2.5 Short-run and long-run costs

Costs in production can be tricky. Short-run costs deal with fixed and variable factors, while long-run costs assume all factors can change. This difference impacts how firms make decisions and manage expenses.

Understanding cost curves is key. They show how costs change with output and help firms find the sweet spot for production. Long-run average cost curves give insights into economies of scale and optimal plant size.

Short-run vs Long-run Costs

Time Horizon and Factor Flexibility

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• Short-run costs vary with output when at least one factor of production remains fixed (typically within a timeframe where firms cannot alter scale of operations)
• Long-run costs adjust over time as all factors of production become variable (allowing firms to change scale of operations)
• Key distinction lies in flexibility of input factors and time horizon for decision-making
  • Short run firms face constraints on adjusting certain inputs
  • Long run all inputs can be varied to optimize production
• Returns to scale concept applies only in long run (involves changes in all production factors)
• Examples of short-run fixed factors
  • Factory size
  • Specialized equipment
• Examples of long-run adjustable factors
  • Labor force size
  • Production technology

Cost Implications and Strategic Decisions

• Short-run cost management focuses on optimizing variable inputs given fixed constraints
• Long-run planning involves strategic decisions about optimal scale and technology
• Firms balance short-term profitability with long-term cost efficiency
• Short-run cost control often targets variable costs (raw materials, labor hours)
• Long-run cost reduction may involve capital investments or restructuring
• Examples of short-run cost decisions
  • Adjusting production shifts
  • Sourcing cheaper raw materials
• Examples of long-run cost decisions
  • Building a larger factory
  • Investing in automated production lines

Components of Short-run Costs

Fixed and Variable Costs

• Fixed costs (FC) remain constant regardless of output level
  • Examples include rent, insurance, salaries of permanent staff
• Variable costs (VC) change directly with output level
  • Examples include raw materials, direct labor, energy costs
• Total cost (TC) equals sum of fixed costs and variable costs for any given output level
  • Formula: $TC = FC + VC$
• Average fixed cost (AFC) calculated by dividing total fixed costs by quantity of output
  • Formula: $AFC = FC / Q$
• Average variable cost (AVC) determined by dividing total variable costs by quantity of output
  • Formula: $AVC = VC / Q$
• Average total cost (ATC) equals sum of average fixed cost and average variable cost
  • Alternative calculation divides total cost by quantity
  • Formula: $ATC = AFC + AVC$ or $ATC = TC / Q$
• Marginal cost (MC) represents additional cost incurred to produce one more unit of output
  • Formula: $MC = ΔTC / ΔQ$

Cost Behavior and Decision Making

• Understanding cost components crucial for pricing and production decisions
• Fixed costs create operating leverage affecting break-even point and profit sensitivity
• Variable costs directly impact profitability of each unit sold
• Marginal cost guides decisions on whether to increase or decrease production
• Cost structure varies by industry and affects competitive strategies
• Examples of industries with high fixed costs
  • Airlines (aircraft leases, airport fees)
  • Pharmaceutical companies (research and development)
• Examples of industries with high variable costs
  • Retail (inventory, sales commissions)
  • Restaurants (food ingredients, hourly wages)

Shape of Short-run Cost Curves

Curve Characteristics and Relationships

• Average fixed cost (AFC) curve slopes downward and approaches both axes asymptotically
  • Reflects spreading of fixed costs over increasing output
• Average variable cost (AVC) curve typically U-shaped
  • Shows initial increasing returns to variable factor followed by diminishing returns
• Average total cost (ATC) curve also U-shaped
  • Combines effects of AFC and AVC curves
• Marginal cost (MC) curve U-shaped and intersects both AVC and ATC curves at their minimum points
  • Intersection occurs because MC below AVC or ATC pulls average down, above pulls average up
• Law of diminishing marginal returns explains upward-sloping portions of AVC, ATC, and MC curves
  • Additional units of variable input yield progressively smaller increases in output
• Relationship between curves illustrates economic principles
  • Economies of scale
  • Optimal production level

Economic Implications and Decision Making

• Shape of cost curves guides firms in determining optimal output levels
• Point where MC intersects ATC identifies profit-maximizing output in perfect competition
• U-shape of ATC curve demonstrates trade-off between fixed cost efficiency and diminishing returns
• Firms operate in region where MC is rising to ensure stable equilibrium
• Cost curve analysis helps in capacity planning and expansion decisions
• Examples of using cost curves for decision making
  • Determining whether to accept a one-time order below normal price
  • Assessing when to shut down production in the short run

Short-run vs Long-run Average Costs

Long-run Cost Curve Derivation

• Long-run average cost (LRAC) curve derived from short-run average total cost (SRATC) curves for different plant sizes or scales of operation
• LRAC curve forms envelope of all possible SRATC curves
  • Represents lowest average cost of production for each output level when all inputs variable
• At any given output level, LRAC curve tangent to most efficient SRATC curve for that output
• Shape of LRAC curve reflects economies of scale, constant returns to scale, and diseconomies of scale as firm expands operations
  • Economies of scale occur when LRAC decreases as output increases
  • Constant returns to scale present when LRAC remains constant as output changes
  • Diseconomies of scale arise when LRAC increases as output expands beyond certain point

Economic Implications and Firm Strategy

• Minimum efficient scale illustrated by point where LRAC curve becomes flat
  • Indicates smallest scale at which long-run average costs minimized
• Relationship between short-run and long-run average cost curves demonstrates how firms adjust scale of operations over time to achieve cost efficiency
• LRAC curve helps firms determine optimal long-term plant size and production capacity
• Shape of LRAC curve influences market structure and competitive dynamics
• Firms use LRAC analysis for strategic planning and investment decisions
• Examples of industries with significant economies of scale
  • Automobile manufacturing
  • Semiconductor production
• Examples of industries with relatively flat LRAC curves
  • Local service businesses (barbershops, small restaurants)
  • Customized professional services (law firms, consulting)