Understanding Production Costs: Short-Term and Long-Term Analysis
Theoretical Support Document No. 7: Production Costs
Total Cost Curves: Short Term
Cost curves illustrate the minimum expense to achieve various production levels, encompassing both explicit and implicit costs. Explicit costs are direct outlays for inputs, while implicit costs relate to the value of company-owned resources used in production (see Case 1).
In the short term, at least one factor of production is fixed. Total fixed costs (TFC) are constant obligations. Total variable costs (TVC) fluctuate with production levels. Total cost (TC) is the sum of TFC and TVC.
Unit Cost Curves: Short Term
Analyzing unit costs is crucial for short-term assessments. Key metrics include average fixed cost (AFC), average variable cost (AVC), average cost (AC), and marginal cost (MC).
- AFC = TFC / Quantity
- AVC = TVC / Quantity
- AC = TC / Quantity = AFC + AVC
- MC = Change in TC or TVC / Change in Quantity
Geometry of Short-Term Unit Cost Curves
Short-term unit cost curves derive from total cost curves, similar to how average product (AP) and marginal product (MP) relate to total product (TP). AFC is the slope from the origin to the TFC curve. AVC is the slope from the origin to the TVC curve. AC is the slope from the origin to the TC curve. MC is the slope of the TC or TVC curve at a specific production level.
Long-Term Average Cost Curve
The long term allows all production factors to vary. There are no fixed inputs or costs, enabling flexible plant sizes.
The long-run average cost curve (LRAC) shows the minimum unit cost for each production level with adaptable plant sizes. LRAC is tangent to all short-run average cost (SRAC) curves, representing potential plant sizes. Mathematically, LRAC is the envelope curve of SRAC curves.
Shape of the Long-Term Average Cost Curve
SRAC and LRAC curves are often U-shaped, but for different reasons. SRAC curves are influenced by the law of diminishing returns (due to fixed short-term inputs). LRAC curves are shaped by economies and diseconomies of scale. Initially, increasing returns to scale cause LRAC to fall. As production grows, diseconomies of scale may dominate, causing LRAC to rise.
Empirical evidence suggests LRAC curves can be U-shaped with a flat section (constant returns to scale) or L-shaped (no diseconomies within observed production levels).
Long-Term Marginal Cost Curve
The long-run marginal cost (LRMC) measures the change in long-run total cost (LRTC) per unit change in output. LRTC is calculated by multiplying LRAC by the output level. Plotting LRMC values creates the LRMC curve, which is U-shaped and reaches its minimum before LRAC. The ascending portion of LRMC intersects LRAC at its lowest point.
Long-Term Total Cost Curve
LRTC is obtained by multiplying output by LRAC for that output level. Plotting LRTC values creates the LRTC curve, showing the minimum total cost for each production level with flexible plant sizes. The LRTC curve is tangent to all short-run total cost (SRTC) curves, representing potential plant sizes. Mathematically, LRTC is the envelope of SRTC curves.
LRAC and LRMC relationships can be derived from the LRTC curve, similar to how SRAC and short-run marginal cost (SRMC) are derived from the SRTC curve. This also explains the relationship between SRAC and LRAC, and between SRMC and LRMC.