Long-Run
Production Costs
Understand how firms adjust all inputs in the long run, the shape of the LRATC curve, and why economies of scale drive real-world business decisions.
AP Microeconomics
What Is the Long Run?
In economics, the long run is the period in which all inputs are variable: a firm can change its factory size, workforce, and technology. There are no fixed costs because every resource can be adjusted.
Short Run
At least one input is fixed (e.g., plant size). Firms operate along a single SRATC curve.
Long Run
All inputs are variable. Firms choose the optimal plant size for any output level.
Key Cost Concepts
LRATC
Long-Run Average Total Cost: the lowest per-unit cost achievable when all inputs are variable.
LRMC
Long-Run Marginal Cost: the additional cost of producing one more unit when all inputs can adjust.
LRTC
Long-Run Total Cost: the total cost of production at each output level, choosing optimal input mix.
The LRATC Curve
The Long-Run Average Total Cost curve is the envelope of all possible short-run ATC curves. Each SRATC represents a different plant size; the LRATC traces the lowest cost at every output level.
Economies and Diseconomies of Scale
Economies of Scale
As output rises, LRATC falls: specialization, bulk purchasing, and spreading setup costs.
Constant Returns
LRATC is flat: doubling inputs exactly doubles output.
Diseconomies of Scale
LRATC rises: coordination problems, bureaucracy, and communication breakdowns.
Returns to Scale: The Formal Rule
If a firm multiplies all inputs by a factor \( k \), output changes by a factor \( m \). The relationship between \( k \) and \( m \) determines the type of returns to scale:
1
Increasing returns to scale (\( m > k \)): Output more than doubles when inputs double. LRATC is falling.
2
Constant returns to scale (\( m = k \)): Output exactly doubles when inputs double. LRATC is flat.
3
Decreasing returns to scale (\( m < k \)): Output less than doubles when inputs double. LRATC is rising.
Short Run vs. Long Run
| Short Run | Long Run | |
|---|---|---|
| Fixed inputs? | Yes (plant, equipment) | No: all inputs variable |
| Fixed costs? | \( FC > 0 \) | \( FC = 0 \) |
| Key cost curve | SRATC (one per plant size) | LRATC (envelope) |
| Shape driver | Diminishing marginal returns | Economies/diseconomies of scale |
| Decision | How much to produce | What size plant to build |
Why the LRATC Is U-Shaped
1
Falling portion (economies of scale): Specialization of labor, volume discounts on inputs, better technology utilization, and ability to spread overhead costs.
2
Flat portion (constant returns): The firm has reached an efficient operating range. Many industries have a wide flat region.
3
Rising portion (diseconomies of scale): Management becomes unwieldy, communication breaks down, worker alienation increases, and coordination costs explode.
How to Choose Optimal Plant Size
1
Estimate target output: Determine the quantity of output the firm expects to produce in the long run.
2
Find the SRATC tangent to LRATC: At your target output, the lowest-cost plant size is the SRATC curve that is tangent to the LRATC at that quantity.
3
Check the region: Are you in the economies, constant, or diseconomies region? This tells you whether scaling up or down would reduce costs.
4
Compare LRATC to market price: If \( P > LRATC \), the firm earns economic profit. If \( P < LRATC \), the firm should consider exiting the industry.
Worked Example: Expanding a Factory
A firm currently produces 100 units at a cost of \( \$10 \) per unit using a small plant. It is considering expanding to produce 200 units. Its cost data:
| Output | SRATC (Small) | SRATC (Medium) | LRATC |
|---|---|---|---|
| 100 | \( \$10 \) | \( \$14 \) | \( \$10 \) |
| 200 | \( \$15 \) | \( \$8 \) | \( \$8 \) |
| 300 | \( \$22 \) | \( \$9 \) | \( \$9 \) |
Worked Example: Returns to Scale
A firm has the production function \( Q = 4L^{0.5}K^{0.5} \). If the firm doubles both labor and capital, what happens to output?
1
Double inputs: Replace \( L \) with \( 2L \) and \( K \) with \( 2K \): \( Q' = 4(2L)^{0.5}(2K)^{0.5} \)
2
Simplify: \( Q' = 4 \cdot 2^{0.5}L^{0.5} \cdot 2^{0.5}K^{0.5} = 4 \cdot 2 \cdot L^{0.5}K^{0.5} = 2Q \)
3
Interpret: Output exactly doubles when inputs double. The exponents sum to \( 0.5 + 0.5 = 1 \), so this firm exhibits constant returns to scale.
Worked Example: Identifying the Region
A firm's LRATC at different output levels is given below. Identify whether the firm experiences economies of scale, constant returns, or diseconomies of scale at each range.
| Output | LRATC | Region |
|---|---|---|
| 50 | \( \$20 \) | Economies of scale |
| 100 | \( \$15 \) | Economies of scale |
| 200 | \( \$12 \) | Economies of scale |
| 300 | \( \$12 \) | Constant returns |
| 400 | \( \$14 \) | Diseconomies of scale |
| 500 | \( \$18 \) | Diseconomies of scale |
LRATC Shape and Market Structure
The shape of the LRATC curve helps explain why different industries have different numbers of firms:
Natural Monopoly
LRATC falls over the entire relevant range. One firm can serve the whole market at lower cost than two firms. Examples: utilities, railroads.
Oligopoly
Economies of scale are significant but eventually exhausted. Only a few large firms can reach the low-cost range. Examples: auto, aircraft manufacturing.
Competitive
Minimum efficient scale is small relative to market demand. Many firms can reach the flat portion. Examples: restaurants, dry cleaners.
LRMC and LRATC Relationship
1
When \(\text{LRMC}\) < \(\text{LRATC}\), the average is being pulled down: economies of scale.
2
\(\text{LRMC}\) intersects \(\text{LRATC}\) at the minimum of LRATC: this is the minimum efficient scale.
3
When \(\text{LRMC}\) > \(\text{LRATC}\), the average is being pulled up: diseconomies of scale.
Common Mistakes to Avoid
✕ Confusing Diminishing Returns with Diseconomies of Scale
Diminishing marginal returns is a short-run concept (one input varies). Diseconomies of scale is a long-run concept (all inputs vary).
✕ Saying LRATC Has Fixed Costs
In the long run, there are no fixed costs. Every cost is variable. The firm can exit entirely and pay nothing.
✕ Thinking Bigger Is Always Better
Economies of scale are not unlimited. After minimum efficient scale, growing larger raises per-unit costs due to coordination problems.
Summary: Long-Run Cost Concepts
| Concept | LRATC Behavior | Meaning |
|---|---|---|
| Economies of Scale | Falling | Output rises faster than cost |
| Constant Returns | Flat | Output rises proportionally to cost |
| Diseconomies of Scale | Rising | Output rises slower than cost |
| Min. Efficient Scale | Minimum point | Lowest per-unit cost achievable |
| LRMC = LRATC | At minimum | MC crosses ATC at its lowest point |
Question 1 of 5
In the long run, a firm experiencing economies of scale will see its LRATC curve:
Economies of scale means the firm's per-unit costs decline as it produces more, because it can specialize labor, buy inputs in bulk, and spread overhead. The LRATC is falling in this region.
Question 2 of 5
A firm has the production function \( Q = 3L^{0.6}K^{0.5} \). This firm exhibits:
For a Cobb-Douglas production function \( Q = AL^{a}K^{b} \), sum the exponents: \( 0.6 + 0.5 = 1.1 > 1 \). Since the sum exceeds 1, the firm has increasing returns to scale: doubling inputs more than doubles output.
Question 3 of 5
The LRATC curve is best described as:
The LRATC is an envelope curve: it is tangent to every possible SRATC curve. At each output level, the LRATC shows the lowest achievable average total cost when the firm can choose any plant size.
Question 4 of 5
A natural monopoly exists when:
A natural monopoly arises when the LRATC declines continuously over the relevant range of demand. One firm can serve the entire market at a lower per-unit cost than two or more firms could. Examples include electric utilities and water systems.
Question 5 of 5
At the minimum efficient scale, which of the following is true?
At the minimum efficient scale, the LRATC reaches its lowest point. At this point, \( LRMC = LRATC \): the marginal cost equals the average cost. This is the same relationship as the short-run MC crossing ATC at its minimum.