✦ Simulator

When losing money is the right decision.

A firm that cannot cover its costs should close. That sounds obvious and it is wrong, and working out exactly why is what the shutdown point is for. Drag the price and watch a business decide whether to keep the lights on.

Profit at this price
$0  
The diagram
The firm produces where the price line meets marginal cost. The shaded rectangle is profit if green and loss if red, measured as the gap between price and average total cost across every unit sold.
marginal cost average total cost average variable cost
Marginal cost is drawn solid above the shutdown point and dashed below it. The solid stretch is the firm's supply curve, and adding it up across every firm is where the market supply curve comes from.
The same thing in totals
The vertical gap between total cost and total variable cost is the fixed cost, and it never changes with output. That constant gap is why the shutdown rule ignores fixed costs.
revenue total cost total variable cost
The market
This firm is small enough that it takes the price as given.
The cost structure
Fixed costs are owed at any output. The other three describe how the cost of actually making things behaves.
$
Average variable cost is a simple bowl: lowest at the efficient scale, rising in both directions. Marginal cost always cuts through the bottom of that bowl.
How the model works

The cost of making things

Average variable cost is a bowl centered on the efficient scale. AVC = a(q − q*)² + m

Everything else follows

Multiply by output for the variable total, add the fixed cost, divide back out for the average. ATC = FC/q + AVC

Marginal cost

The derivative of total cost. It passes through the bottom of the AVC bowl exactly at the efficient scale. MC = a(q − q*)(3q − q*) + m

How much to make

Set price equal to marginal cost and take the rising branch. 3aq² − 4aq*q + aq*² = P − m

The two thresholds

Shut down below the bottom of AVC, which is simply m. Break even at the bottom of ATC, found where marginal cost crosses it.

Profit

The gap between price and average total cost, across every unit sold. π = (P − ATC)·q

What you are actually watching

This is the diagram that explains where the supply curve comes from, and it contains one deeply counterintuitive result: a firm losing money every month can be making exactly the right decision by staying open.

Why marginal cost cuts through the bottom of the averages

The most striking feature of the diagram is that marginal cost passes through the lowest point of both average curves. That is not a coincidence or a drawing convention, it is the arithmetic of averages.

Think about a batting average or a course grade. If the next score is below your average, the average falls. If it is above, the average rises. The average therefore turns exactly where the next value crosses it. Cost works identically: while one more unit costs less than the running average, the average is pulled down, and the moment it costs more, the average starts climbing.

This is why the shutdown point sits precisely where marginal cost meets average variable cost. There is no separate rule to memorise, the crossing is forced.

Why the firm produces where price meets marginal cost

A firm this small cannot move the market price, so it earns exactly the market price on every unit. The extra revenue from one more unit is therefore just the price.

So the question for each unit is simple: does it earn more than it costs? While the price is above marginal cost, making one more adds to profit. Once marginal cost passes the price, making one more subtracts. The best output is where they meet, on the rising part of the curve. Nothing about fixed costs enters that decision at all, which turns out to matter enormously.

The result that sounds wrong

Load the "Losing but still open" preset. The firm loses money at every level of output and it should still produce. This is what the diagram exists to show.

The fixed costs are owed whether the factory runs or not. The rent is due, the loan payment is due, the insurance is due. Those are sunk for this decision, and a cost you cannot avoid should never influence a choice.

So the only live question is whether the revenue from a unit beats the cost of making that unit. If the price is $15 and each unit costs $11 of materials and labour, every unit sold contributes $4 toward the rent. Producing loses money. Closing loses more money, because the rent still arrives and nothing comes in to offset it. Between the break-even price and the shutdown price, staying open is the cheaper of two bad options.

Two prices worth knowing apart

The break-even price is the bottom of average total cost. At exactly that price the firm covers everything, including the fixed costs, and earns zero economic profit. Above it, there is real profit.

The shutdown price is the bottom of average variable cost, and it is always lower. Below it, no output level covers even the direct cost of production, so making anything makes the hole deeper.

The gap between the two is where the interesting cases live. Load the heavy fixed costs preset and look at how wide that band becomes. An airline with enormous fixed costs and a low cost per extra passenger can sit in that band for years, visibly losing money, entirely rationally. That is also why the last seats on a flight get sold so cheaply: anything above the cost of carrying one more passenger is worth having.

Where the supply curve actually comes from

Drag the price up and down and watch the chosen output move along the marginal cost curve. For every price above the shutdown point, the firm's output is read straight off marginal cost. That relationship between price and quantity supplied is a supply curve.

The firm's supply curve is its marginal cost curve above the shutdown point, drawn solid on the diagram. Add that up across all the firms in a market and you have the market supply curve, the upward-sloping line in every supply and demand diagram. It slopes up for one reason: costs rise as firms push past their efficient scale.

What this model leaves out

This is a price taker in perfect competition, so it sells all it wants at the market price and has no pricing power. A firm with market power faces a downward-sloping demand curve and stops well short of this output, which is the monopoly case.

Fixed costs here are truly unavoidable in the short run. Real firms can often shed some of them by subletting space or ending a contract, which pushes the effective shutdown price up. There is no time dimension, so nothing captures the cost of mothballing a plant and restarting it later, which is why real firms tolerate losses below the theoretical shutdown price rather than close. And "economic profit" counts the return the owners could have earned elsewhere, so zero economic profit is a perfectly acceptable outcome rather than a disaster.

Things to try

Each takes a few seconds and lands a point the diagram alone will not.

1Cross the shutdown point

Lower the price a dollar at a time through $10. Watch output shrink, then jump to nothing the moment price drops below the bottom of average variable cost.

2Prove fixed costs are irrelevant

Change the fixed cost from $200 to $600. The quantity produced does not move at all, because marginal cost is untouched. Only the profit changes.

3Find long-run equilibrium

Set the price equal to the break-even figure shown. Profit lands on zero and output sits at the bottom of average total cost, which is where competition drives everyone.

4Widen the danger band

Load the heavy fixed costs preset and compare the two threshold prices. The bigger the fixed costs, the longer a firm can rationally bleed.

5Flatten the cost curve

Drop the cost steepness toward 1. Marginal cost flattens, the firm becomes far more responsive to price, and its supply curve gets much more elastic.

6Trace out the supply curve

Note the output at four or five different prices and plot them. You have just derived the firm's supply curve by hand from its costs.

Common questions about costs and the shutdown point

Why does a firm keep producing while losing money?

Because the fixed costs are owed whether it produces or not. If the price covers the variable cost of making each unit and leaves anything over, that surplus goes toward the rent and loan payments the firm owes regardless. Shutting down would mean losing the entire fixed cost rather than only part of it, so producing at a loss is frequently the smaller of two losses. It stops being the right call only when the price falls below average variable cost.

What is the shutdown point?

The lowest point on the average variable cost curve. Below that price there is no level of output where a unit earns back even its own variable cost, so every unit produced adds to the loss and the firm does better producing nothing. Marginal cost passes through average variable cost exactly at its minimum, which is why the shutdown point sits at that crossing rather than somewhere arbitrary.

Why does marginal cost cross average cost at its lowest point?

It is the arithmetic of averages rather than anything specific to economics. While the next unit costs less than the running average, it pulls the average down. Once the next unit costs more than the average, it pulls the average up. The average therefore stops falling and starts rising precisely where marginal cost passes through it, which is exactly how a batting average or a course grade behaves.

Why produce where price equals marginal cost?

A price-taking firm earns the market price on every unit it sells, so the extra revenue from one more unit is simply the price. While the price exceeds the cost of producing that unit, making it adds to profit. Once the cost of the next unit exceeds the price, making it subtracts from profit. The best output is therefore where the two are equal, taken on the rising part of the marginal cost curve.

What is the difference between the shutdown price and the break-even price?

The break-even price is the bottom of average total cost, where the firm covers everything including fixed costs and earns exactly zero economic profit. The shutdown price is the bottom of average variable cost, which is always lower because it ignores fixed costs entirely. Between the two the firm loses money but still covers its variable costs, so it keeps operating in the short run and exits only if the price is expected to stay there.

How does this connect to the market supply curve?

The firm's supply curve is its marginal cost curve above the shutdown point, because for any price in that range the firm chooses the output where price meets marginal cost. Add up that portion across every firm in the market and you have the market supply curve. This is where the upward-sloping supply line in a supply and demand diagram comes from, and it slopes up because costs rise as firms push past their most efficient scale.

Is zero economic profit a bad outcome?

No, and the name is misleading. Economic profit is measured after subtracting what the owners could have earned by putting their money and effort somewhere else, so zero economic profit means the business is doing exactly as well as the next best alternative. An accountant would still record a healthy profit. It is the outcome competition drives firms toward in the long run, not a sign of failure.

About this model: a single price-taking firm in perfect competition, with a smooth cost curve, fixed costs that cannot be shed in the short run, and no cost to stopping and restarting production. Real firms face lumpy capacity, partly avoidable fixed costs, and switching costs that make them tolerate losses below the theoretical shutdown price. Use this to understand the logic of the two thresholds, not to decide whether an actual business should close.