5.2 Short-run and long-run cost curves

In production theory, understanding cost curves is crucial. Short-run costs involve fixed and variable components, while long-run costs are entirely variable. This distinction shapes how firms make decisions about output and resource allocation over different time horizons.

Cost curves illustrate the relationship between production levels and expenses. Short-run curves show immediate cost changes, while long-run curves reveal optimal plant sizes. These concepts help businesses plan efficiently and adapt to market conditions, balancing short-term flexibility with long-term strategy.

Short-Run vs Long-Run Costs

Time Horizons and Input Flexibility

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• Short run defined as period where at least one factor of production remains fixed (typically capital)
• Long run allows all factors of production to be variable
• Economic time concept based on input flexibility rather than calendar time
• Short-run planning horizon typically less than one year
• Long-run decisions may span several years
• Firms adjust output by changing variable inputs in short run
• Firms can adjust all inputs, including plant size, in long run

Cost Characteristics

• Short-run costs include both fixed and variable components
• Long-run costs entirely variable as all inputs can be adjusted
• Short-run cost curves derived from production function with fixed input
• Long-run cost curves envelop multiple short-run curves
• Fixed costs (rent, insurance) remain constant in short run regardless of output
• Variable costs (raw materials, labor) change with output level in short run

Types of Short-Run Costs

Fixed and Variable Costs

• Total Fixed Cost (TFC) remains constant regardless of output level
  • Examples: rent, insurance premiums, property taxes
• Total Variable Cost (TVC) changes with output level
  • Examples: raw materials, direct labor wages, utilities
• Total Cost (TC) equals sum of TFC and TVC
  • Represents all expenses incurred in production
  • $TC = TFC + TVC$
• Average Fixed Cost (AFC) decreases continuously as output increases
  • Demonstrates spreading of fixed costs over larger quantities
  • $AFC = \frac{TFC}{Q}$, where Q is quantity produced

Average and Marginal Costs

• Average Variable Cost (AVC) typically exhibits U-shaped curve
  • Reflects law of diminishing returns
  • $AVC = \frac{TVC}{Q}$
• Average Total Cost (ATC) equals sum of AFC and AVC
  • Also typically U-shaped
  • $ATC = AFC + AVC = \frac{TC}{Q}$
• Marginal Cost (MC) represents change in total cost for each additional unit of output
  • Intersects both AVC and ATC at their minimum points
  • $MC = \frac{\Delta TC}{\Delta Q}$
• Relationship between MC and average costs
  • When MC < ATC, ATC is decreasing
  • When MC > ATC, ATC is increasing
  • When MC = ATC, ATC is at its minimum point

Short-Run and Long-Run Cost Curves

Relationship Between Short-Run and Long-Run Curves

• Long-run average cost (LRAC) curve derived from envelope of short-run average total cost (SRATC) curves
• Each point on LRAC curve represents tangency point with different SRATC curve
  • Indicates optimal plant size for that output level
• LRAC curve typically flatter than individual SRATC curves
  • Reflects greater flexibility in input adjustment over long run
• Economies of scale represented by downward-sloping portion of LRAC curve
  • Average costs decrease as output expands
• Diseconomies of scale shown by upward-sloping portion of LRAC curve
  • Average costs increase with output expansion

Planning Horizon and Efficiency

• Minimum point on LRAC curve indicates most efficient scale of production
  • Neither economies nor diseconomies of scale exist at this point
• Relationship between SRATC and LRAC curves illustrates concept of planning horizon
  • Demonstrates firm's ability to optimize production over time
• Short-run cost minimization constrained by fixed inputs
• Long-run cost minimization allows for full input adjustment
  • Firms can choose optimal plant size for each output level

Long-Run Average Cost Curve Behavior

Economies and Diseconomies of Scale

• Long-run average cost (LRAC) curve typically U-shaped or L-shaped
  • Reflects different stages of returns to scale
• Economies of scale occur when LRAC curve slopes downward
  • Average costs decrease as output expands
  • Sources: specialization, technological advantages, bulk purchasing power
• Constant returns to scale represented by flat portion of LRAC curve
  • Average costs remain constant as output changes
• Diseconomies of scale shown by upward-sloping LRAC curve
  • Often due to management inefficiencies or resource constraints
  • Examples: communication breakdowns, coordination problems

Industry Structure and Efficiency

• Minimum efficient scale (MES) smallest output level minimizing long-run average costs
  • Determines optimal plant size for cost efficiency
• Industry structure influenced by shape of LRAC curve
  • Industries with significant economies of scale tend to be more concentrated (fewer, larger firms)
  • Industries with constant returns to scale may have many firms of different sizes
• Learning curves can affect LRAC
  • Firms may experience decreasing costs over time
  • Results from improved efficiency and knowledge accumulation
  • Examples: increased worker productivity, refined production processes