Production structure of the sawmilling industry of the Lake States (Michigan, Minnesota, Wisconsin)

This study examined the production structure of the sawmilling industry of the Lake States (Michigan, Minnesota and Wisconsin) in order to determine elasticities of substitution, elasticities of demand, technological change, the bias of technological change and returns to scale. A homogeneous translog cost function was estimated using pooled time-series data for the period 1963–1996.; Results for the Allen Partial Elasticity of Substitution (AES) indicate that labor and materials were inelastic substitutes while labor and capital were elastic complements. Materials and capital were also inelastic substitutes. Materials and capital have the greatest substitutability but only slightly more so than labor and materials.; The Morishima Elasticity of Substitution (MES) results indicate that all three inputs were inelastic substitutes with the greatest substitutability between capital/material. The results for the substitutability of labor/material and material/labor were similar to the AES results. The labor/capital and material/capital rates of substitution were much less than the capital/labor and capital/material rates.; The own-price elasticities of demand were all inelastic and negative indicating downward sloping demand curves. All other elasticities were inelastic and indicate that materials was a substitute for labor and capital but labor and capital were complements. Changes in the price of materials had a relatively large, but inelastic, effect on the demand for capital with a cross-price elasticity of 0.56. Changes in the price of labor also had a relatively large effect on the demand for capital, but in a complementary fashion, with an elasticity of −0.46. Changes in the price of materials had a greater effect on the demand for labor than the other way around with cross-price elasticities of 0.55 and 0.30, respectively.; Variable costs increased by 0.8% per year over the study period ceteris paribus. The results for bias of technical change showed that it was materials and capital-using and labor-saving. The labor savings were not as high as other lumber producing regions of North America with an average value of −0.62%/year. The bias of technical change for materials was 0.31%/year and for capital, it was 0.30%/year. These figures are important in that they may limit the competitiveness of the industry in the Lake States with respect to other regions because labor productivity was not increasing as fast as it was elsewhere.; The hypothesis of constant returns to scale could not be rejected at the 1% level. This was common for studies of the sawmill industry but seems particularly common to regions where the industry was made up primarily of small mills. Constant returns to scale in a mature sawmill industry would lead to the outcome of many mills of similar size as all economies of scale have been exhausted and the industry has settled into an equilibrium firm size near the minimum of the long run cost function. Nevertheless, this does not explain why the average mill size in the Lake States is small compared to the Pacific Northwest and Southeastern U.S.