Breakeven and shutdown points

What does a profit-maximizing firm produce?

Whatever the market structure, a firm maximizes profit by producing the quantity where marginal revenue equals marginal cost, provided marginal cost is rising. It then sets the price from the demand curve at that quantity.

$$MR = MC \quad (\text{with } MC \text{ rising})$$

Average revenue is revenue per unit, which is simply the price. Marginal revenue is the extra revenue from selling one more unit. A price taker sells every unit at the market price, so price, average revenue and marginal revenue are the same number. A firm with some pricing power faces a downward-sloping demand curve: to sell one more unit it must cut the price on all units, so marginal revenue is below price.

What counts as profit?

Economists measure profit after charging every cost, including the cost of the owners’ own money and time. Economic profit is total revenue less total economic cost, which is explicit (accounting) cost plus implicit cost.

Economic profittotal revenue less total economic cost

• Explicit (accounting) costs wages, materials, rent, interest
• Implicit costs Use it what the owners' capital and time could earn elsewhere at the same risk

$$\text{Economic profit} = TR - (\text{explicit costs} + \text{implicit costs})$$

A firm that earns exactly zero economic profit earns normal profit : its owners get the return their capital would earn elsewhere at the same risk, and no more. That is not a poor result. It is what competition pushes firms towards in the long run. A firm can show a positive accounting profit and still have negative economic profit.

Where is the breakeven point?

A firm breaks even when total revenue equals total cost, so price (average revenue) equals average total cost and economic profit is zero. For a price taker the breakeven point is the minimum of the ATC curve.

$$TR = TC \;\Leftrightarrow\; P = ATC$$

At that price the firm covers all its costs, fixed and variable, including the return owners could earn elsewhere. It is the best a firm can do when entry is easy, because any profit above it attracts competitors.

When should a firm shut down?

Memorize

In the short run the firm should stop when revenue does not even cover its total variable cost (TVC), that is when price is below average variable cost at every output. The shutdown point is the minimum of the AVC curve.

$$TR < TVC \;\Leftrightarrow\; P < AVC \;\Rightarrow\; \text{shut down}$$

The reason is the sunk cost logic. Some fixed costs, such as a lease that cannot be broken, are owed whether the firm produces or not. They cannot be avoided, so they must be ignored in the decision. What matters is whether producing adds more revenue than variable cost. If it does, the gap helps pay the fixed cost, and the loss is smaller than the fixed cost. If it does not, producing adds to the loss.

Compare revenue with cost

• TR ≥ TC Memorize price at or above ATC: breakeven or profit
  • Short run: operate
  • Long run: stay in the market
• TVC ≤ TR < TC Memorize price between AVC and ATC: a loss, but smaller than the fixed cost
  • Short run: operate at a loss each unit still adds to fixed cost
  • Long run: exit
• TR < TVC Memorize price below AVC
  • Short run: shut down loss equals the fixed cost
  • Long run: exit

Revenue vs cost	Short run	Long run
TR ≥ TC	Operate	Stay in the market
TVC ≤ TR < TC	Operate (loss smaller than fixed cost)	Exit
TR < TVC	Shut down (loss = fixed cost)	Exit

In the long run every cost is avoidable, so the test tightens: a firm stays only if revenue covers total cost, and it leaves otherwise.

$$\pi = (P - AVC)\,Q - TFC$$

The interactive below uses a bottler with U-shaped cost curves (minimum AVC EUR 8, minimum ATC about EUR 13.89), so its output changes with the price and its figures differ a little from the example above. The rules are the same.

Exam tip Two questions, in order: does price cover average variable cost (operate or not), and does it cover average total cost (profit or loss)?

How do you read breakeven off a table?

Use it

A firm with some pricing power has a falling price as it sells more, so you look for the rows where profit is zero or highest. Here demand is $P = 100 - 5Q$ and total cost is $TC = 140 + 20Q$ (Q in thousand units, money in EUR thousand).

Q	P	TR	TC	Profit
0	100	0	140	−140
2	90	180	180	0
4	80	320	220	100
6	70	420	260	160
8	60	480	300	180
10	50	500	340	160
12	40	480	380	100
14	30	420	420	0
16	20	320	460	−140

1. Breakeven at Q = 2 and Q = 14, where TR = TC. Between them the firm is profitable.
2. Maximum profit of 180 at Q = 8, where MR = 100 − 10Q = 20 = MC.
3. Revenue peaks at Q = 10 (MR = 0) with profit of only 160. Choosing the revenue peak is the classic mistake.

Go deeper Why sunk costs are ignored in the short-run decision

Only avoidable costs change with the decision. A non-cancellable lease costs the same whether the plant runs or sits idle, so it cannot tip the balance. Counting it would make a firm that covers its variable cost shut down and lose the whole fixed cost for nothing. The same logic applies in everyday decisions: money already spent and unrecoverable should not decide what to do next.

Go deeper Normal profit versus accounting profit

Accounting profit subtracts only explicit costs. Economic profit also subtracts the return the owners could have earned elsewhere. A firm can report a healthy accounting profit and still earn less than its capital would earn in an alternative of equal risk. Analysts use that gap to judge whether a business is really creating value.

Go deeper How long is the long run?

It depends on the industry. A coffee cart can add or drop equipment in weeks. A smelter or a chip plant takes years to build or to retire. The long run is simply the period over which every input, including the plant, can be changed and firms can enter or leave. Analysts apply the same breakeven logic to start-ups and turnarounds: how far can sales fall before the business stops making sense?