Assuming perfect competition, I think that firms are price takers in the labor/capital markets as well (in the short and long run), correct?
And I know that the Long-run total cost curve is derived by getting
- a production function q
- having a given wage and rental rate (price of labor and capital)
- optimizing C given q and plugging in w and r.
Then we differentiate LRTC to get Long-run MC and equate that to the price (MR) and that gives us the amount to produce.
Therefore the LRTC function is really a function of 3 inputs, we just keep r and w constant and say that it is a function of only q.
But in the short run, aren't w and r still constant? R certainly is. In that case, how is the LRTC different (mathematically) from the SRTC?
In other words, how is production determined in the short-run? If it's all the same, how is LRTC different from SRTC? Is it also a function of q, as well as w and r?