Theory of cost: Short-run and long-run cost curves

In Economics, Cost refers to the expenditure incurred by a firm to produce goods or services. It includes both Explicit costs (monetary payments like wages, rent and raw material expenses) and Implicit costs (opportunity costs of using resources owned by the firm).

Economists like Alfred Marshall emphasized the importance of cost curves in understanding production, pricing and profit. By analyzing costs, firms can make informed decisions about resource allocation, output levels and pricing strategies.

Cost in the Short Run vs. Long Run

1. Short Run: A period where at least one input (like capital) is fixed, while others (like labor) are variable. Firms can only adjust production by changing variable inputs.
2. Long Run: A timeframe where all inputs are variable. Firms can adjust both capital and labor to find the most efficient production level.

Short-run Cost Curves

In the short run, costs are divided into Fixed costs (unchanged regardless of output) and Variable costs (change with output). This division gives rise to distinct short-run cost curves:

1. Total Cost (TC)

• Formula: $$TC = TFC + TVC$$Where:
  • $TFC$: Total Fixed Cost
  • $TVC$: Total Variable Cost

2. Average Costs

• Average Fixed Cost (AFC): Fixed cost per unit of output.

  $$AFC=\frac{TFC}{Q}$$
  • AFC decreases as output increases (spreading overhead effect).

• Average Variable Cost (AVC): Variable cost per unit of output.

  $$AVC=\frac{TVC}{\mathrm{Q}}$$
  • AVC initially decreases due to increased efficiency, then rises due to diminishing returns.

• Average Total Cost (ATC): Total cost per unit of output.

  $$ATC=\frac{TC}{Q}=AFC+AVC$$

3. Marginal Cost (MC)

• The cost of producing one additional unit of output. $$MC=\frac{\mathrm{\Delta }TC}{\mathrm{\Delta }\mathrm{Q}}$$
• Relationship with Other Costs: MC intersects AVC and ATC at their minimum points, indicating optimal production efficiency.

Long-run Cost Curves

In the long run, firms have the flexibility to adjust all inputs. There are no fixed costs—everything becomes variable. Long-run costs depend on the Returns to scale:

1. Increasing Returns to Scale (Economies of Scale):
   • As output increases, long-run average cost (LRAC) decreases due to factors like specialization, bulk purchasing and improved technology.
2. Constant Returns to Scale:
   • LRAC remains constant as output increases.
3. Decreasing Returns to Scale (Diseconomies of Scale):
   • LRAC increases as output grows due to inefficiencies like management complexity and resource constraints.

Long-run Average Cost (LRAC) Curve

• Envelope Curve: The LRAC curve is derived from the tangency points of various short-run average cost (SRAC) curves. Each SRAC represents a specific plant size or capital level.

Short-run vs Long-run Costs

Examples of Cost Curves

1. Short Run:
   • A bakery renting a shop (fixed cost) can only hire additional bakers or buy more flour (variable costs) to increase output.
2. Long Run:
   • The same bakery might invest in a larger shop or advanced equipment, altering both fixed and variable costs to scale operations.

Applications

1. Business Applications:
   • Firms use cost curves to determine optimal production levels and pricing strategies.
2. Policy Implications:
   • Governments analyze cost behavior to regulate industries, ensuring efficient resource allocation.

Understanding the theory of cost, especially short-run and long-run cost curves, is vital for both theoretical and practical economics. It helps us grasp how businesses operate, scale and adapt to changes.