# Economic Analysis of Limitation Laws

• Ragnar Frisch

## Abstract

Let us consider a variation within the reduced factor diagram (v 1, ..., v n ) with v n +1,..., v n as shadow factors. When we speak of a partial variation we mean — as in the case of (12j.2) and (12j.3) — a partial variation within the reduced factor diagram, with the shadow factors always following. Let q 1 ..., q n , q n+1, ..., q N be the factor prices. We shall call the cost of the basis factors, that is to say, those on which the reduced product function depends:
$$The{\kern 1pt} reduced{\kern 1pt} \cos t = {q_{1}}{v_{1}} + \ldots + {q_{n}}{v_{n}} = \sum\limits_{{i = 1}}^{n} {{q_{i}}{v_{{_{i}}}}} \left[ {cf.(10a.1)} \right]$$
(13a.1)
By contrast we have
$$The{\kern 1pt} reduced{\kern 1pt} \cos t = b = {q_{1}}{v_{1}} + \ldots + {q_{n}}{v_{n}} + {q_{n}} + {}_{1}{v_{n}} + 1 + \ldots + {q_{N}}{v_{N}} = \sum\limits_{{i = 1}}^{n} {{q_{i}}{v_{{_{i}}}}}$$
(13a.2)
.

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