Industrial and Environmental Applns of Direct and Large-Eddy by S. Biringen, et al.,

By S. Biringen, et al.,

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Example text

Taking Vm as the dependent variable in the equation of the isoquant X(VI' V2, ... , vm)=x, the partial derivatives 15vm /15v, (i=l, 2, ... , m-1) at a point of the isoquant represent the directions of the tangent plane at the point; they are continuous and differentiable functions of VI, V2, ... , Vm-l in the interior of the region of substitution so that factor substitution-movements along the efficient part of the isoquant-is continuous, characterized by continuous variation in the marginal rates of substitution.

N) (3) since negative output is economically meaningless. Finally, for those inputs which represent the services of fixed factors we have capacity limitations of the form (4) This is the linear production model. Its linear properties are implicit in the underlying assumption that the input-output proportions VUe I Ak are independent of the particular Ak (constant coefficients of production within each activity) as well as of all other activity levels 1 ; the activities are then divisible and additive so that total output and total inputs are linear functions of the activity levels.

If the inputs are available in amounts corresponding to point P in Fig. 7 (the technology being the same as in Fig. 6), the maximum output that can be produced is the same as in point D; the amounts consumed of the two inputs are also the same, that part of WI which corresponds to DP being wasted. Hence the isoquant consists not only of the broken line ABO D but also of half-lines from A and D parallel to the axes, as shown in Fig. 7. g. P), though representing maximal x for given WI and W2, are inefficient in that it is possible to produce the same x with less of one input and the same amount of the otherl.

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