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# Determining long run equilibrium output

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A perfectly competitive constant cost industry contains a number of firms, each of which has the following long-run total cost function, where q is annual output:
TC = 0.01q3 - 1.2q2 + 111q
The market demand curve for the product is:
Q = 5,800 - 20p
where Q is annual industry sales.
(a) Calculate the long-run equilibrium output of the industry.
(b) How many firms are there in the industry in long run?

https://brainmass.com/economics/general-equilibrium/determining-long-run-equilibrium-output-212689

#### Solution Preview

Please refer attached file for better clarity of algebraic expressions.

Solution:

TC = 0.01q3 - 1.2q2 + 111q
Average Total Cost = TC/Q=0.01 q2 -1.2q+111
d(ATC)/dq=0.02q-1.2
We are ...

#### Solution Summary

The solution describes the steps for finding long run equilibrium output for perfectly competitive environment. It also determines number of firms working in long run.

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