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The long run expansion path of a firm will not be linear when for higher levels of outputs the optimal mix of labor and capital changes. This causes the Isoquant's slope to be different at each level of output and makes the expansion path bend.
Whether this exists in real life or not, I don't know. I can think of an example though. For smaller scale operations a different "type" of capital could be used that requires more labor to be utilized. Maybe a small landscaping company choses to use shovels for a small project and a backhoe for a larger project, which requires less labor.
For the short run capital is fixed, so in that case the firms expansion path will always be linear.
hope this helps.
What else can I help you with?
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