When does a unprofitable firm shut down?

Like many questions in economics

the answer is it depends.

Let's go back to our firm cost graph.

Remember, we've got costs and revenues

in dollars per unit

on the vertical axis,

and the firm's output on the horizontal.

We've seen that

sometimes the market price can drop

below the break-even point for a firm.

This causes the firm to lose money

on every item it produces.

First we need to make a distinction

between the short-run and the long-run.

In the short-run

the firm can change its variable costs;

raw materials, inputs, and wages

by changing its level of output

but it can't change its fixed costs

like capital, advertising, or research.

In the long-run the firm is free

to change both variable and fixed costs.

The firm's choice in the long-run is clear,

if the market price is below the break-even

and is expected to stay there;

the firm will always shut down

in the long-run

and can even exit the industry.

Unless it has a dollar printing press

in its basement

no firm can keep spending

more than it's making year after year.

In the short-run, however,

the firm has a choice to make.

When the market price is so low

that the firm is making losses,

the firm is faced with two bad options

and it needs to pick the one

that is less bad.

The first bad option

is to keep producing at a loss

in the short-run

even though you know

you'll exit in the long-run.

As always the firm picks the output

where marginal cost is equal

to marginal revenue.

The per unit loss

is the difference

between the average total cost and the price

and the total loss is that

per unit loss times the number of units.

The firm picks this quantity

because any other quantity

would actually give it a much worse loss.

The second option

is to shut down immediately

in the short-run.

Output goes to zero

which means revenue goes to zero

and variable costs go to zero.

However, by definition in the short-run

the firm is still stuck

with paying its fixed cost.

So the loss in this case

is equal to the fixed cost.

The firm will choose

whichever path results in a smaller loss

and that actually depends

on the often-overlooked average variable cost.

We know that when price equals

minimum average total cost,

the firm is just breaking even.

At a higher price it's making profits

and at a lower price it's making losses.

For deep mathematical reasons

that we won't explore here

it turns out

that minimum average variable cost

is the break point

between producing for a loss in the short-run

and shutting down in the short-run.

At prices between minimum ATC and minimum AVC

the loss incurred by producing

is smaller than the fixed cost.

So rather than shutting down

and trying to pay your fixed cost

without any revenue,

it's better to produce at that smaller loss.

At prices below minimum AVC

the loss from production

actually grows larger than the fixed cost.

So it's actually better to shut down

on the short-run

and pay the fixed costs

you are stuck with

even without any revenue.

Remember that the firm's

marginal cost curve

is really its supply curve.

Tell it a price

and the marginal cost tells them

how much to produce

to maximize profits or minimize losses.

Our shutdown rule

breaks the marginal cost curve

into three parts.

At prices above minimum ATC,

you're making profits

so go ahead and produce.

At prices between minimum ATC

and minimum AVC

you'll keep producing at a loss

in the short-run

but shutdown in the long-run

when you can get out

from under your fixed costs.

And at prices below minimum AVC

you want to shut down immediately

in the short-run.

That's why some textbooks

will show the firm's

supply curve like this.

Production will always be zero

at prices below the minimum AVC.