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LONG PERIOD ANALYSIS:
Long period refers to a time when all the factors are variable. Earlier in the short period analysis, we had considered capital (K) to be fixed factor. Here in this part, we assume both L and K to be variable factors. Therefore, the production function would be:
q = F(L, K)
The producer can now employ L and K units at her will to produce output q as per the production technology. Therefore, in the K - L input space the producer can choose any combination of K and L to produce output.
Slutsky Theorem - Mathematical Presentation: We already know from the first order conditions of utility Maximisation that, where D ij is the co-factor of the ith ro
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