Rybczynski Theorem
What is Rybczynski Theorem?
The Rybczynski theorem says that, at constant prices, increasing one factor's endowment raises output of the good using it intensively more than proportionally and reduces output of the other good.
Another pillar of the Heckscher-Ohlin model, it shows how factor growth reshapes production. If a country's capital stock grows (or it gains labor through immigration), the capital-intensive industry expands disproportionately while the labor-intensive industry actually contracts in absolute terms, holding goods prices fixed. It is used to analyze the effects of investment, immigration, and emigration on a trading economy's output mix.
Rybczynski Theorem: a worked example
Auralia builds robots (5 machines and 1 worker each) and rugs (1 machine and 5 workers each), with 600 machines and 600 workers fully employed. Solving 5R + G = 600 and R + 5G = 600 gives 100 robots and 100 rugs. Now foreign investment lifts machines to 720 while the workforce is unchanged and goods prices hold. Solving 5R + G = 720 and R + 5G = 600 gives R = 125 and G = 95. Capital rose 20%, robot output rose 25%, and rug output fell outright, because the extra machines still needed workers and the only place to get them was the rug sector.
The mistake students make with rybczynski theorem
The natural guess is that more capital means more of everything, since the economy has more to work with. At fixed goods prices it does not. Labor is fully employed, so the expanding capital-intensive sector can staff itself only by hiring away the other sector's workers, and rug output falls in absolute terms, from 100 to 95 above. Growth diagrams reinforce the wrong intuition by pushing the whole production possibilities frontier outward, which shows what the economy could make rather than what it will make at unchanged prices. Keep Rybczynski (endowments move, prices fixed) apart from Stolper-Samuelson (prices move, endowments fixed).
Rybczynski Theorem questions
How does immigration affect output under the Rybczynski theorem?
Immigration raises a country's labor endowment, so the Rybczynski theorem predicts output of the labor-intensive good grows more than proportionally while output of the capital-intensive good falls, with goods prices held fixed. The mechanism is reallocation rather than scarcity: the capital-intensive sector releases both the workers and the machines the expanding sector needs. The result assumes full employment and unchanged prices, so it describes the production mix, not living standards.
What is the difference between the Rybczynski theorem and the Stolper-Samuelson theorem?
The Rybczynski theorem holds goods prices constant and asks what a change in factor supplies does to output. The Stolper-Samuelson theorem holds factor supplies constant and asks what a change in goods prices does to factor incomes. One runs from endowments to quantities, the other from prices to wages and rents. Both sit inside the same two-good, two-factor Heckscher-Ohlin framework, which is why they get swapped so easily.
Why does the Rybczynski theorem produce a magnification effect?
The Rybczynski theorem magnifies because the growing sector absorbs the new factor in the fixed proportion its technology requires, and it must pull the complementary factor out of the other sector to do so. In the worked case machines rose 20% while robot output rose 25%, since the shrinking rug sector surrendered 5 machines on top of the 120 newly installed ones, plus the 25 workers the robot sector needed. The percentage change in output exceeds the percentage change in the endowment.
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Common comparisons
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