Revenue, Costs and Profits
Revenue, Costs and Profits
FREE RESOURCES
EXAM RESOURCES
PREMIUM
Total revenue is all the money a firm receives from its sales: the price of each unit times the number sold.
Ravelo, a small firm that bottles drinking water in the town of Minto, sells crates of bottled water. Its owner is Amira. Every day, buyers in Minto pay Ravelo for the crates they buy.
Total revenue (TR): the total amount a firm receives from selling its output.
Put simply, total revenue is all the money from the day's sales, counted before Ravelo pays for anything. Today Ravelo sells 80 crates a day at $30 each, so $2,400 comes in each day.
Revenue is not profit. Profit is what is left after the firm's costs are paid. So a firm can receive $2,400 a day and still lose money, if its costs are more than $2,400 a day.
How many crates Ravelo can sell depends on its price. A table of the quantity demanded at each price is a demand schedule. This is Ravelo's demand schedule in Minto, and its last row multiplies the price by the quantity.
Each total revenue figure has a meaning. At $40, Ravelo sells 40 crates, so it receives $1,600 a day. At $25 it sells 100 crates and receives $2,500, the most anywhere on the schedule.
As the price falls from $45, total revenue rises at first. It is greatest at $25 and 100 crates. Below $25 it falls again, back to $900 at $5. So a lower price does not always bring more revenue. Two things change at once: Ravelo sells more crates, but each crate sells for less.
Exam Matters: When a question gives a price and a quantity, write the price times the quantity with both figures, then the answer with its time period, such as $1,600 a day.
Average revenue is the revenue a firm receives for each unit it sells, and when every unit sells at one price it equals that price.
Average revenue (AR): total revenue per unit sold.
Put simply, average revenue is what one crate brings in once the day's total revenue is shared equally among all the crates sold. Work it out from two columns of Ravelo's demand schedule.
Every crate sells at the same price, so each crate brings in that price. When every crate brings in the same amount, the average per crate is that amount. So when every unit sells at one price, average revenue is the price.
The demand curve shows, for each quantity, the price buyers will pay. That price is Ravelo's revenue per crate, so the demand curve is also the average revenue curve.
Some firms can sell any quantity they choose at one price. For such a firm, each extra unit brings in that same price, and the units already sold keep their price. So average revenue and marginal revenue, the extra revenue from one more unit, both equal the price. On a diagram, AR and MR are one horizontal line at that price.
Ravelo is different. To sell more crates, it must lower its price, so its AR curve slopes downwards: from $45 at 20 crates to $5 at 180. Its marginal revenue lies below the price, because the lower price must be paid on every crate it sells, not only on the extra ones.
Marginal revenue is the extra revenue from one more unit sold. It is below the price when a lower price applies to every unit.
Marginal revenue (MR): the change in total revenue from selling one more unit.
Put simply, marginal revenue tells Ravelo what selling more crates adds to its revenue, per extra crate. Ravelo's schedule moves in steps of 20 crates, so MR is the change in total revenue divided by 20.
Ravelo sells 40 crates a day at $40. To sell 60, it must charge $35. Ravelo charges one price to all its buyers in Minto. So at $35, buyers pay $35 for every crate, including the 40 that used to sell at $40.
Why doesn't total revenue rise by the full $700? Because the price cut costs Ravelo $200 on crates it was already selling. So each extra crate adds $25 to revenue, less than the $35 it sells for. Whenever a firm must lower its price on every unit to sell more, marginal revenue is below the price.
Read along the rows. On Ravelo's schedule, each step of 20 crates lowers AR by $5 but MR by $10, so MR falls twice as fast as AR. MR falls by $10 a step for two reasons. First, each new price is $5 lower. Second, each lower price is paid on 20 more earlier crates than on the step before. That loses another 20 × $5 = $100, or $5 more for each of the 20 extra crates.
MR is $5 on the step up to 100 crates and −$5 on the step after it. MR changes from positive to negative at 100 crates, so it is zero there. That is where total revenue is greatest, $2,500. Beyond 100 crates MR is negative: one more crate lowers total revenue, because the loss on the earlier crates is now larger than the gain on the extra ones.
Price elasticity of demand compares the percentage change in quantity demanded with the percentage change in price.
A price cut sells more crates but earns less on each. Whether total revenue rises depends on how strongly the quantity demanded responds.
Price elasticity of demand (PED): the responsiveness of the quantity demanded of a good to a change in its own price.
Put simply, PED tells you how many per cent the quantity demanded changes for each 1% change in price. It is negative, because a lower price raises the quantity demanded. Ignore the minus sign and look at its size. Above 1, the quantity demanded changes by a larger percentage than the price: demand is price elastic. Below 1, it changes by a smaller percentage: demand is price inelastic. At exactly 1, the two percentages are equal: demand is unit elastic.
Measure each percentage change against the value before the change, because a percentage compares a change with where it started. Divide the change by that starting value and multiply by 100. So the same $5 cut is a different percentage at different prices.
Both cuts start from a total revenue of $1,600. In the first, the 20 extra crates bring in $700 and the 40 earlier crates lose $200, so total revenue rises by $500. In the second, the 20 extra crates bring in only $100 and the 160 earlier crates lose $800, so total revenue falls by $700. The difference is where each cut starts. At $40, a 12.5% cut raises the quantity demanded by 50%. At $10, a 50% cut raises it by only 12.5%.
So PED is not one number for the good: it depends on where on the demand schedule the price change starts. Demand for Ravelo's water is price elastic at high prices and inelastic at low ones.
Exam Matters: In a Calculate question, show both percentage changes before the PED, and keep the minus sign in your answer.
Whether a price change raises or lowers total revenue depends on how price elastic demand is at that price.
Along Ravelo's schedule, PED changes, and so does what a price change does to total revenue. Demand is price elastic where the size of PED is above 1, unit elastic where it is exactly 1, and price inelastic where it is below 1. The pattern has three stretches.
How are PED and MR linked? When demand is elastic, a price cut raises the quantity demanded by a larger percentage than the price falls. So the gain on the extra crates, sold at the new price, is larger than the loss on the crates already sold. MR is positive, and total revenue rises. When demand is inelastic, the quantity demanded rises by a smaller percentage than the price falls. The gain is then smaller than the loss, so MR is negative and total revenue falls.
At $25, the middle of the schedule, PED is −1, so demand is unit elastic for a small price change. Total revenue is greatest there, $2,500, and MR is zero. A $5 step is not a small change, so on the schedule the balance is not exact: a $5 rise or a $5 cut from $25 lowers total revenue by $100 a day, to $2,400 a day.
A price rise has the opposite effect in each stretch. In the elastic stretch it lowers total revenue, because the quantity demanded falls by a larger percentage than the price rises. In the inelastic stretch it raises total revenue, because the quantity demanded falls by a smaller percentage than the price rises.
The gain is larger because the price rises by 50% but the quantity demanded falls by only 12.5%. This gives a test. If the price and total revenue move the same way, demand is price inelastic. If they move in opposite ways, demand is price elastic. If total revenue does not change, demand is unit elastic.
In the inelastic stretch, a higher price raises total revenue. Selling fewer crates also means producing fewer, which costs less. Profit is total revenue minus costs, so it rises on both counts. A firm that wants more profit would therefore not choose a price in the inelastic stretch.
When one factor of production is fixed, each extra worker eventually adds less output than the worker before.
Ravelo, the water-bottling firm in Minto, has one plant: a building with one bottling line. Amira can hire another worker today, but a new building and line would take months to arrange. Economists name these two periods by which factors of production can change, not by months. The factors of production are the inputs a firm uses: here, the building, the line and the workers.
Short run: the period in which at least one factor of production is fixed.
Long run: the period in which all factors of production can be varied.
Put simply, the short run is Ravelo today: more workers, but the same plant. The long run is long enough for Amira to change the plant itself. Its length differs by industry, because some factors take longer to change: a shop can often move in weeks, but a power station can take years to build.
In the short run, Ravelo can raise its output only by putting more workers on its one line.
At first, each new worker adds more than the one before: 10 crates, then 20, then 30. A worker alone must fill, cap, pack and load. With two or three workers, each one can concentrate on one or two of these tasks and does not stop to switch. So the line runs faster, and each new worker adds more crates.
Law of diminishing returns: as more units of a variable factor are added to a fixed factor, the extra output from each additional unit of the variable factor will eventually fall.
Put simply, once the plant is busy, each new worker adds fewer crates than the last. At Ravelo this starts with the fourth worker, who adds 20 crates, and the fifth adds only 10.
Why? The new workers are just as able. But the plant is fixed, so each new worker shares the same line with more people. Each one has less time on the line to work with, so each adds fewer crates. The fixed factor is spread thinner.
Notice the word "eventually": the extra output rose before it fell. Total output still rises, from 80 to 90 crates; only the extra output from each worker falls.
Exam Matters: When you explain diminishing returns, name the fixed factor in the case first. Then say why each extra worker has less of it to use.
Average product rises while each new worker adds more than the average, and falls once a new worker adds less.
Total product (TP): the total output produced by the factors of production employed.
Put simply, total product is Ravelo's whole output in a day: 60 crates with three workers.
Marginal product (MP): the change in total product from employing one more unit of the variable factor.
Put simply, marginal product is what the newest worker adds. The third worker raises total product from 30 to 60 crates, so the third worker's marginal product is 30 crates.
Average product (AP): total product per unit of the variable factor.
Put simply, average product is output per worker. Three workers bottle 60 crates, so the average product is 20 crates a worker.
How do the two rows affect each other? Think of a class's average mark. A new student with a mark above the average raises it. A mark below the average lowers it. A mark equal to the average leaves it unchanged. Each new worker's marginal product is added into the average in the same way.
AP rises while MP is above it, and it falls once MP is below it. So AP is at its highest where MP equals it: 20 crates a worker, with the fourth worker. On a diagram, the MP curve crosses the AP curve at AP's highest point. This is true of every marginal and its average, not only of workers and crates.
Some of a firm's costs change when its output changes and some do not, and total cost adds the two.
Ravelo pays two kinds of cost. Some stay the same however many crates it bottles. Others rise with its output.
Total fixed cost (TFC): costs that do not change with the level of output in the short run.
Put simply, a fixed cost is the same whether Ravelo bottles no crates or 90. Ravelo's total fixed cost is $720 a day. Of this, $600 is for the plant: the rent of the building and the loan on the bottling machine.
The other $120 is Amira's own cost. In her next best job she could earn $120 a day, so running Ravelo costs her that $120: it is her opportunity cost. Economists count it as a cost, because if Ravelo could not earn Amira at least $120 a day, she would do better to leave and take the other job. The $120 is the same however many crates Ravelo bottles, so it is a fixed cost.
Total variable cost (TVC): costs that change with the level of output.
Put simply, a variable cost grows as output grows. Ravelo's schedule counts one variable cost, its wage bill: the bottles and other inputs are left out to keep the sums short. Each worker costs $180 a day, so total variable cost is $180 for each worker it hires.
Total cost (TC): the whole cost of producing a given level of output.
Put simply, total cost is the full daily cost of bottling that many crates, Amira's $120 included.
With three workers, for example, Ravelo bottles 60 crates. Its total cost is $1,260 a day: the $720 fixed cost plus $540 for three workers' wages.
"Fixed" means a cost does not change when output changes. It can still change for other reasons. If the landlord raises the rent next year, the rent is still a fixed cost, because it does not change when Ravelo bottles one more crate.
In the long run, though, nothing is fixed. Amira can end the lease, sell the machine or take the other job. Every cost can then change with the firm's choices, so in the long run there are no fixed costs.
Each average cost shares a total cost over the crates produced, so it shows what one crate costs.
Total cost tells Amira what a day costs Ravelo. To compare her costs with the price of a crate, she needs the cost of one crate. Each average shares a total over the day's output.
Average cost (AC): total cost per unit of output.
Average fixed cost (AFC): total fixed cost per unit of output.
Average variable cost (AVC): total variable cost per unit of output.
Put simply, AC is the full cost of one crate. AFC is each crate's share of the plant and Amira's $120. AVC is each crate's share of the wages.
AC = AFC + AVC at every output, not only at 60 crates. Total cost is fixed cost plus variable cost, and both are divided by the same output.
AFC falls as output rises, because the same $720 is shared over more crates. However many crates Ravelo bottles, each crate still carries part of the $720, so AFC never reaches zero.
AVC falls from $18 to $9, then rises to $10 at 90 crates. Each worker costs the same $180, so AVC rises once the crates per worker start to fall: the fifth worker adds only 10 crates, fewer than the average.
AC falls steeply at first, because AFC falls fast. Later it follows AVC more closely. Between 80 and 90 crates, AVC rises from $9 to $10, but AC stays at $18, because AFC falls from $9 to $8 at the same time. So AVC reaches its lowest point first, at 60 to 80 crates, and AC reaches its lowest point later, at 80 to 90 crates.
Marginal cost is the extra cost of one more unit, and it decides whether average cost is falling or rising.
Marginal cost (MC): the change in total cost from producing one more unit of output.
Put simply, marginal cost is what one more crate adds to Ravelo's daily cost. Fixed cost does not change when output changes, so it has no effect on marginal cost. Only the variable cost counts.
Ravelo's output rises one worker at a time, so each change in output is a step of several crates, such as 20 crates from 60 to 80. Marginal cost is the change in total cost over one step, divided by the crates in that step.
So $9 a crate means that each of the 20 extra crates the fourth worker bottles adds $9 to Ravelo's total cost.
The lowest MC, $6, comes with the third worker. After that, diminishing returns push MC back up to $18.
Now compare MC with the averages. A marginal below the average pulls the average down, as a low new mark lowers a class's average, and a marginal above it pulls it up. So while MC is below AC, AC is falling, and once MC is above AC, AC is rising. AC stops falling and starts rising at the output where MC equals it, so MC crosses AC at AC's lowest point. The same is true of AVC.
Ravelo's schedule shows both crossings. From 60 to 80 crates, MC is $9, equal to AVC's lowest, $9. From 80 to 90 crates, MC is $18, equal to AC's lowest, $18. MC meets AVC first. AC is AVC plus AFC, so it lies above AVC, and MC must rise further before it reaches AC.
Ravelo pays every worker the same wage, so the cost of a crate depends on how many crates each worker adds.
Every worker at Ravelo costs the same $180 a day, but each adds a different number of crates. So the cost of a crate depends on the wage and on the crates that wage pays for.
Marginal cost is the cost of each extra crate. The extra crates come from the newest worker, who costs $180. So the marginal cost of a crate is the wage shared over that worker's marginal product.
Average variable cost works the same way with the average. AVC is the whole wage bill shared over the whole output. Three workers cost $540 and bottle 60 crates, so they cost $180 for every 20 crates, and 20 crates is the average product. So AVC is the wage shared over the average product.
MP and MC move in opposite directions. While MP rises, MC falls: $18, $9, then $6. Once diminishing returns make MP fall, MC rises: $9, then $18. AP and AVC also move in opposite directions, so AVC is lowest where AP is highest.
Total product and total cost show the same link. Total cost rises in equal steps of $180, one wage for each worker. Total product rises in unequal steps: 10, 20, 30, 20, then 10 crates. Where total product rises fast, each $180 pays for many crates, so the cost of a crate is low.
MP and AP both rise and then fall. So MC and AVC both fall and then rise: each is U-shaped.
In the long run a firm can choose its plant, so its long-run average cost is the lowest that any plant offers.
In the short run, Ravelo's plant is fixed, so it has one short-run average cost curve. It falls at first, as the fixed cost is shared over more crates, and rises later, once diminishing returns raise the cost of each extra crate. Its lowest point is $18 a crate, at 80 to 90 crates a day.
Each plant size has its own short-run AC curve. Suppose Amira could build a larger plant with two bottling lines, designed for 200 crates a day. With that plant, AC would be $16 a crate at 200 crates. At only 90 crates, it would be $26 a crate.
Why would the larger plant cost more at 90 crates? Its fixed cost is much larger: a bigger building and two lines. Shared over only 90 crates, that fixed cost makes each crate expensive.
So the cheaper plant depends on the output. At 90 crates, the small plant is cheaper: $18 a crate against $26. For 200 crates, only the large plant makes sense. On the small plant, each extra worker would add fewer and fewer crates, so its AC at 200 crates would be higher than its lowest, $18, and so higher than the large plant's $16.
In the long run, Amira can choose either plant, because all factors can be varied: the lease can end and the machine can be sold, so there are no fixed costs.
Long-run average cost (LRAC): the lowest average cost of producing each level of output when all factors of production can be varied.
Put simply, LRAC is the cost of a crate once Amira has picked the best plant for that output. For Ravelo, LRAC is $18 at 90 crates and $16 at 200.
So the LRAC curve is the lower edge of all the short-run AC curves: at each output, it is the lowest of them, the AC of the best plant for that output. It can never lie above a short-run curve. Keeping the plant it already has is always one of the firm's long-run choices, so its long-run cost can be lower than that plant's, but never higher.
As a firm grows in the long run, its cost per unit usually falls at first, then stays flat, and then rises again.
Ravelo, Amira's water-bottling firm in Minto, sells its crates only in Minto today. Amira plans to grow and to sell across the towns around Minto. First she wants to know what a crate would cost at each size.
These are long-run costs. In the long run every factor can be varied, so Amira can choose the plant as well as the workers. Each figure is the average cost of a crate when that output is made in the plant best suited to it.
From 90 to 400 crates a day, the cost of each crate falls from $18 to $11. A bigger Ravelo makes each crate more cheaply. This fall has a name.
Economies of scale: the fall in long-run average cost as a firm increases its scale of production.
Put simply, growing makes each unit cheaper to produce, so a bigger firm can charge less, or earn more on each unit, than a smaller one.
From 400 to 600 crates, LRAC stays at $11: growing neither lowers nor raises the cost of a crate. Beyond 600 crates, LRAC rises again, to $14 at 800.
Diseconomies of scale: the rise in long-run average cost as a firm increases its scale of production beyond a certain point.
Put simply, past a certain size a firm becomes harder to run, so growing makes each unit more expensive, not cheaper.
Minimum efficient scale (MES): the lowest level of output at which long-run average cost is at its minimum.
Put simply, MES is the smallest size at which a firm has all its economies of scale. Ravelo's lowest LRAC is $11, at both 400 and 600 crates a day. MES is the first output that reaches the lowest cost, so Ravelo's MES is 400 crates, not 600.
Why does MES matter? It tells you how large a firm must be to produce at the lowest cost. A Ravelo making 200 crates a day would pay $16 a crate, against $11 at MES. The region around Minto buys about 2,000 crates a day. That is enough for only about five firms producing 400 crates a day each.
Exam Matters: For a percentage change in LRAC, divide the change by the starting cost, not the new one, then multiply by 100.
An economy of scale is internal or external depending on whose growth lowered the cost: the firm's own, or its industry's.
Economies of scale lower long-run average cost as output grows. But the growth that lowers it can happen in two places: inside the firm, or in the industry around it.
Internal economies of scale: economies of scale that come from the growth of the firm itself.
Put simply, the firm lowers its own cost per unit by becoming bigger. If Ravelo installs a faster filling line to bottle 400 crates a day, its cost per crate falls because Ravelo itself has grown.
External economies of scale: economies of scale that come from the growth of the industry in which the firm operates.
Put simply, the firm's cost per unit falls because its industry has grown around it. Suppose more drinks firms open in Minto. A bottle supplier then opens a depot in the town to serve them all, and Ravelo's bottles cost less to deliver.
To tell them apart, ask whose growth lowered the cost. If it was the firm's own growth, the economy is internal. If it was the industry's growth, it is external.
So even a small firm can gain an external economy. Ravelo gains the cheaper bottles even if it stays at its size today, because the depot serves the whole industry, not Ravelo alone.
The difference matters because the firm controls one kind and not the other. Ravelo keeps an internal economy for as long as it stays large. An external economy can be lost if the drinks industry in Minto shrinks: if other firms close, the depot may close too, whatever Ravelo does.
A growing firm gains internal economies of scale from six sources, and each one lowers its cost per unit.
Suppose Ravelo grows from 80 crates a day to 400. Its cost per crate falls for six reasons, the six sources of internal economies of scale. In each, some cost does not rise in proportion to output, so each crate carries less of it.
The other four sources also lower a cost per crate:
A cost that rose in proportion to output, such as a wage paid for each crate filled, would give no economy of scale.
Exam Matters: Take each source to cost per unit, not total cost. A growing firm's total cost usually rises, while its cost per unit falls.
When an industry grows in one place, three of a firm's costs can fall, even if the firm itself stays the same size.
Suppose more drinks firms open in Minto, and the town's drinks industry grows. Ravelo stays the same size, yet three of its costs per crate can fall. Each comes from the industry's growth, so each is an external economy of scale.
Not every fall in cost is an economy of scale, though. If an input becomes cheaper for every firm, whatever its size or its industry's size, the fall does not come from growth. So it is neither an internal nor an external economy of scale.
Ravelo can also lose these economies without changing anything itself. If the drinks industry in Minto shrinks, the college may end its course and fewer firms share what they learn. Ravelo's cost per crate can then rise, although its own output, plant and managers have not changed.
Past a certain size, a firm becomes harder to run, so its long-run average cost rises.
Suppose Amira keeps growing until Ravelo bottles 800 crates a day, in plants in three towns. Its long-run average cost rises from $11 at 600 crates to $14 at 800. Ravelo now has diseconomies of scale. They have three sources: communication problems, coordination problems and X-inefficiency. All three come from a firm that is harder to run.
X-inefficiency: when a firm's average cost is higher than the lowest average cost possible for the output it produces.
Put simply, the firm wastes money because nothing forces it to keep costs down. When Ravelo was small, Amira saw every bill. In a large Ravelo, a plant manager may keep paying a supplier's high price, and nobody notices. Its crates then cost more than they need to.
Both make a cost curve rise, so students often mix them up. They happen in different periods, for different reasons.
So ask what changed. If the firm added workers to a fixed plant, the cause is diminishing returns. If it grew in every factor, the cause is diseconomies of scale.
Exam Matters: A rise in average cost after a firm grows is not always a diseconomy of scale. Check whether input prices rose for every firm, because that would raise cost at any size.
Whether a firm makes a profit or a loss depends on its total revenue against its total cost.
Ravelo, the water-bottling firm in Minto, has one plant making 80 crates a day. Its total cost is $1,440 a day, or $18 a crate. That cost includes $120 a day for Amira, the owner: what she could earn in her next best job, an opportunity cost.
To see how Ravelo is doing, compare total revenue with total cost, or, per crate, average revenue (the price) with average cost. Both give the same answer, because each average is its total divided by the same 80 crates.
Normal profit: the minimum profit needed to keep a firm in its current market.
Put simply, normal profit is what the owner must earn to stay instead of leaving. For Ravelo it is Amira's $120 a day, the pay she gives up by not taking her next best job.
Supernormal profit: profit above normal profit.
Loss: when total revenue is less than total cost, so the firm earns less than normal profit.
Put simply, supernormal profit is anything beyond Amira's $120. At $30, Ravelo earns $960 a day beyond Amira's $120. With a loss, she earns less than $120, so her next best job would pay more. Ravelo still sells 80 crates a day, but suppose rivals in Minto change the price it gets. The table shows three possible prices, with the same total cost of $1,440 each time.
At $18, total revenue minus total cost is zero. Yet Amira is still paid, because her $120 is already inside the $1,440 of total cost. So she earns exactly what she could earn elsewhere, and has no reason to leave.
On the diagram, the supernormal profit and the loss are each a rectangle, named by the letters at its corners. At $18 there is no rectangle, because total revenue equals total cost. A, B and E are the points on the price axis at $30, $18 and $13. C is the point on the AC curve at 80 crates. D is the point at 80 crates and $30, and F is the point at 80 crates and $13.
In the short run, a firm making a loss keeps producing while the price covers its average variable cost.
A rival firm opens in Minto, and the price Ravelo gets falls to $13 a crate. Ravelo now loses $400 a day on its 80 crates. Should Amira stop producing? The answer is not obvious, because stopping does not end Ravelo's fixed cost.
In the short run, Ravelo's fixed cost of $720 a day is owed whether it produces or not. The rent and the loan on the bottling machine must be paid even when Ravelo stops producing. Nor can Amira take her next best job while the lease lasts, so her $120 is given up either way. So if Ravelo stops producing, it loses the whole $720 a day.
So the real question is not whether Ravelo makes a loss. It is which loss is smaller: the loss from producing, or the $720 loss from stopping.
So Ravelo keeps producing at $13 and shuts down at $7.
Short-run shutdown point: the price at which a firm's revenue only just covers its variable costs, where price equals the lowest average variable cost.
Put simply, it is the price below which a firm loses less by stopping than by producing. For Ravelo it is $9, its lowest AVC. Why the lowest? Ravelo's AVC is never below $9, at any output. So a price below $9 cannot cover the variable cost of a crate, whatever Ravelo produces.
Above $9, each crate adds something towards the fixed cost, so producing loses less than stopping. Below $9, each crate adds to the loss, in addition to the fixed cost, so stopping loses less than producing.
In the long run, a firm stays in its industry only if the price covers its average cost.
In the long run there are no fixed costs: the lease on the building can end, the bottling machine can be sold, and Amira can take her next best job. So nothing is owed whatever Ravelo does, and stopping costs nothing. If total revenue is less than total cost, staying loses money while leaving loses none. So to stay, Ravelo's total revenue must cover its total cost, including Amira's $120.
Long-run shutdown point: the price at which a firm's revenue only just covers its total costs, where price equals the lowest average cost.
Put simply, it is the lowest price at which the owner chooses to stay in the industry. For Ravelo's plant today it is $18 a crate, its lowest AC. At $18 Ravelo earns normal profit, the least that keeps Amira in the industry.
Why does the same $13 give two answers? The two rules answer two different questions. The short-run rule asks whether to keep the plant running while the $720 is owed anyway. At $13 the answer is yes, because producing loses $400 instead of $720.
The long-run rule asks whether to stay in the industry once nothing is owed. At $13 the answer is no, because each crate sells for $5 less than its average cost at today's plant. Over 80 crates that is a loss of $400 a day, while leaving would lose nothing. So Ravelo keeps producing until the lease ends, and then it leaves. A larger plant would not help: its $11 a crate needs 400 crates a day, and Ravelo sells only 80.
Total revenue is all the money a firm receives from its sales: the price of each unit times the number sold.
Average revenue is the revenue a firm receives for each unit it sells, and when every unit sells at one price it equals that price.