samuelson Theorem

if the relative price of a good increases, then the real factor price used intensively in the production of that good increases, while the real price of the other factor decreases.

Changes in prices change income distribution between labour and capital owners.

Factor and good prices

Let \(\frac{P_C}{P_F} \uparrow\) (labor intensive):

• Labour’s income goes up relative to capital income. (\(\frac{w}{r} \uparrow\))
• the ratio \(\frac{K}{L} \uparrow\) in both industries.
• labour’s real income goes up, while capitalist’ real income goes down.

Factor and good prices

\[ P_F=a_{LF}(.)w+ a_{KF}(.)r \\ P_C=a_{LC}(.)w+ a_{KC}(.)r \]

Do a total differentiation. Since \(a_{ij}(.)\) is not a function of output prices, a small change in output price does not change them.

\[ dP_F=a_{LF}(.)dw+ a_{KF}(.)dr \\ dP_C=a_{LC}(.)dw+ a_{KC}(.)dr \]

Factor and good prices

• divide with \(P_j\)

\[ \frac{dP_F}{P_F}=\frac{a_{LF}(.)}{P_F}dw+ \frac{a_{KF}(.)}{P_F}dr \\ \frac{dP_C}{P_C}=\frac{a_{LC}(.)}{{P_C}}dw+ \frac{a_{KC}(.)}{P_C}dr \] - Multiply with \(\frac{w}{w}\) and \(\frac{r}{r}\)

\[ \frac{dP_F}{P_F}=\frac{a_{LF}(.)w}{P_F}\frac{dw}{w}+ \frac{a_{KF}(.)r}{P_F}\frac{dr}{r} \\ \frac{dP_C}{P_C}=\frac{a_{LC}(.)w}{{P_C}}\frac{dw}{w}+ \frac{a_{KC}(.)r}{P_C}\frac{dr}{r} \]

Factor and good prices

• \(\frac{dx}{x}=\) percentage change \(=\hat{x}\)
• let \(\theta=\) cost share where: \(\theta_Lj=\frac{a_{Lj}(.)w}{P_j},\theta_Kj=\frac{a_{Kj}(.)r}{P_j}, \theta_{Lj}+\theta_{Kj}=1\)

Then:

\[ \hat{P_F}=\theta_{LF}\hat{w}+\theta_{KF}\hat{r} \\ \hat{P_C}=\theta_{LC}\hat{w}+\theta_{KC}\hat{r} \]

Price changes

Let cloth price goes up (\(\hat{P_C}>0\)) while food price stays (\(\hat{P_F}=0\))

\[ 0=\theta_{LF}\hat{w}+\theta_{KF}\hat{r} \\ \hat{P_C}=\theta_{LC}\hat{w}+\theta_{KC}\hat{r} \]

It must be the case that one factor increase price while the other goes down.

Price change

Remember, C is labour intensive. Meaning:

\[ \frac{\theta_{LF}}{\theta_{KF}}<\frac{\theta_{LC}}{\theta_{KC}} \]

Weight for \(\hat{w}\) is higher in \(C\) than in \(F\). Since \(\hat{P_C}>0\), then it must be the case that \(\hat{w}>0\) and \(\hat{r}<0\).

\[ \hat{w} > \hat{P_C} > 0 > \hat{r} \]

Rybczynski Theorem

If output prices stay the same and one factor of production increase, then the production of the good that intensive in that factor rises while the production of the good that is not intensive in that factor reduces.

In short, a sudden increase in the abundance of one factor changes income distribution.

Resources and output

• Imagine a sudden increase in labour (think of something like immigration or demographic bonus) so \(\frac{L}{K} \uparrow\)
• PPF will goes up, but biased toward \(C\)
• If \(\frac{P_C}{P_F}\) does not move, labour-capital ratio won’t change.
• To expand, \(C\) will take capital from \(F\).

PPF

• PPF goes up but biased toward cloth.
• There’s a “Rybczynski line” for labor.

Resources and output

• Economy with high \(\frac{L}{K}\) ratio will have a large production in labor-intensive goods.
• If \(\frac{L}{K}>\frac{L^*}{K^*}\) then home will be more efficient in making C.

\[ \hat{L}=\lambda_{LF}\hat{F}+\lambda_{LC}\hat{C} \\ \hat{K}=\lambda_{KF}\hat{F}+\lambda_{KC}\hat{C} \]

• Where \(\lambda_{ij}=\) factor share. e.g., \(\lambda_{LF}=a_{LF}\frac{L}{F}\) is \(\frac{L_F}{L}\)

Factor change

• Let \(\hat{L}>0\) and \(\hat{K}=0\)

\[ \hat{L}=\lambda_{LF}\hat{F}+\lambda_{LC}\hat{C} \\ 0=\lambda_{KF}\hat{F}+\lambda_{KC}\hat{C} \]

-Since C labor-intensive, then

\(\frac{\lambda_{LC}}{\lambda_{KC}}>\frac{\lambda_{LF}}{\lambda_{KF}}\)

\[ \hat{C}>\hat{L}>0>\hat{F} \]

H-O and trade

• Just like ricardian, H-O predict global price convergence.
• Countries with many labour will make many C.
• When this country opens to trade, it will sell C and import F
• \(P_C \uparrow\) while \(P_C^* \downarrow\) and they will be equal.

Hecksher-Ohlin Theorem

The country that is abundant in a factor exports the good whose production is intensive in that factor

In general:

Countries tend to export goods whose production is intensive in factors with which the countries are abundantly endowed.

Distribusi pendapatan

• At home, trade benefits labour cuz what they produce by a lot is expensive in the gloal market (\(P_C>P_C^*\)) while they get access to cheaper food (\(P_F>P_F^*\))

• For the other side, On the other hand, trade benefits capital owners.

Owners of a country’s abundant factors gain from trade, but owners of a country’s scarce factors lose

Factor abundance change matters

• If a country suddenly have a lot of labour, then the economic structure of that country will shift to labour-intensive goods.
• Relative prices of this good will drop, and its export will go up regardless of technology intensity.

Factor price equalization

• Since \(\frac{w}{r} \propto \frac{P_C}{P_F}\), then Trade goods = trade factor of production.
  • If \(P_C=P_C^*\), then \(w=w^*\) and \(r=r^*\)
• That’s why trade leads to factor price equalization in all countries.
  • wage for unskilled labour in the US will drop to equalize wage in the countries which they import labour-intensive goods from.
  • This is not the case in the real world.

Factor price equalization?

• H-O assumes both countries trade a perfect substitute:
  • Imported food have the same quality as domestic food.
• H-O also assumes same technology, which isn’t the case. Also: countries’tech change!
• No trade barriers in this model too.
• Free movement of factors aren’t real (in the short term at least).

Welfare change

• Ultimately what we care about is welfare change,

• So far, the ultimate goal of trade is that we can acquire more goods by excessively produce goods we good at, import those we bad at.

• Therefore, relative price of export and import goods matter a great deal:

  • We are better-off if the world market prices of an exported goods go up and/or imported goods go down.

Terms of trade

• Terms of trade \(=\frac{P_X}{P_M}\) which are just price indices of exported and imported goods.

• ToT is often used to show welfare changes: Higher number is better, lower number is worse

• Note that lower ToT still better than autarky. If it’s worse, we can always return to autarky.

• Price indices also subject to change. e.g., Indonesia used to be oil exporter, now net oil importer.

Wrapping up

• Trade is good thanks to specialization and options to go along the ToT line.

• Factor immobility create winners & losers in the short-run.

• Factor relative abundance & factor-intensity create winners & losers in the long-run.

• The last two creates incentive for losers to ban trade, often enough for losers to act.

• But since overall economy still gain, a compensation mechanism makes sense.

Wrapping up

• To appreciate all of these insights, however, you must understand where this gain come from.

• Remember, economic model we uses so far have very specific assumptions:

  • Price takers in the world market (small country assumption)

  • Static (no intertemporal consumption & saving)

  • no barriers to entry (fixed cost is very small)

  • fixed technology (no learning by doing)

The new trade theory

• As usual, a government intervention is desirable under the presence of market failures.

  • Big countries can set prices.

  • Capital market imperfection.

  • Large fixed cost as a barrier to entry.

• That is, under these setting, an intervention may indeed improve gains over free trade.

• Next week we will learn these market failures and trade dynamics.