Factor Demand In The Sawmill Industry Of The Lake States

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 and elasticities of demand. A homogeneous translog cost function was estimated using pooled time-series data for the period 1963-1996 with inputs labor, materials and capital. Based on the model selection process, the estimated model imposes constant returns to scale and allows for nonunitary elasticities of substitution amongst the inputs. 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 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 average cost curve. 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. Results for the Allen Partial Elasticity of Substitution (AES) indicate that labor and materials were inelastic substitutes with an elasticity of 0.76 while labor and capital were elastic complements with an elasticity of -1.38. Materials and capital were also inelastic substitutes and had an elasticity of substitution of 0.80. The labor/materials elasticity of substitution is high compared to almost all studies of softwood lumber producing regions. The Morishima Elasticity of Substitution (MES) results indicate that labor/materials, materials/labor, materials/capital, capital/materials and labor/capital were inelastic substitutes with the greatest substitutability between labor/materials. The MES for capital/labor was -0.017 indicating a complementary relationship. 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 0.51. 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 -0.44. 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 0.48 and 0.24, respectively.