Editing Stolper–Samuelson theorem

{{Short description|Macroeconomic trade theorem}}
{{use mdy dates|date=September 2020}}
{{Use American English|date=September 2020}}
The '''Stolper–Samuelson theorem''' is a [[theorem]] in [[Heckscher–Ohlin model|Heckscher–Ohlin]] [[trade]] theory. It describes the relationship between relative prices of output and relative [[Factors of production|factor]] returns—specifically, [[real wage]]s and [[Real versus nominal value (economics)|real]] returns to capital.

The theorem states that—under specific [[economic]] assumptions (constant [[returns to scale]], [[perfect competition]], equality of the number of [[Factors of production|factors]] to the number of products)—a rise in the [[relative price]] of a good will lead to a rise in the real return to that factor which is used most intensively in the production of the good, and conversely, to a fall in the real return to the other factor.

==History==
It was derived in 1941 from within the framework of the [[Heckscher–Ohlin model]] by [[Wolfgang Stolper]] and [[Paul Samuelson]],<ref>{{Cite journal  |last1=Stolper |first1=W. F. |last2=Samuelson |first2=Paul A. | author-link1 = Wolfgang Stolper | author-link2 = Paul Samuelson | title = Protection and real wages | journal = [[The Review of Economic Studies]] | volume = 9 | issue = 1 | pages = 58–73 | doi = 10.2307/2967638 | jstor = 2967638 | date = November 1941 |s2cid=153734773 }}</ref> but has subsequently been derived in less restricted models. As a term, it is applied to all cases where the effect is seen. [[Ronald W. Jones]] and [[José Scheinkman]] show that under very general conditions the factor returns change with output prices as predicted by the theorem.<ref>{{Cite journal  |last1=Jones |first1=Ronald W. |last2=Scheinkman |first2=Jose A. | author-link1 = Ronald W. Jones |  author-link2 = Jose Scheinkman | title = The relevance of the two-sector production model in trade theory | journal = [[The Journal of Political Economy]] |volume=85 |issue=5 |pages=909–935 | jstor = 1830339 | date = 1977 |doi=10.1086/260615 }}</ref> If considering the change in real returns under increased [[international trade]] a robust finding of the theorem is that returns to the scarce factor will go down, [[ceteris paribus]]. An additional robust corollary of the theorem is that a [[Payment|compensation]] to the scarce factor exists which will overcome this effect and make increased trade [[Pareto optimal]].<ref name=neary>{{cite book | last = Neary | first = J. Peter | author-link = J. Peter Neary | title = The Stolper–Samuelson theorem | url = http://users.ox.ac.uk/~econ0211/papers/pdf/stolpers.pdf | publisher = [[Centre for Economic Policy Research]] | location = London | year = 2004 }}</ref>
The original [[Heckscher–Ohlin model]] was a two-factor model with a labor market specified by a single number. Therefore, the early versions of the theorem could make no predictions about the effect on the unskilled labor force in a high-income country under trade liberalization. However, more sophisticated models with multiple classes of worker productivity have been shown to produce the Stolper–Samuelson effect within each class of labor: Unskilled workers producing traded goods in a high-skill country will be worse off as international trade increases, because, relative to the world market in the good they produce, an unskilled [[first world]] production-line worker is a less abundant factor of production than capital.

The Stolper–Samuelson theorem is closely linked to the [[factor price equalization theorem]], which states that, regardless of international factor mobility, factor prices will tend to equalize across countries that do not differ in technology.

==Derivation==
Considering a two-good economy that produces only wheat and cloth, with labor and land being the only factors of production, wheat a land-intensive industry and cloth a labor-intensive one, and assuming that the price of each product equals its marginal cost, the theorem can be derived.

The price of cloth should be:

: (1) <math>P(C)= ar + bw, \, </math>

with ''P''(''C'') standing for the price of cloth, ''r'' standing for rent paid to landowners, ''w'' for wage levels and ''a'' and ''b'' respectively standing for the amount of land and labor used, and do not change with the prices of goods.

Similarly, the price of wheat would be:

: (2) <math>P(W) = cr + dw \, </math>

with ''P''(''W'') standing for the price of wheat, ''r'' and ''w'' for rent and wages, and ''c'' and ''d'' for the respective amount of land and labor used, and also considered to be constant.

If, then, cloth experiences a rise in its price, at least one of its factors must also become more expensive, for equation&nbsp;1 to hold true, since the relative amounts of labor and land are not affected by changing prices. It can be assumed that it would be labor—the factor that is intensively used in the production of cloth—that would rise.

When wages rise, rent must fall, in order for equation&nbsp;2 to hold true. But a fall in rent also affects equation&nbsp;1. For it to still hold true, then, the rise in wages must be more than proportional to the rise in cloth prices.

A rise in the price of a product, then, will more than proportionally raise the return to the most intensively used factor, and decrease the return to the less intensively used factor.

==Criticism==
The validity of the Heckscher–Ohlin model has been questioned since the classical [[Leontief paradox]]. Indeed, Feenstra called the Heckscher–Ohlin model "hopelessly inadequate as an explanation for historical and modern trade patterns".<ref>{{Citation |last=Feenstra |first=Robert C. |title=Advanced International Trade: Theory and Evidence |pages=4 |year=2004 |location=Princeton, New Jersey |publisher=Princeton University Press |isbn=9780691114101}}.</ref> As for the Stolper–Samuelson theorem itself, Davis and Mishra recently stated, "It is time to declare Stolper–Samuelson dead".<ref>{{Citation |last1=Davis |first1=Donald R. |name-list-style=amp |first2=Prachi |last2=Mishra |year=2006 |contribution=Stolper-Samuelson is dead, and other crimes of both theory and data |editor-first=Ann E. |editor-last=Harrison |title=Globalization and Poverty: NBER Conference Report | pages= 87–107 | publisher= University of Chicago Press | location=Chicago, Illinois | isbn = 9780226318004 | postscript = .}}</ref> They argue that the Stolper–Samuelson theorem is "dead" because following [[Free trade|trade liberalization]] in some developing countries (particularly in Latin America), [[Income inequality metrics|wage inequality]] rose, and, under the assumption that these countries are labor-abundant, the SS&nbsp;theorem predicts that wage inequality should have fallen. Aside from the declining trend in wage [[Latin America#Inequality|inequality in Latin America]] that has followed trade liberalization in the longer run (see Lopez-Calva and Lustig), an alternative view would be to recognize that technically the SS&nbsp;theorem predicts a relationship between output prices and relative wages.<ref>{{cite book | editor-last1 = Lopez-Calva | editor-first1 = Luis | editor-last2 = Lustig | editor-first2 = Nora | title = Declining inequality in Latin America a decade of progress | publisher = United Nations Development Programme [[Brookings Institution|Brookings Institution Press]] | location = New York Washington, D.C | year = 2010 | isbn = 9781282558304 }}</ref>

Papers that compare output prices with changes in relative wages find moderate-to-strong support for the Stolper–Samuelson theorem for [[Chile]],<ref>{{Cite journal |last1=Beyer |first1=Harald  |last2=Rojas |first2=Patricio |last3= Vergara |first3= Rodrigo | title = Trade liberalization and wage inequality | journal = [[Journal of Development Economics]] | volume = 59 | issue = 1 | pages = 103–123 | doi = 10.1016/S0304-3878(99)00007-3 | date = June 1999 }}</ref> [[Mexico]],<ref>{{Cite journal |last= Robertson |first= Raymond | title = Relative prices and wage inequality: evidence from Mexico | journal = [[Journal of International Economics]] | volume = 64 | issue = 2 | pages = 387–409 | doi = 10.1016/j.jinteco.2003.06.003 | date = December 2004 |citeseerx= 10.1.1.607.7566 }}</ref> and [[Brazil]].<ref>{{Cite journal |last1=Gonzaga |first1=Gustavo |last2=Filho |first2=Naércio Menezes |last3= Terra |first3= Cristina | title = Trade liberalization and the evolution of skill earnings differentials in Brazil | journal = [[Journal of International Economics]] | volume = 68 | issue = 2 | pages = 345–367 | doi = 10.1016/j.jinteco.2005.07.008 | date = March 2006 |hdl=10438/12362 | url = https://www.econstor.eu/bitstream/10419/175988/1/td503.pdf | hdl-access = free }}</ref>

==See also==
{{Portal|Economics}}
* [[Wage insurance]]
*[[Heckscher–Ohlin model]]

==Further reading==
* {{Cite journal | last1 = Marjit | first1 = Sugata | last2 = Jones | first2 = Ronald W. | author-link1 = Sugata Marjit | title = A simple production model with Stolper-Samuelson properties | journal = [[International Economic Review]] | volume = 26 | issue = 3 | pages = 565–567 | doi = 10.2307/2526703 | jstor = 2526703 | date = October 1985 }}
* {{cite book | last = McCulloch | first = Rachel | title = Protection and real wages: the Stolper–Samuelson theorem | url = http://people.brandeis.edu/~rmccullo/wp/Stolper-Samuelson0405.pdf | publisher = [[Brandeis University]] | location = Waltham, Massachusetts | year = 2005 }}

==References==
{{Reflist|30em}}

{{DEFAULTSORT:Stolper-Samuelson Theorem}}
[[Category:Economics theorems]]