Long-Run Costs: Economies of Scale and Minimum Efficient Scale

A phone-case company doubles its output, and every case gets cheaper to make. Years later, much bigger, it doubles output again. This time every case costs more to make. Same company, same cases. So why would growing help the first time and hurt the next? This is Module 3.3, Long-Run Production Costs.

First, what makes it the long run? In the short run, at least one input is stuck: the company can hire more workers, but its factory stays the same size.

Quick refresher from Module 3.2: total cost is fixed cost plus variable cost. Say the factory costs $7,000 a day, even at zero output, and plastic and wages for 2,000 cases cost $11,000. Total cost: $18,000.

In the long run, the company can change every input: build a bigger factory or switch to a smaller one. So that $7,000 becomes a choice, and all $18,000 is variable cost. The long run isn't a set number of months. It's however long it takes until every input can change. Each factory size has its own short-run ATC curve. A small factory is cheapest at low output, a big factory at high output. In the long run, the company picks the factory with the lowest average cost for the output it plans. Trace that lowest cost at every output, and you get the long-run average total cost curve.

So what just happened? One: in the short run, the factory's $7,000 is fixed. Two: in the long run, the factory is a choice, so every cost is variable. Three: the lowest average cost at each output traces long-run ATC.

Long-run ATC has three parts. Where it falls as output grows: economies of scale. Where it's flat: constant returns to scale, also called the efficient scale. Where it rises: diseconomies of scale. Exam trap: recent AP exams used both names for the flat part, so learn both. Here are the company's long-run total costs at four outputs, each one double the last.

Quick refresher from Module 3.2: an average cost is a total divided by quantity. So long-run ATC is long-run total cost divided by output: $18,000 over 2,000 cases is $9 a case.

Now 4,000 cases: $24,000 over 4,000 is $6 a case. Output went up, and cost per case fell from $9 to $6. That's economies of scale. Exam trap: total cost rose too, from $18,000 to $24,000. That alone proves nothing about scale, because total cost almost always rises with output. Judge scale by the average. At 8,000 cases, $48,000 over 8,000 is $6 again: flat, the efficient scale. At 16,000, $112,000 over 16,000 is $7. Cost per case rose: diseconomies of scale. That answers the opening question. The first doubling, 2,000 to 4,000, was on the falling part. The second, 8,000 to 16,000, climbed the rising part.

So what just happened with the phone cases? One: we divided long-run total cost by output at each level. Two: $9 fell to $6, economies of scale. Three: $6 stayed at $6, the efficient scale. Four: $6 rose to $7, diseconomies of scale.

Drawing note: the flat bottom belongs to this long-run curve. When you draw a firm's short-run ATC, give it one clear lowest point, with marginal cost passing through it.

Why does the curve bend like that? Scale. Returns to scale compare inputs with output when every input grows together. Say 10 workers and 4 machines make 2,000 cases a day. Double every input: 20 workers, 8 machines, twice the floor space. If output more than doubles, say to 5,000, that's increasing returns to scale. If it exactly doubles, to 4,000: constant returns. Less than double, say 3,000: decreasing returns. Now link it to cost. At the same input prices, doubling every input doubles cost. If output more than doubles, each case gets cheaper: increasing returns bring economies of scale. Exactly double, and cost per case holds steady: the flat part.

So what just happened? One: we doubled every input. Two: output went from 2,000 to 5,000, more than double: increasing returns to scale. Three: cost doubled but output more than doubled, so cost per case fell: economies of scale.

Exam trap: keep the two apart. Returns to scale: inputs versus output. Economies of scale: cost per unit versus output. Given costs, answer economies or diseconomies of scale, not increasing or decreasing returns. And neither one is diminishing marginal returns. That's a short-run idea: one input added to a factory that stays fixed.

Quick refresher from Module 3.1: marginal product is the extra output from one more worker. In a fixed factory, if the fifth worker adds 300 cases and the sixth adds only 200, marginal product is falling: diminishing marginal returns.

What causes economies of scale? A bigger operation lets each worker specialize in one task and get faster at it. And a big setup cost, like a pricey molding machine, gets spread over more cases. Diseconomies of scale usually come with sheer size. A giant company is hard to coordinate: messages pass through more layers, and organizing everyone costs more.

One more idea. The minimum efficient scale is the smallest output where long-run ATC reaches its lowest level. Here, that's 4,000 cases a day, where cost per case first hits $6. It helps decide how many firms a market holds. If buyers want 400,000 cases a day in all, up to 100 firms could each make 4,000 at that lowest cost. Room for many firms: expect a competitive market. Now picture a firm that must lay pipes under every street first. If its average total cost keeps falling across the whole range of market demand, its minimum efficient scale lies beyond the whole market. One firm can serve everyone more cheaply than several could: a natural monopoly, coming in Unit 4. Exam trap: explain a natural monopoly with average total cost falling over the entire range of demand, not with marginal cost. On a recent AP exam, only about three students in ten earned that point.

So what just happened? One: minimum efficient scale is the first output at the lowest long-run ATC, 4,000 cases here. Two: small next to the market means many firms. Three: average total cost falling across all of demand means one firm, a natural monopoly.

Exam moment: two questions the way the AP exam asks them, then one free-response part.

In the long run, a skateboard maker doubles all its inputs, and its output rises from 400 to 1,000 boards a week. Which term describes this relationship between its inputs and output? A) Diminishing marginal returns B) Increasing returns to scale C) Constant returns to scale D) Decreasing returns to scale E) Diseconomies of scale

The answer is B. Inputs doubled, but output rose two and a half times, from 400 to 1,000. More than in proportion: increasing returns to scale. A is a short-run idea, with other inputs fixed. C needs exactly 800 boards. D needs fewer than 800. E describes cost per unit, not inputs and output.

A kayak maker's long-run total cost is $21,000 for 30 kayaks a month, $30,000 for 60, $36,000 for 90, $48,000 for 120, and $67,500 for 150. What is its minimum efficient scale? A) 30 kayaks B) 60 kayaks C) 90 kayaks D) 120 kayaks E) 150 kayaks

The answer is C. Divide each total by output: $700, $500, $400, $400, then $450 a kayak. The lowest average, $400, first appears at 90 kayaks. A has the lowest total cost, not the lowest average. B is the biggest drop, not the bottom. D is at $400 too, but it isn't the smallest such output. E is where the average rises again.

In the long run, a juice company raises output from 1,500 to 2,500 bottles a day, and its total cost rises from $6,000 to $8,750. Is it experiencing economies of scale, diseconomies of scale, or the efficient scale? Explain using numbers.

To earn the point, state economies of scale, then explain that long-run ATC falls from $4.00 a bottle, which is $6,000 over 1,500, to $3.50, which is $8,750 over 2,500. The costly mistake: pointing at total cost, which rose here, or giving the right answer without both averages. On a recent AP exam, fewer than one student in five earned this point.

So what just happened? One: we divided total cost by output at both levels. Two: long-run ATC fell from $4.00 to $3.50. Three: so it's economies of scale, even though total cost rose.

Recap: in the long run, every cost is variable. Long-run ATC falls with economies of scale, stays flat at the efficient scale, and rises with diseconomies. And the minimum efficient scale helps set how many firms a market holds. Next: Module 3.4, Types of Profit.