Long-Run Cost Curves

• Short run: At least one factor (like plant size, machinery) is fixed; the firm can change only variable factors like labour and raw materials.
• Long run: All factors are variable; the firm can also change plant size or build a new plant.
• In the long run, the firm has enough time to choose the best (optimum) plant size for each level of output and produce at the lowest possible cost.

Definition:

• Long-run total cost (LTC) is the minimum total cost of producing different levels of output when all factors of production (including plant size) are variable.

Shape and features:

(i) LTC starts from the origin (0,0):

• If output is zero, the firm can avoid all cost in the long run (no fixed cost).

(ii) It slopes upwards:

• As output increases, LTC also increases.

(iii) Inverse S-shape:

• At first, LTC increases at a decreasing rate (curve is concave downward).
• After a certain output (say OQ), LTC increases at an increasing rate (curve is concave upward).

Reason:

• Initially, the firm enjoys economies of scale → cost rises slowly.
• Later, the firm faces diseconomies of scale → cost rises faster.

Link with short run:

• LTC is the envelope of many short-run total cost (STC) curves.
• For each output level, the firm chooses the plant (STC) that gives the least cost; joining these least-cost points gives the LTC curve.

Definition:

• Long-run average cost (LAC) = Long-run total cost (LTC) ÷ output (Q).
• It shows the minimum per unit cost of producing each level of output when all inputs, including plant size, are variable.

LAC and plant size:

• Each short-run average cost (SAC) curve corresponds to one plant size.
• In the short run, the firm is “stuck” with one SAC (one plant).
• In the long run, the firm can choose the best SAC (best plant) for each output.
• LAC is a smooth curve that is tangent to many SAC curves → it is called an “envelope curve” or “planning curve”.

Shape:

• LAC is generally U-shaped and flatter than individual SAC curves.
• As output increases:
  1. LAC falls at first.
  2. Reaches a minimum at some output (say OQ).
  3. Rises after that.

Reason for U-shape:

• Falling part: economies of scale (average cost falls as scale of production increases).
• Rising part: diseconomies of scale (average cost rises when the scale is too large).

Definition:

• Long-run marginal cost (LMC) is the addition to long-run total cost when the firm produces one extra unit of output in the long run (after optimally adjusting all inputs).

Shape and relation with LAC:

• When LAC is U-shaped, LMC is also U-shaped.
• The relation between LAC and LMC is the same as between SAC and SMC:
  1. When LMC < LAC → LAC is falling.
  2. When LMC = LAC → LAC is minimum and constant at that point.
  3. When LMC > LAC → LAC is rising.
• LMC cuts LAC at the minimum point of LAC and from below.

Meaning:

• Economies of scale: Advantages of large-scale production that reduce average cost when output increases.
• Diseconomies of scale: Disadvantages of too large a scale that increase average cost when output increases.

Economies of scale (reasons for falling LAC):

• Technical economies: better, more efficient machines.
• Managerial economies: specialised managers and better supervision.
• Purchasing economies: buying raw materials in bulk at lower prices.
• Marketing and financial economies: lower cost of advertising, easier and cheaper finance.

Diseconomies of scale (reasons for rising LAC):

• Management becomes difficult; communication delays.
• Control and supervision problems.
• Coordination problems when the firm becomes too large.

Effect on LAC:

• At low and medium output: economies of scale dominate → LAC falls.
• At optimum output, economies are fully used; LAC is minimum.
• Beyond optimum output: diseconomies dominate → LAC rises.

• Long run = all inputs variable, no fixed cost, firm can change plant size and method of production.
• LTC shows minimum total cost for each output in the long run.
• It starts from origin, slopes upwards, and is inverse S-shaped.
• It is formed as the envelope of STC curves.
• LAC gives the lowest possible average cost for each output in the long run.
• It is U-shaped and flatter than SAC.
• It is the envelope curve of SACs and is used for long-run planning.
• LMC measures the change in long-run total cost for one more unit.
• Both LAC and LMC are U-shaped.
• LMC cuts LAC at LAC’s minimum point.
• U-shape of LAC is explained by economies (left side) and diseconomies (right side) of scale.
• The minimum point of LAC is called the optimum point or optimum scale of production.