Prices and Wages in Trade Theory

Henry Thompson

Auburn University

December 2007

Abstract. There is a common thread of a link between prices and wages in classical, neoclassical, factor proportions, specific factors, and monopolistic general equilibrium models of production and trade. The present paper focuses on the effect of a fall in the import price on the wage in high wage countries across this range of models. The issue is the prediction of a falling wage in the face of a falling price of labor intensive imports.

There may be a presumption from trade theory that wages in countries with relatively high wages fall with a move to free trade. In classical trade theory with the single labor input, however, the wage increases along with income, and neoclassical trade theory stresses utility gains without separating the wage effect. In general equilibrium production theory, the focus shifts to factor markets and the wage in the high wage country falls in the two factor model.

The present paper reviews the wage effect of a falling import price across a variety of general equilibrium production models including classical fixed unit inputs, neoclassical cost minimization, specific factors, and monopoly pricing. The issue is the robustness of the prediction of a falling wage.

While the theoretical literature relates wages to changes in trade prices, the empirical literature generally relates wages to trade levels. Feenstra and Hanson (1995) attribute a third of the decline in the production wage relative to the non-production (mostly skilled) wage in US manufacturing during the 1980s to the increased trade volume, while Wood (1994), Slaughter (1998), and Leamer (2000) uncover larger effects. Mokhtari and Rassekh (1989), Rassekh (1992), Ben-David (1993), and Sachs and Warner (1995) find evidence of a positive link between the trade level and per capita income, and Rassekh and Thompson (1996) explore the theoretical link between per capita income and the wage. Batra and Slotje (1992, 1993, 1994) believe US trade with Japan during the 1980s was a fallacy due to the falling relative production wage while Rassekh (1994) and Marjit (1994) disagree. Copeland and Thompson (2007) uncover a small negative time series link between the US import price index and the production wage between 1964 and 1997, suggesting the declining tariffs of those years had a positive impact on the wage.

The average trade weighted US manufacturing tariff for 459 industries at the 6-digit SIC level has fallen to 4% but with a strong right skew toward a maximum of 19%. Other developed countries are similar with average tariffs of 5% in the EU, UK, Australia, and Canada, and 2% in Japan. Effective protection rates are higher and import competition promises to continue with increased imports of manufactures from low wage countries.

The present review is limited to models with two sectors facing exogenous world prices with constant production functions and factor endowments. The lower import price may be due to changes on world markets or lower tariffs. A few novel models fill gaps in the logical progression of models.

1. Prices and wages with classical fixed coefficients

In the classical model the move to trade prices raises national income and the wage due to efficiency gains from specialization with fixed unit inputs implying constant opportunity costs for the single input. There is no wage prediction, however, when there is more than the minimal single input as the following examples show.

Jones (1973) presents the production model with two inputs in fixed proportions and inequality employment constraints. In the related model with full employment, input ratios must span the endowment point as in a_KX/a_LX > K/L > a_KM/a_LM. Changing prices do not affect outputs but wages adjust according to factor intensity. A decrease in the price of labor intensive imports lowers the wage, and the surprise in this fixed factor proportions model is that the size of the wage adjustment is identical to the Stolper-Samuelson (1941) result in the model with substitution. This factor intensity link is the basis of the presumption that the wage falls in high wage countries.

The missing link model of Ruffin (1988, 1992) has fixed unit input coefficients for labor L and skilled labor S each producing either of two products independently. Factors are employed in their comparative advantage sector and factor proportions determine the direction of trade. Suppose labor has a comparative advantage in imports M relative to exports X, a_SX/a_SM < a_LX/a_LM. For a range of preferences in autarky, each factor is employed by its comparative advantage sector implying L = a_LMq_M and S = a_SXq_X where the q_j are outputs. It follows that w = p_M/a_LM and w_S = p_X/a_SX with the wage w_L tied to the import price. Moving to world prices at p_X* > p_X and p_M* < p_M the wage w_L falls to p_M*/a_LM unless the increase in p_X* is large enough to attract labor to that sector. The condition for a lower wage is a_LX/a_LM > p_X*/p_M*. Reversing that inequality the economy specializes with labor moving to the export sector and w increasing to p_X*/a_LX.

Consider a model with fixed labor unit coefficients, other factors of production, and labor inessential to production. Suppose labor is employed in the protected import competing sector with w_M = (1+t)p_M*/a_LM greater than the potential export sector wage w_X = p_X*/a_LX. Free trade prices lower the wage to the higher of p_M*/a_LM or w_X. Labor remains in the import sector if the relative price of imports is greater than its opportunity cost of producing exports, p_M*/p_X* > a_LM/a_LX. Percentage changes in both w_M and the domestic price of imports equal -t/(1+t) and the real wage falls. If p_M*/p_X* < a_LM/a_LX labor moves to the export sector and the percentage fall in the wage [(a_LMp_X/a_LX(1+t)p_M) – 1] is greater than the percentage fall in the import price -t(1+t) and the effect on the real wage then depends on consumption shares.

In summary, fixed labor input coefficients do not imply a necessary effect of a falling import price on the wage.

2. Prices and wages with cost minimization

Neoclassical production theory introduces cost minimization requiring at least two inputs. As the neoclassical economy adjusts to trade prices along its concave production frontier, labor demand and the wage adjust as the value of consumption rises and the value of production falls at autarky prices.

Stolper and Samuelson (1941) show a falling relative price of labor intensive imports lowers the relative wage in the 2x2 model as both sectors become more labor intensive. The price taking import sector faces a lower price and production falls. The magnification effect of Jones (1965) implies a decline in the real wage regardless of consumption shares.

Moving beyond the minimal two inputs, a wide range of potential wage adjustments emerge. In the 3x2 model, factor intensity and substitution jointly determine wage adjustment as developed by Suzuki (1982), Jones and Easton (1983), Ruffin (1981), and Thompson (1985). Suppose labor L is the most intensive input in the import sector and skilled labor S the most intensive in export production in the ranking a_LM/a_LX > a_KM/a_KX > a_SM/a_SX. A falling import price might lower the wage but a low degree of labor intensity would imply little wage pressure. If labor and capital were complements, a falling capital return would increase labor demand. Cost in the labor intensive import sector may fall in spite of the higher wage. The array of potential 3x2 wage adjustments is illustrated by the 13 magnification effects of Thompson (1993).

Reasonably realistic models of production and trade have more factors of production. The typical assumption of only two skilled labor groups is questioned by Leamer (1994). In fact, Clark, Hofler, and Thompson (1988) show there are at least 6 separate labor skill groups in US manufacturing. The typical aggregation can lead to distortions including opposite qualitative comparative static results for factors not involved in the aggregation as discussed by Thompson (2005). Natural resources are the foundation of a good deal of international trade. The literature includes the high dimensional models of Chipman (1979), Chang (1979), Ethier (1984), and Thompson (1987). If the fundamental model includes various labor inputs as well as numerous types of natural resources and capital, there is no presumption a falling import price will lower the wage.

In summary, falling import prices imply an unambiguous decline in the wage only with two factors of production.

3. Prices and wages with specific factors of production

In the specific factors model of Jones (1971) and Samuelson (1971) each sector employs its own capital K_j along with shared labor, and the effect of the fall in the import price on the wage depends on factor intensity and substitution. A falling import price lowers the wage, but the size of the wage decline depends on factor substitution, and the effect on the real wage depends on consumption shares in the neoclassical ambiguity examined by Ruffin and Jones (1977).

If labor were specific to the import competing sector and capital the shared input, a falling import price would lower the real wage. Suppose, however, there is shared skilled labor as well with the export sector employing only the shared factors as capital in Thompson (1989). A falling import price would lower the wage of import specific labor but the third input affords flexibility and a number of possible adjustments. If labor is a complement with capital and the capital return falls, the demand for labor increases and the wage may rise even with the falling price of its only output.

Consider a model not in the literature with specific capital K_X and K_M in each sector and shared inputs of labor L and skilled labor S. With labor intensive imports a_LM/a_SM > a_LX/a_SX a falling import price would seem destined to lower the wage. Aggregate substitution terms S_hk describe the input of factor h with respect to the price of factor k, a positive (negative) S_hk indicating substitutes (complements) as developed by Jones and Scheinkman (1979). Constant returns imply Σ_hw_hS_hk = 0 and rescaling factors to w_h = 1 implies Σ_hS_hk = 0. The comparative static model in (1) is derived with full employment in the first four equations and competitive pricing in the last two. Returns to capital are r_X and r_M in the system

S_LL S_LS S_LX S_LM a_LX a_LM dw dL 0

S_LS S_SS S_SX S_SM a_SX a_SM ds dS 0

S_LX S_SX S_XX 0 a_XX 0 dr_X = dK_x = 0 (1)

S_LM S_SM 0 S_MM 0 a_MM dr_M dK_m 0

a_LX a_SX a_XX 0 0 0 dq_X dp_x 0

a_LM a_SM 0 a_MM 0 0 dq_M dp_m dp_m .

Consider a comparative static decrease in the import price p_M in the vector of exogenous variables holding the export price p_X and factor endowments constant in the last column of (1). Chang (1979) shows this system determinant is positive with neoclassical production. Cramer’s rule leads to the solution δw/δp_M.

With no loss of generality, rescale products to unit capital inputs a_MM = a_XX = 1 and standardize inputs to a_SM = a_SX = a_LX = 1. Also assume skilled labor is a substitute for other inputs and labor a substitute with export capital in the substitution terms S_LS = S_LX = S_SX = S_SM = 1. The focus is squarely on labor and import capital in the a_LM term for factor intensity and the S_LM term for substitution.

Suppose a_LM = 1.1 making the import sector labor intensive, and S_LM = -0.1 with labor and import capital complements. It follows that δw/δp_M = -0.02, an elasticity with the scaling. A fall in the import price raises the wage, the expanding export sector substituting toward labor as its capital price increases. As the price of import capital falls, the declining import sector increases demand for complementary labor. If labor and import capital were substitutes and S_LM = 1 it would follow that δw/δp_M = 0.18 and the real wage would rise if labor spends more than 18% of its income on imports.

In specific factors models, the only necessary effect of a falling import price on the real wage occurs if labor is specific to the import competing sector and there is a single shared factor.

4. Prices and wages with monopolistic pricing

Monopoly price searching introduces demand and optimal pricing to the general equilibrium. Melvin and Warne (1973) and Casas (1989) analyze the aggregate utility effects of trade with monopoly pricing on world markets by domestic monopolies.

Thompson (2002) shows monopolistic pricing can be modeled as a parametric relaxation of competitive pricing, and the wage effect of a lower import price is then weaker but in the same direction as in the competitive model. If a labor intensive import competing monopoly in a small open economy faces the exogenous international price p_M, the wage falls with the import price but by less than with competitive pricing and may fall by less than the import price. The implication is that a relaxed magnification effect with monopoly pricing.

Introducing domestic demand, imports are the difference between quantity demanded q_D and optimal output q_opt. With a lower import price, q_opt falls and q_D rises implying increased imports. Higher domestic income reinforces imports if they are normal products.

As in the previous sections there is no prediction of a wage effect beyond the minimal number of inputs. Similar conclusions hold with monopolistic competition in the import competing sector with average cost equal to the import price.

5. Conclusion

Various strands in the trade theory literature stress broken connections between the import price and the wage relaxing sufficient conditions such as elastic factor supply, full employment, perfect factor markets, competitive pricing, and constant returns. Thompson (2003) shows, however, that the link is robust to parametric specifications of these relaxed assumptions. The present paper stresses that the link is not necessary when more than the minimal number of inputs are included in the general equilibrium.

The empirical literature examining relative wages seems to implicitly disregard capital and natural resource inputs. With more than the minimal number of inputs, there is no simple theoretical prediction regarding the wage. The lesson of the present paper is that any study claiming evidence relevant to the Stolper-Samuelson theorem must be based on an explicit general equilibrium model with only two factors of production.

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