# Production for multiplant firm?

A multi-plant firm will never produce at a plant with an increasing marginal cost when they own another plant with a decreasing marginal cost. Is this true?

My reasoning behind this is that firms would want to minimize their cost so they would prefer to produce at a plant with a decreasing marginal cost.

• Does decreasing marginal cost imply that it is smaller than the increasing marginal cost? If not, I don't understand your reasoning. If yes, why? – Giskard Nov 12 '19 at 18:16
• @Giskard Wouldn't the cost of the additional unit produced be cheaper for the plant with the decreasing marginal cost? The total cost will therefore be lower if the firm owner produce from the plant with decreasing marginal cost. – MGInt Nov 12 '19 at 19:09
• Would the cost of the additional unit produced be cheaper for the plant with the decreasing marginal cost? Why? – Giskard Nov 12 '19 at 19:13
• The trick is that, though at a cursory glance it seems that if the sequence $a_n$ is decreasing in $n$, $\lim_{n\to \infty} a_n = -\infty$ is true, this is not the case. As a counterpoint: one can (probably) think of several sequences where $\lim_{n\to \infty} a_n = 0$. Perhaps it is also possible that $\lim_{n\to \infty} a_n = 1$? – Giskard Nov 12 '19 at 19:14
• Looking at your list of questions: you are asking about 2SLS but you do not understand limit terms? That seems like a peculiar economics program. – Giskard Nov 12 '19 at 19:35