Lerner-Samuelson theorem

The Lerner – Samuelson theorem ( the factor pricing equalization theorem ^[1] ) is an integral part of the Heckscher – Olin – Samuelson foreign trade model . Formulated in 1948 by Paul Samuelson , regardless of the work of Abba Lerner in 1933. According to the Lerner – Samuelson theorem, with the same production technologies with constant returns to scale, free trade in goods will ensure full equalization of factor prices of production through equalization of commodity prices until both regions produce both goods even when there is no external migration of these factors of production ^[1] .

Content

Creation History

The works of Eli Heckscher, 1919, “The Impact of Foreign Trade on the Distribution of Income” (reprinted in English in 1949 ^[2] ) and Bertil Olin, “Interregional and International Trade” in 1924 (reprinted in English in 1933 ^[3] ), formulating the foundations of the Heckscher-Olin-Samuelson model , were further developed. So Abba Lerner wrote the article “Prices on factors of production and international trade” in 1933 ^[4] (reprinted in English in 1952), where he formulated a theorem of price equalization and gave a graphical illustration of the theorem using the Lerner chart . In parallel and independently of this, this theorem was formulated and given a full mathematical description by Paul Samuelson , publishing a number of articles: “International Trade and Alignment of Prices of Factors of Production” 1948 ^[5] , “Once Again on the International Alignment of Prices of Factors of Production” 1949 ^[6] and “Prices of factors of production and goods in a state of social equilibrium” of 1953 ^[7] . Subsequently, the theorem on the equalization of prices for factors of production in the foreign trade model of Heckscher-Olin-Samuelson was named after the creators.

Assumptions

A number of prerequisites are required ^[8] :

There is an initial 2x2x2 model - two factors of production, two goods, two regions;
factors of production are completely mobile within a region and not mobile between regions;
all markets are competitors ;
the supply of factors of production is fixed;
full use of factors of production;
transport and information costs are absent;
trade is free ;
production functions are identical, linearly homogeneous, constant returns to scale;
do not possess the property of reversibility of factor intensity;
after the establishment of trade, both regions continue to produce both goods ^[6] .

Definition of a theorem

Equalization of prices for factors of production theorem : if all assumptions are fulfilled, trade between regions leads to equalization of prices for goods and factors of production, so that wage and rent rates are equal in the regions regardless of the existing structure of demand or supply with factors of production ^[8] .

Graphical illustration of the theorem

Lerner chart

The Heckscher – Olin – Samuelson model demonstrates the emergence of comparative advantages of interregional trade due to differences in regions with endowed production factors, and since the region exports excess factors, there is an increase in demand for this factor and an increase in its price ^[9] .

On the graph “Lerner chart” in connection with the assumption of constant returns to scale, the isoquants of unit value have the form:

X_{1}

{\ displaystyle X_ {1}}

and

Y_{1}

{\ displaystyle Y_ {1}}

where

XP_{X}=YP_{Y}

{\ displaystyle XP_ {X} = YP_ {Y}}

.

A single isocost $f=w/r$ ${\ displaystyle f = w / r}$ where $w$ ${\ displaystyle w}$ - the cost of labor $r$ ${\ displaystyle r}$ - the price of capital, $1/r$ ${\ displaystyle 1 / r}$ and $1/w$ ${\ displaystyle 1 / w}$ - the intersection points of the isocosts with the coordinate axes, $f$ ${\ displaystyle f}$ - factor price equal to the slope $w/r$ ${\ displaystyle w / r}$ .

The touch of two isoquants and isocosts shows the ratio of capital and labor in two sectors $k_{X}$ ${\ displaystyle k_ {X}}$ and $k_{Y}$ ${\ displaystyle k_ {Y}}$ between which two goods are produced in the area of the diversification cone, and in the case where the ratio of labor to capital is $k_{X}$ ${\ displaystyle k_ {X}}$ or $k_{Y}$ ${\ displaystyle k_ {Y}}$ , the economy is fully specialized in goods $X$ ${\ displaystyle X}$ or $Y$ ${\ displaystyle Y}$ respectively. Production functions are identical, therefore, trade equalizes commodity prices, which leads to the fact that isoquants of unit value $X_{1}$ ${\ displaystyle X_ {1}}$ and $Y_{1}$ ${\ displaystyle Y_ {1}}$ for regions A and B are also identical. Since the general ratio of capital to labor $k_{A}$ ${\ displaystyle k_ {A}}$ and $k_{B}$ ${\ displaystyle k_ {B}}$ in regions A and B fall into the diversification cone , then regions A and B have equal ratios of labor and capital costs - $f$ ${\ displaystyle f}$ ^[9] .

Trade equalizes commodity prices, equalizes the ratio of the cost of labor and capital in the production of two goods and the same production functions. If the relative endowment of factors of one of the regions will lie outside the borders of the diversification cone, then although commodity prices will equalize, there is no labor-capital ratio: one region will fully specialize in the production of one product, and the second will continue to produce two goods ^[9] .

Corollary of the theorem

Based on the theorem on equalizing prices for factors of production, we can conclude that trade in goods replaces the movement of factors of production between regions, and if the differences in the ratio of factors of production in the regions are not too large, then free trade completely replaces their movement. Thus, when the prices of factors are aligned, the movement of factors of production between regions, if we make an assumption about the mobility of factors between regions, will not bring benefits ^[10] .

Criticism

The factor-price equalization theorem has been successfully tested at the regional level within one country, where there are no trade barriers and transport costs leading to distortion of commodity prices.

The weaknesses of the Lerner – Samuelson theorem remain common with the Heckscher – Olin – Samuelson model regarding the unrealistic assumptions ^[9] :

perfect competition, a fixed supply of labor and capital, the existence of only two factors of production;
common technology in the regions, common preferences in different regions;
homogeneity of labor and capital, the need to introduce the concepts of skilled and unskilled labor;
constant returns to scale in the strength of the fact that there is always an internal economies of scale or agglomeration effect.

The gradual abandonment of the prerequisites introduced leads to improved testing results and the emergence of a ^[9] .

Notes

↑ ¹ ² Comparative Advantages // Economic Theory / Ed. J. Ituella et al. - M .: Infra-M, 2004 .-- S. 122-133 . - ISBN 5-16-001750-X.
↑ Heckscher E.F. Influence of foreign trade on income distribution // Milestones of economic thought . T. 6. International Economics / A. P. Kireev. - M .: TEIS, 2006 .-- S. 154-173 . - ISBN 5-7598-0439-1 .
↑ Olin B. Interregional and International Trade // Milestones of Economic Thought. T. 6. International Economics / A. P. Kireev. - M .: TEIS, 2006 .-- S. 174-187 . - ISBN 5-7598-0439-1 .
↑ Lerner AP Factor Prices and International Trade // Economica. - 1952. - T. 73 , No. 19 . - S. 1–15 .
↑ Samuelson PA International Trade and the Equalization of Factor Prices // Economic Journal. - 1948. - June ( t. 58 , No. 230 ). - S. 163-184 .
↑ ¹ ² Samuelson P. Once again on the international equalization of prices of factors of production // Milestones of economic thought. T. 6. International Economics / Ed. A.P. Kireeva. - M .: TEIS, 2006 .-- S. 205-219 . - ISBN 5-7598-0439-1 .
↑ Samuelson P. Prices of factors of production and goods in a state of social equilibrium // Milestones of economic thought. T. 6. International Economics / Ed. A.P. Kireeva. - M .: TEIS, 2006 .-- S. 391-409 . - ISBN 5-7598-0439-1 .
↑ ¹ ² Lindert P. Economics of World Economic Relations. - M .: Progress, 1992 .-- S. 72.
↑ ¹ ² ³ ⁴ ⁵ Limonov L. E. Regional Economics and Spatial Development . - M .: Yurayt, 2015 .-- T. 1. - S. 228-233. - ISBN 978-5-9916-4444-0 .
↑ Bloomfield A.I., Etier V. Development of the theory of international economic relations // Modern Economic Thought / Afanasyev BC, Entov PM - M.: Progress, 1981.

[:0-1] ¹ ² Comparative Advantages // Economic Theory / Ed. J. Ituella et al. - M .: Infra-M, 2004 .-- S. 122-133 . - ISBN 5-16-001750-X.

[:1-2] Heckscher E.F. Influence of foreign trade on income distribution // Milestones of economic thought . T. 6. International Economics / A. P. Kireev. - M .: TEIS, 2006 .-- S. 154-173 . - ISBN 5-7598-0439-1 .

[:2-3] Olin B. Interregional and International Trade // Milestones of Economic Thought. T. 6. International Economics / A. P. Kireev. - M .: TEIS, 2006 .-- S. 174-187 . - ISBN 5-7598-0439-1 .

[:7-4] Lerner AP Factor Prices and International Trade // Economica. - 1952. - T. 73 , No. 19 . - S. 1–15 .

[:8-5] Samuelson PA International Trade and the Equalization of Factor Prices // Economic Journal. - 1948. - June ( t. 58 , No. 230 ). - S. 163-184 .

[:3-6] ¹ ² Samuelson P. Once again on the international equalization of prices of factors of production // Milestones of economic thought. T. 6. International Economics / Ed. A.P. Kireeva. - M .: TEIS, 2006 .-- S. 205-219 . - ISBN 5-7598-0439-1 .

[:4-7] Samuelson P. Prices of factors of production and goods in a state of social equilibrium // Milestones of economic thought. T. 6. International Economics / Ed. A.P. Kireeva. - M .: TEIS, 2006 .-- S. 391-409 . - ISBN 5-7598-0439-1 .

[:5-8] ¹ ² Lindert P. Economics of World Economic Relations. - M .: Progress, 1992 .-- S. 72.

[:6-9] ¹ ² ³ ⁴ ⁵ Limonov L. E. Regional Economics and Spatial Development . - M .: Yurayt, 2015 .-- T. 1. - S. 228-233. - ISBN 978-5-9916-4444-0 .

[:9-10] Bloomfield A.I., Etier V. Development of the theory of international economic relations // Modern Economic Thought / Afanasyev BC, Entov PM - M.: Progress, 1981.