The diagram above is a simplified version of the below diagram. In the above diagram, it assume average revenue is constant, making marginal revenue constant as well. This means there is only one line for both MR and AR, so explanation is much simpler.
In the short-run, as long as a firm can cover its variable cost, it will continue production,
even if fixed costs are not covered.
IF the firm shuts down, it will incur a
greater loss than if it continues production. The firm will at least make a little contribution to covering fixed costs if it continues production, but if it shuts down,
all fixed costs are lost.
So the firm stays in the industry as long as its AR is even a little greater than AVC.
But, if a firm isn't able to cover the variable cost, it will cease production. This is because all the fixed cost cannot be covered anyway, and remaining in business would yield greater losses.
So the shutdown point is when the firm earns less than its variable cost.
So:
Shutdownpoint=>AVC=ARIn the diagram, average revenue(P
2) is less than average variable costs(P
3) so it will cease production.
However this is in the
short run, so the firm is only interested in covering up fixed costs. But in the long run, the firm will shutdown even if it earns less than the Total Cost. Just remember that. But if you want an explanation, see the spoiler.
To sum up,
In the short-run, the firm will shutdown if
AVC>ARIn the long-run, the firm will shutdown if
AC>AR.
I don't know how to simplify this further, so anyone else is welcome to do better explanation or point out any flaws in mine.