Long-Run Production Costs: Study Guide (Microeconomics 3.3)

Short run and long run

In Topic 3.2 you met the short run: a period in which at least one input is fixed. A bakery cannot build a second oven room overnight, so the rent on its building is a fixed cost. It must be paid even if the bakery makes nothing.

The long run is a period long enough for a firm to change all its inputs. It can move to a bigger building, buy more machines, sell its old ones or close completely. Two results follow:

• There are no fixed inputs in the long run, so all costs are variable. If a firm plans to make zero output in the long run, its long-run total cost is zero.
• The firm chooses its scale: the size of its plant and the amount of every input it uses.

The long run is not a set number of months. It is a planning horizon. Think of the short run as “operating the plant you have” and the long run as “choosing which plant to have”.

Returns to scale: when every input grows

In the short run you added more of one input (labour) to a fixed amount of capital. That led to diminishing marginal returns. In the long run, a firm can increase all inputs together. The question then is: if every input rises by the same percentage, what happens to output?

If all inputs rise by 10%, output rises by…	Name	Example
more than 10%	increasing returns to scale	output rises 15%
exactly 10%	constant returns to scale	output rises 10%
less than 10%	decreasing returns to scale	output rises 6%

Returns to scale are about physical quantities: inputs and output. They are a long-run idea, because they need every input to change.

From returns to scale to long-run costs

Suppose the price of each input does not change as the firm grows. Then:

• Increasing returns to scale: cost rises in proportion to inputs, but output rises faster, so cost per unit falls.
• Constant returns to scale: cost and output rise at the same rate, so cost per unit stays the same.
• Decreasing returns to scale: output rises more slowly than cost, so cost per unit rises.

Long-run average total cost (LRATC) is the lowest possible average total cost of producing each level of output when the firm can choose any plant size:

LRATC = long-run total cost ÷ quantity of output

Each plant size has its own short-run average total cost (SRATC) curve. Once a plant is built, the firm is on that SRATC curve. In the long run it can pick the plant that gives the lowest average cost for the output it plans to make. The LRATC curve joins these best choices. It is sometimes called the envelope of the short-run curves, because it touches each SRATC curve at one point and lies below all of them everywhere else.

The shape of the LRATC curve

A typical LRATC curve has three regions.

1. Economies of scale: LRATC falls as output rises. Causes include:

• Specialisation and division of labour. In a larger firm, workers and managers can each focus on one task and become faster at it.
• Spreading large indivisible costs. Some inputs come in one big piece, such as a production line, a design team or a computer system. A larger output spreads that cost over more units.
• Large-scale technology. Some efficient machines only make sense at high output.
• Buying in bulk. Large buyers often pay lower prices per unit for materials.

2. Constant returns to scale: LRATC is flat. The firm has used up its economies of scale but has not yet run into diseconomies. Output and cost rise at the same rate. This is the range of the efficient scale: average cost is at its lowest.

3. Diseconomies of scale: LRATC rises as output rises. Causes include:

• Coordination problems. More layers of management make decisions slower and messages less accurate.
• Monitoring and motivation. In a very large firm, it is harder to check each worker’s effort, and workers may feel less connected to results.
• Duplication and waste. Different departments may repeat the same work.

Diseconomies of scale are not the same as diminishing marginal returns. Diminishing marginal returns happen in the short run because one input is fixed. Diseconomies of scale happen in the long run when all inputs grow, but the firm becomes harder to run.

A change in input prices or technology is different again. If wages rise at every scale, the whole LRATC curve shifts up. That is not a movement along the curve and not a diseconomy of scale.

Minimum efficient scale and market structure

The minimum efficient scale (MES) is the smallest output at which LRATC reaches its minimum. A firm producing less than the MES has higher average costs than it needs to.

The MES matters for how many firms a market can hold. Compare it with the quantity buyers want at a price equal to the lowest LRATC:

Largest number of firms that can each produce at least the MES ≈ market quantity ÷ MES

• If the MES is small compared with the market, many firms can each reach the lowest cost. The market tends to have many firms (low concentration).
• If the MES is large compared with the market, only a few firms can each reach the lowest cost. A small firm would face higher costs and struggle to compete. The market tends to have few firms (high concentration).
• If the MES is larger than the whole market, one firm can supply the market more cheaply than two or more. You will meet this case, a natural monopoly, in Unit 4.

Worked example 1: returns to scale and LRATC at Tallis Tiles

Question. Tallis Tiles, a fictional firm, grows by adding identical “bundles” of inputs. One bundle is 5 workers at $150 a day each plus one kiln hired for $450 a day. Input prices do not change as the firm grows.

Bundles	1	2	3	4	5	6	7
Output (boxes of tiles per day)	400	1,000	1,800	2,400	3,000	3,200	3,360

(a) Find long-run total cost and LRATC for each scale. (b) Identify the returns to scale between each pair of scales. (c) Identify the regions of economies of scale, constant returns to scale and diseconomies of scale, and the MES.

(a) One bundle costs 5 × $150 + $450 = $1,200 per day. Long-run total cost = 1,200 × number of bundles.

Bundles	1	2	3	4	5	6	7
LRTC ($ per day)	1,200	2,400	3,600	4,800	6,000	7,200	8,400
LRATC ($ per box)	3.00	2.40	2.00	2.00	2.00	2.25	2.50

For example, at 2 bundles: 2,400 ÷ 1,000 = $2.40 per box.

(b) Compare the percentage change in inputs with the percentage change in output.

Move	Inputs	Output	Returns to scale
1 → 2	+100%	+150%	increasing
2 → 3	+50%	+80%	increasing
3 → 4	+33.33%	+33.33%	constant
4 → 5	+25%	+25%	constant
5 → 6	+20%	+6.67%	decreasing
6 → 7	+16.67%	+5%	decreasing

For example, from 1 to 2 bundles, inputs double but output rises from 400 to 1,000, which is 2.5 times as much.

(c)

• Economies of scale from 400 to 1,800 boxes: LRATC falls from $3.00 to $2.00.
• Constant returns to scale from 1,800 to 3,000 boxes: LRATC stays at $2.00.
• Diseconomies of scale above 3,000 boxes: LRATC rises to $2.25, then $2.50.
• MES = 1,800 boxes per day, the smallest output at the lowest LRATC.

Check. The returns to scale match the cost regions: where output grows faster than inputs, LRATC falls; where they grow at the same rate, LRATC is constant; where output grows more slowly, LRATC rises. This works because input prices stayed the same.

Worked example 2: how many firms can a market hold?

Question. (a) At a price of $2.00 per box, buyers in the fictional country of Ellaran want 90,000 boxes of tiles per day. Every tile firm has costs like Tallis Tiles. How many firms can each produce at the MES or more? (b) In Ellaran’s cement industry, the MES is 400,000 tonnes per year, and LRATC stays at its lowest level up to 600,000 tonnes. At a price equal to the lowest LRATC, buyers want 1,000,000 tonnes per year. How many cement firms can each reach the lowest cost? (c) Compare the likely structure of the two industries.

(a) 90,000 ÷ 1,800 = 50 firms. Because the flat part of LRATC runs to 3,000 boxes, firms of different sizes between 1,800 and 3,000 can all reach $2.00, so between 30 and 50 low-cost firms could share the market (90,000 ÷ 3,000 = 30).

(b) 1,000,000 ÷ 400,000 = 2.5. Firms cannot come in halves. Two firms, each producing 500,000 tonnes (inside the flat range), can both reach the lowest cost. With three firms sharing the market equally, each would produce about 333,333 tonnes, below the MES, so all three would have higher costs.

(c) The tile industry can support many firms, so it is likely to be competitive with low concentration. The cement industry can support only two firms at the lowest cost, so it is likely to be highly concentrated, with a few large firms. A new small cement firm would have a higher average cost than its large rivals, which makes entry hard.

Interpretation. The MES is a cost fact about the technology of an industry. Combined with the size of demand, it helps explain why some markets have thousands of sellers and others only a handful.

Common misconceptions

• “Firms still have fixed costs in the long run.” In the long run every input can change, so every cost is variable.
• “Diseconomies of scale and diminishing marginal returns are the same thing.” Diminishing marginal returns are short-run and come from a fixed input. Diseconomies of scale are long-run, with all inputs variable.
• “If output rises when inputs rise, there are increasing returns to scale.” Output almost always rises. Compare the percentage changes: output must rise by a larger percentage than inputs.
• “The MES is the output where LRATC is lowest.” If the bottom is flat, many outputs share the lowest cost. The MES is the smallest of them.
• “Higher wages are a diseconomy of scale.” A change in input prices shifts the whole LRATC curve. Diseconomies of scale are a movement along the curve to a larger output.
• “A big firm always has lower costs.” Only up to the MES and across the flat range. Beyond that, diseconomies of scale raise LRATC.

Where this leads

Long-run costs explain why firms choose a particular size and why some markets have few sellers. Next, in Topic 3.4, Types of Profit, you will see how a firm compares revenue with all of its costs, including implicit ones, to decide whether it is earning an economic profit. If you need to revise short-run costs first, go back to Topic 3.2. Test yourself with the practice questions, then use the revision notes and the checklist to consolidate.