A Study on the Difference of Heterogeneous Firms in Productivity, Production Scale and Production Technology

Abstract

Lots of empirical researches using firm-level data from several countries have proved that there is substantial difference in productivity, production scale and production technology of firms which are classified into same industry. This document constructs a theoretical model to explain this phenomenon and uses micro-level data in China to testify the theoretical conclusion. The result indicates that foreign export affiliates, foreign affiliates, domestic export firms and domestic firms are significantly different in the production scale, productivity, and production technology. Introduction Lots of recent empirical researches using firm-level data from several countries have proved that there is substantial difference in productivity, production scale, production technology of firms which are classified into same industry. Bernard (1995) used U.S. data to analyze the difference between export firms and non-export firms. It indicated that not all firms in the same industry choose to export, and the productivity and production scale of export firms are much bigger that non-export firms [1]. Aw and Hwang (1995) by using data from Taiwan indicated that productivity and production scale of export firms is significant higher than non-export firms’ [2]. Dixit and Stiglitz (1977) constructed a monopolistic competition model and brought the heterogeneous goods into theoretical research. Hopenhayn(1992) set up a heterogeneous-firm model with exogenous firm’s markups because of symmetric elasticity of substitution between final varieties [3]. Bernard Eaton Henson and Kortum (2000) henceforth BEJK also introduced heterogeneous firms into a theoretical model combined with industry-specific factor comparative advantage, based on Dormbush (1997) and indicated that only firms with higher productivity will serve the foreign market by exporting [4]. Melitz (2003) is another footing stone for heterogeneous-firm researches. Melitz (2003) based on Hopenhayn (1992) incorporated productivity difference between firms and develop the Krugman(1980) and concluded that the firms with highest productivity will export, the firms with second highest productivity will produce domestically and the firms with the lowest productivity will exit the market[5]. Although the assumptions of BEJK model and Melitz (2003) are different, both of them considered that there is difference between firms in the same industry and their strategies are different as well. Then Grossman (2006) based on Melitz (2003) and Yeaple(2003) and constructed a theoretical model on optimal strategies of heterogeneous firms which concluded that firms with least productivity will exit market, firms with middle productivity will produce and sale the final goods domestically, the firms with high productivity will export to foreign market and firms with the highest productivity will choose FDI strategy [6]. This document constructs a theoretical model to explain the difference of firms in same productivity, production scale and production technology, and use micro-level data in China to testify the theoretical conclusion. Setup of the Model Production There are two countries in the world. Home country is abundant with labor, while foreign country is abundant with capital. There are two sectors of producing final goods, one is sector Y producing International Conference on Management Engineering and Management Innovation (ICMEMI 2015) © 2015. The authors Published by Atlantis Press 187 homogeneous final goods y, and the other is sector X producing heterogeneous goods. Two kinds of factors are important to production, which are labor and capital. Production of homogeneous good y only needs 1 unit labor input. Heterogeneous good xi is assembled by intermediate good mi without any variety cost. Intermediate goods mi can be produced in both home country and foreign country but only be assembled into final good xi in home country. Intermediate good mi is capital intensive and its marginal cost function is   1 j w j j r C  , 2 1   and F , H j  (1) where r is capital income and w is labor income. Each heterogeneous firm entering into X sector has pay a fixed cost of e f and know its productivity i  . Production of Intermediate good in foreign country needs fixed cost of p f . Therefore foreign country has variety cost advantage of producing intermediate good but has an additional fixed cost for production. Demand Both countries have the same preference of representative consumer which is     1 X Y U , s.t.    i i y x p y E p j (2) where py is the price of homogeneous goods y and pi is the price of heterogeneous goods xi in sector X and     / 1 i x   X . Ej is national income of country j. The demand of heterogeneous good xi in country j is