An interrelated factor demand approach was used to study the long-term productivity of and demand for inputs in the Canadian lumber industry covering the period of 1955 to 1982. The long-run, least-cost amounts of labour, capital, roundwood, and energy were obtained by imbedding a cross-stock adjustment process in the share equations of the translog cost function. These least-cost amounts, from which the short-run adjustments were removed, were then used to obtain the long-run productivity of each input. The percentage deviations of the observed amounts of each input from their least-cost levels were computed to determine the degrees of allocative inefficiencies with respect to the individual inputs. Similar deviations of the observed productivity and real total factor costs from their long-run levels were also computed. The results indicated that (i) factor demands in the Canadian lumber industry are actually interrelated, i.e., a disequilibrium in the demand for an input creates compensating adjustments in the demand for other inputs; (ii) there are economies of scale in production of lumber in Canada, but technological progress is unobservable; (iii) simulation of the actual and the least-cost paths of factor utilizations indicated substantial misallocation of each input over major parts of the sample years; (iv) the observed labour productivity increased at the rate of 2.9% per annum while, net of short-run conditions, the rate was 3.7% per annum over the sample period; and (v) productivities of other three inputs declined both on the observed and the long-run productivity paths, but such declines were relatively slower on the long-run paths.
Interrelated Factor Demand with Nonconvex Adjustment Costs