Short-Run and Long-Run Cost Functions in Economics – Concepts, Differences, and Cost Behavior
25/June/2025 01:25
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Short-Run and Long-Run Cost Functions – Explained in Detail
In economics, cost functions describe the relationship between a firm's output level and its cost of production. These functions vary based on whether the firm is operating in the short run or the long run.
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? Short-Run Cost Function
In the short run, at least one factor of production is fixed—usually capital (like machinery or building). The firm can only change variable inputs like labor or raw materials.
Main Types of Short-Run Costs:
1. Fixed Costs (FC): Do not change with output. E.g., rent, salaried staff.
2. Variable Costs (VC): Change with output. E.g., raw materials, hourly wages.
3. Total Cost (TC):
TC = FC + VC
AC = \frac{TC}{Q}
Additional cost of producing one more unit.
MC = \frac{\Delta TC}{\Delta Q}
Behavior:
MC and AC first fall due to increasing returns and then rise due to diminishing returns.
U-shaped curves represent this behavior.
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? Long-Run Cost Function
In the long run, all inputs are variable. Firms can change plant size, labor, technology, etc. There are no fixed costs in the long run.
Main Types of Long-Run Costs:
1. Long-Run Total Cost (LRTC): Total cost when all inputs are variable.
2. Long-Run Average Cost (LRAC):
LRAC = \frac{LRTC}{Q}
3. Long-Run Marginal Cost (LRMC): Change in LRTC due to an extra unit of output.
Behavior:
Initially, economies of scale reduce LRAC.
Eventually, diseconomies of scale increase LRAC.
Result: A U-shaped LRAC curve.
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? Key Differences Between Short-Run and Long-Run Cost Functions
Basis Short-Run Cost Function Long-Run Cost Function
Input Flexibility At least one input is fixed All inputs are variable
Time Frame Limited, operational period Sufficient to adjust all factors
Cost Behavior Involves fixed and variable costs Only variable costs
Curve Shape U-shaped due to diminishing returns U-shaped due to economies/diseconomies of scale
Planning Use Tactical (day-to-day) Strategic (expansion/investment)
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✅ Conclusion
Understanding short-run and long-run cost functions helps firms make informed production, pricing, and expansion decisions. The short run focuses on efficiency with fixed capacity, while the long run allows structural changes for cost optimization and competitive growth.
