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A General Equilibrium Re-appraisal of the Stolper-Samuelson Theorem Forthcoming in Journal of Economics Wen Li Cheng
Abstract This paper conducts a general equilibrium
analysis of the HO model in which product price is endogenized. It
applies both marginal and infra-marginal comparative static analyses
to examine the co-movement of factor and product prices. It shows
that the Stolper-Samuelson Theorem's prediction does not always hold,
in particular, it does not always hold inside the diversification
cone when changes in production parameters lead to changes in prices;
or when the general equilibrium jumps from one structure to another.
The result of this paper supports the "everything possible"
theorem and casts doubt on the general applicability of other core
trade theorems derived from the same framework as the Stolper-Samuelson
Theorem. Trade theorists often claim that these theorems are
general equilibrium comparative static results of the traditional
HO model. And partly due to the belief that the traditional HO model
is able to derive unambiguous comparative static results with very
general functional forms, the HO model has dominated the field of
international trade for the past few decades. The dominance of the
traditional HO model did face some challenge, most notably from mathematical
economists well respected in the field of general equilibrium theory.
Sonnenschein (1973) Mantel (1974) and Debreu (1974) show that without
explicit model specifications, no unambiguous comparative statics
results can be derived from a general equilibrium model except that
Walras' law holds, and that the excess demand function is homogenous
of degree zero (the "everything possible" theorem). The
"everything possible" theorem thus questions the validity
of the claim that the trade theorems mentioned above are indeed general
equilibrium comparative static results. The inconsistency between the "everything possible"
theorem and unambiguous predictions of the traditional HO model can
be explained by the fact that the traditional HO model differs from
a typical general equilibrium model in various ways. Most importantly,
in the traditional HO model, product prices (when the SS theorem and
the RY theorem are proved) or factor prices (when the HO theorem is
proved) are assumed to be exogenous. When prices are assumed to be
exogenous, the interactions between prices and other parameters (such
as endowments) are excluded from the analysis, consequently the predictions
of the model become less unambiguous despite that no specific functional
forms are assumed. With exogenous product price, it is possible to describe,
for instance, how factor prices would change in response to a change
in product price (that is, to formulate the Stolper-Samuelson Theorem).
However, the response of factor price to product price is not part
of comparative statics of general equilibrium. In a general equilibrium
model, all prices are endogenously determined. As a result, it is
not appropriate to describe how factor prices would change in response
of a change in product price. It is possible however to describe how parameter changes
would affect factor price and product price differently and thus describe
the features of the co-movement of factor and product prices. In this paper, we develop a general equilibrium analysis
of the HO model with endogenous prices and conduct comparative static
analysis to examine the co-movement of factor and product prices.
In particular, we assess whether the general prediction of the Stolper-Samuelson
theorem holds as a comparative static result of equilibrium. Apart from that prices are endogenous, our analysis
differs from the traditional analysis of the HO model in another important
aspect. When the core trade theorems are proved, comparative statics
of general equilibrium are analyzed within the diversification cone.
The shift of equilibrium across the border of the diversification
cone is explained by changes in prices rather than by changes in parameters.
Hence, the analysis of shift is not really part of comparative statics
of general equilibrium, which should explain changes in trade structure
by changes in parameters. Our analysis however considers all eight
feasible trade structures. Which structure occurs in equilibrium is
endogenously determined by values of all parameters. Since all feasible
trade structures can occur in equilibrium depending on parameter values,
when parameter values change, there can be two types of comparative
static responses. First, endogenous variables change continuously
in response to a change in parameter values. Second, when a change
in parameter values exceeds some threshold, the equilibrium structure
discontinuously jump and the values of endogenous variables jump discontinuously
as well. We refer to the first type of response as marginal comparative
statics and the latter as infra-marginal comparative statics. We examine the Stolper-Samuelson Theorem in this paper
applying both the marginal and infra-marginal comparative static analysis.
The main conclusion of the paper is that the general prediction of
the Stolper-Samulson Theorem is not always consistent with the comparative
statics results derived from a specific general equilibrium HO model.
In particular, the Stolper Samuelson Theorem's prediction does not
always hold when changes in production parameters lead to changes
in prices even within the diversification cone; or when the general
equilibrium jumps from one structure to another. By rejecting the general applicability of the Stolper-Samuelson,
our finding confirms the "everything possible" theorem.
It also raises questions as to the general applicability of other
core trade theorems derived from the same framework as the Stolper-Samuelson
Theorem. The rest of the paper is organized as follows. Section 2 presents the general equilibrium HO model. Section 3 conduct the marginal and infra-marginal comparative statics to examine the general validity of the Stolper-Samuelson theorem. Section 6 concludes the paper. Inframarginal Economics Society www.inframarginal.com |