Rybczynski Theorem

	1. Labor and Capital Growth
Growth in a recession	During a recession, resources are not fully utilized. Proper economic policies may be adopted to stimulate economic growth. (US and Germany before WWII) German unemployment rose to about 30% at the height of the Great Depression (1932). Similarly, when resources are not mobile within an economy, infrastructure investment may increase mobility and stimulate economic growth (e.g., China, Roman Empire, US after WWII) These changes cause a movement toward the PPF. PPF can also expand through labor or capital growth.
Neutral growth	The supply of a factor grows over time. Capital and labor skills grow more rapidly in LDCs than in the US. How does factor growth affect international trade and welfare of trading countries? Production: Labor and capital growth may increase the output of both the exportable and the importable by the same rate. This kind of growth is called neutral growth. For example, if K and L grow by 5% (^K = ^L = 5%), then neutral growth occurs because both the outputs of the exportable and the importable grow by the same rate.
Ultra-export biased growth	If the production of the exportable grows faster than that of the importable (^y₁ > ^y₂ > 0) it is called export-biased growth. If the output of the exportable increases and that of the importable decreases (^y₁ > 0 > ^y₂) the growth is ultra-export biased. Ultra-import biased growth is similarly defined. The following figure shows neutral, import biased, export biased, ultra export biased and ultra import biased growth.
war	Instead of shifting outward, sometimes the PPF contracts inwards. For instance, during World War II, significant amounts of resources were diverted away from civilian consumption goods to produce defense goods. North Korea is an example.
consumption bias	The growth of a factor endowment does not necessarily increase the output of every good. The growth of a factor does not necessarily increase exports. Figure below shows that export may decline, if a consumption bias exists.
Small country	Factor growth in a small country always increases national income and welfare (because growth does not affect prices)
Immiserizing Growth	If the terms of trade deteriorate sufficiently, growth can be immiserizing, lowering income and welfare. miserari = to pity in Latin. immiserize = to become poorer, pitiful.
	Varanasi, India. Annual media per capita income in India was $2170 in 2019 (IMF) Immiserizing Growth

	2. Rybczynski Theorem
Assumption	Output prices are held constrant. Accordingly, factor prices are fixed. This deals with growth of a small open economy. input-output coefficients remain constant.
Rybczynski Theorem	An increase in labor endowment increases the output of the labor-intensive industry and decreases the output of the other industry (L and the L-intensive industry are friends.)
resource constraints	1. The relationship between input and output a_L1 y₁ + a_L2 y₂ = L, (i.e., L₁ + L₂ = L) a_K1 y₁ + a_K2 y₂ = K. (i.e., K₁ + K₂ = K.) The a_ij's depend on w and r, not fixed as in Ricardian model. What combinations of outputs can be obtained from given resource constraints on capital and labor endowments? This is a system of two (nonlinear) equations involving two unknowns. Under plausible conditions, there is a unique solution. If the input-output coefficients are fixed parameters, it would take five minutes or so if they are not linear (as in the Ricardian model). Even if they are not linear, the system is solvable in principle (there are two unknowns and two equations). It would be a tedious procedure to find a solution in a non-linear system. But a graphical solution is instantaneous.
2. The Rybczynski Theorem	The above equations show that the sum of the inputs used in the two industries must add up to the nation's input supplies. (L₁,K₁) + (L₂,K₂₎ = (L,K). This relationship between inputs and outputs are shown below. An increase in the endowment of labor increases the production of labor intensive good and decreases the production of the other good (capital intensive good). The cone of diversification can be used to illustrate Rybczynski Theorem in the output spac e. An increase in the endowment of one factor results in either an ultra-export or import biased growth. Figure. The Rybczynski Theorem
Rybczynski effects	© Example of ultra export biased growth When the supply of only one factor increases, two goods move in opposite directions.

3. The Magnification Effect

An increase in labor endowment increases the output of labor-intensive good more than proportionately.
You may skip this proof.
a_L1 y₁ + a_L2y₂ =L,
a_L1Δy₁ + a_L2 Δy₂ = ΔL
= a_L1 y₁ (Δy₁/y₁) + a_L2 y₂ (Δy₂/y₂).

Intuition divide both sides by L
^L = λ_L1 ^y₁ + λ_L2 ^y₂.
where λL1 = a_L1 y₁/L = L₁/L = the percentage of labor forced employed in industry 1.
For example, if the labor shares were the same, labor growth rate is simply 50% × ^y₁ + 50% ^y₂. If the labor shares are 30% and 70%, then the labor growth rate is =
^L = 30% × ^y₁ + 70% × ^y₂
This shows that the percentage change in labor is a weighted average of the growth rates of the two outputs. That is, labor growth lies somewhere between the two output growth rates, ^y₁ and ^y₂.
If both outputs grew at the same rate, say 10%, then labor demand would also grow by the same rate.
The trouble is, by the Rybczynski Theorem, the output of one industry actually declines. This implies that the other industry must grow more than proportionately. That is, if labor grows by 10%, one industry declines. Thus, the other industry must grow more than 10%. This is the intuition behind the Magnification Effect.
For example, assume that labor shares of two industries are equal (50%) and that labor supply rises by 10% and the capital-intensive industry contracts by 5%. the above equation reduces to:
10% = (1/2)^y₁ + (1/2)(-5%).
Even when industry 2 does not contract, output of the labor intensive industry must expand 20% ( which is more than 10%). Since the capital-intensive sector declines, industry 1 has to grow even faster to offset this negative effect.

Exercises 1. Using the iso-unit cost curves, evaluate the impacts of an increase in the price of a labor intensive good to returns to capital and labor. Restate the Stolper-Samuelson theorem and the magnification effect.
2. Evaluate the effects of an increase in the endowment of capital on the production of labor intensive and capital intensive goods. Restate the Rybczynski Theorem and its magnification effect.

Washington National Gallery
Cultural Impacts of Trade

What is this cardinal showing off in this portrait?

Venetians built a shipyard (Arsenale di Venezia) in 1104. Arsenale Nuovo (New Arsenal) built in 1320 used assembly lines to mass produce warships, thereby accumulating huge trade surpluses (in gold) [Note that the Rybczynski effect increases GDP].

After the fall of Constantinople in 1453, many intellectuals left Constantinople and moved to other cities of the Byzantine Empire, where they were well treated. By the time of Reformation (1517) the church became rich. They began to commission various masters to paint on religious subjects.

The church needed paintings to educate the illiterate public just enough to collect offerings. In the process, the Roman Catholic church stimulated the development of Western painting.

Venice became the trade center in Europe, and together with Florence (known for banking, silk, and textile) provided the financial support for the Renaissance. The Medici family spent 600,000 florins. Compare this amount to the annual spending of the Florintine government (The signoria spent $100,000 florins per year.)

Proof But if you insist on proof, it is given below.
λ_L1 + λ_L2 = 1.
^y₁ - ^L = (1 - λ_L1) ^y₁ - λ_L2 ^y₂ = λ_L2 (^y₁ - ^y₂) > 0.
Remark: If both outputs, y₁ and y₂, were to increase 10%, labor demand would also increase 10%. However, by the Rybczinski theorem, an increase in labor decreases the output of the capital-intensive good, y₂. Since y₂ is declining, in order to effect a 10% growth in labor force, output of y₁ must increase by more than 10%, hence a magnification effect.

	3. The Magnification Effect
	An increase in labor endowment increases the output of labor-intensive good more than proportionately. You may skip this proof. a_L1 y₁ + a_L2y₂ =L, a_L1Δy₁ + a_L2 Δy₂ = ΔL = a_L1 y₁ (Δy₁/y₁) + a_L2 y₂ (Δy₂/y₂).
Intuition	divide both sides by L ^L = λ_L1 ^y₁ + λ_L2 ^y₂. where λL1 = a_L1 y₁/L = L₁/L = the percentage of labor forced employed in industry 1. For example, if the labor shares were the same, labor growth rate is simply 50% × ^y₁ + 50% ^y₂. If the labor shares are 30% and 70%, then the labor growth rate is = ^L = 30% × ^y₁ + 70% × ^y₂ This shows that the percentage change in labor is a weighted average of the growth rates of the two outputs. That is, labor growth lies somewhere between the two output growth rates, ^y₁ and ^y₂. If both outputs grew at the same rate, say 10%, then labor demand would also grow by the same rate. The trouble is, by the Rybczynski Theorem, the output of one industry actually declines. This implies that the other industry must grow more than proportionately. That is, if labor grows by 10%, one industry declines. Thus, the other industry must grow more than 10%. This is the intuition behind the Magnification Effect. For example, assume that labor shares of two industries are equal (50%) and that labor supply rises by 10% and the capital-intensive industry contracts by 5%. the above equation reduces to: 10% = (1/2)^y₁ + (1/2)(-5%). Even when industry 2 does not contract, output of the labor intensive industry must expand 20% ( which is more than 10%). Since the capital-intensive sector declines, industry 1 has to grow even faster to offset this negative effect.
Exercises	1. Using the iso-unit cost curves, evaluate the impacts of an increase in the price of a labor intensive good to returns to capital and labor. Restate the Stolper-Samuelson theorem and the magnification effect. 2. Evaluate the effects of an increase in the endowment of capital on the production of labor intensive and capital intensive goods. Restate the Rybczynski Theorem and its magnification effect.
Washington National Gallery	Cultural Impacts of Trade What is this cardinal showing off in this portrait? Venetians built a shipyard (Arsenale di Venezia) in 1104. Arsenale Nuovo (New Arsenal) built in 1320 used assembly lines to mass produce warships, thereby accumulating huge trade surpluses (in gold) [Note that the Rybczynski effect increases GDP]. After the fall of Constantinople in 1453, many intellectuals left Constantinople and moved to other cities of the Byzantine Empire, where they were well treated. By the time of Reformation (1517) the church became rich. They began to commission various masters to paint on religious subjects. The church needed paintings to educate the illiterate public just enough to collect offerings. In the process, the Roman Catholic church stimulated the development of Western painting. Venice became the trade center in Europe, and together with Florence (known for banking, silk, and textile) provided the financial support for the Renaissance. The Medici family spent 600,000 florins. Compare this amount to the annual spending of the Florintine government (The signoria spent $100,000 florins per year.)
Proof	But if you insist on proof, it is given below. λ_L1 + λ_L2 = 1. ^y₁ - ^L = (1 - λ_L1) ^y₁ - λ_L2 ^y₂ = λ_L2 (^y₁ - ^y₂) > 0. Remark: If both outputs, y₁ and y₂, were to increase 10%, labor demand would also increase 10%. However, by the Rybczinski theorem, an increase in labor decreases the output of the capital-intensive good, y₂. Since y₂ is declining, in order to effect a 10% growth in labor force, output of y₁ must increase by more than 10%, hence a magnification effect.