Cost Concepts and Production Economics (Short Run & Long Run)

Fixed Cost (FC)

Definition: costs that do not vary with the level of output in the short run
Example from transcript: rent for a building; the firm may start by renting because not enough capital is available yet
Key property: FC is constant regardless of output; in a schedule it appears as a horizontal line when plotting cost against output
Relationship to total cost: total cost TC(Q) = FC + VC(Q)
In a diagram: FC is the intercept on the cost axis; as output changes, FC remains fixed

Average Fixed Cost (AFC)

Definition: fixed cost per unit of output, AFC(Q) = rac{FC}{Q}
Behavior: falls as output increases; tends toward zero with large Q
Curve: rectangular hyperbola (falls continuously as Q grows)
Important identity: FC = AFC(Q) imes Q (area interpretation related to fixed cost across output levels)

Variable Cost (VC)

Definition: costs that vary with the level of output (e.g., raw materials, wages, fuel, power)
VC(0) = 0 when no output is produced
Shape depends on production function and use of the variable input; in the short run the law of variable proportions applies
Transcript note: as output increases, VC increases; in short run there can be increasing returns at low output followed by diminishing returns as output expands
In diagrams: VC curve rises with output; the slope is the marginal cost in other contexts

Average Variable Cost (AVC)

Definition: variable cost per unit of output, AVC(Q) = rac{VC(Q)}{Q}
Behavior: typically U-shaped; initially falls (economies of scale in variable input) and then rises (diseconomies of scale in variable input)
Shape explanation (from transcript): the AVC curve falls, reaches a minimum, then increases

Semi-Variable (Semi-Fixed) Cost

Definition: costs that are fixed up to a certain level of output, then become variable (or vice versa)
Examples: electricity bill with a fixed charge up to a usage threshold; beyond that, usage costs vary with output
Alternate forms described: fixed first then variable, or variable first then fixed

Total Cost (TC) in the Short Run

Definition: sum of fixed and variable costs at a given level of output
Formula: TC(Q) = FC + VC(Q)
Graphical intuition: TC starts at the FC intercept and tracks the VC curve as output increases
Relationship to averages: ATC = TC/Q, and ATC = AFC + AVC

Average Total Cost (ATC)

Definition: total cost per unit of output, ATC(Q) = rac{TC(Q)}{Q} = AFC(Q) + AVC(Q)
Shape: typically U-shaped in the short run
Key interaction: the MC curve intersects ATC at its minimum point

Marginal Cost (MC)

Definition: the additional cost of producing one more unit, MC(Q) = rac{dTC}{dQ} = rac{
{ ext{change in }TC}{ ext{change in }Q}}
or via finite differences, MC = rac{ΔTC}{ΔQ}
Interpretation: slope of the TC curve; also the slope of VC when FC is constant
Shape: often U-shaped in many theories; MC falls initially (due to increasing marginal returns to the variable input) and then rises due to diminishing marginal returns
Key property (standard): MC intersects AVC and ATC at their respective minima

Short Run Cost Summary Diagram (textual description)

TC is the vertical sum of FC plus VC
VC grows with Q; FC is a constant vertical intercept
The ATC curve lies above AVC (ATC = AFC + AVC) and is U-shaped; MC intersects AVC at its minimum and intersects ATC at its minimum

Long Run vs Short Run in Cost Theory

Short Run (SR): at least one input is fixed; there are fixed costs (FC > 0) and variable costs (VC)
Long Run (LR): all inputs are variable; there are no fixed costs (FC = 0); TCLR(Q) = VCLR(Q)
In the long run, firms can adjust all inputs and plant size; hence costs are more flexible
Long-run Average Cost (LRAC) is the envelope of the short-run average cost curves (the lowest possible ATC for each Q across all SRAC curves)
LRAC is kinematically the lowest attainable average cost for producing each level of output by choosing the optimal plant size

Economies of Scale and the Long Run

Economies of scale: average costs fall as output increases due to increased efficiency
Minimum Efficient Scale (MES): the output level at which LRAC is minimized; beyond MES, further growth may not reduce costs and may even raise them (diseconomies of scale)
The long-run average cost curve is explained by the aggregation of different short-run curves (envelope of SRAC curves)
The concept of bulk production and bulk-buying advantages (economic scale) is a primary source of economies of scale

Types of Economies of Scale (Internal vs External)

Internal economies of scale: cost advantages that accrue to a single firm as it grows bigger
- Technical economies: more efficient production techniques, better equipment, specialization of labor
- Commercial economies: bulk buying, bulk marketing, more efficient distribution
- Financial economies: cheaper financing terms due to higher creditworthiness or access to capital
- Risk-bearing economies: diversification of product lines reduces risk per unit of output
External economies of scale: cost advantages that accrue to all firms in an industry when the industry expands in a location or region
- Examples: improved infrastructure, better supplier networks, trained labor pools, shared knowledge spillovers

Semi-Variable vs Internal vs External (Recap for exam)

Semi-variable costs: partly fixed, partly variable depending on output thresholds
Internal economies of scale: efficiencies within the firm as it expands
External economies of scale: efficiencies arising from industry growth in a region

Returns to Scale and Costs (SR vs LR) – Conceptual links

Law of variable proportions (SR): with fixed inputs, initially increasing marginal returns to the variable input, followed by diminishing marginal returns
Returns to scale (LR): when all inputs are increased by the same proportion, output may increase by more (increasing returns to scale), the same (constant), or by less (decreasing/diseconomies of scale)
Economic interpretation: economies of scale are often realized as LRAC slopes downward; MES is the level of output where LRAC is minimized

Revenue Concepts (TR, AR, MR) and Competitive Environments

Total Revenue (TR): TR(Q) = P(Q) imes Q in general; if price is constant, TR = P imes Q with P fixed
Average Revenue (AR): AR(Q) = rac{TR(Q)}{Q} = P(Q) in general
Marginal Revenue (MR): MR(Q) = rac{dTR}{dQ}; in a linear case, MR slope is related to the slope of AR
In Perfect Competition:
- Price is given and constant; AR = MR = TR/Q = P
- The AR curve is also theDemand facing the firm; MR = AR = Price and is a horizontal line when price is fixed
In Imperfect Competition (e.g., monopoly, monopolistic competition):
- AR > MR; MR lies below AR and typically has twice the slope of AR when demand is a straight line
- Price is not taken as given; firms have some power to set price above marginal cost
Economic intuition: the MR curve shows the additional revenue from selling one more unit; the AR curve shows revenue per unit; the two coincide in perfect competition but diverge in imperfect competition

Profit Maximization: Two Approaches

Approach 1: Total-Cost (TC) / Total-Revenue (TR) gap maximization
- Profit: ext{Profit}(Q) = TR(Q) - TC(Q)
- The profit-maximizing output is the Q that maximizes the vertical gap between TR and TC; graphically, where the gap is widest
- In practice this often aligns with the condition MR = MC (with MC rising) when using differential calculus
Approach 2: Marginal-Revenue (MR) / Marginal-Cost (MC) approach (MCMO)
- Profit is maximized where MR(Q) = MC(Q) and MC is rising (to ensure a maximum rather than a minimum of profit)
- This applies to both perfect and imperfect competition, but MR differs between the two contexts (MR = P in perfect competition; MR < AR in imperfect competition)
Equilibrium condition (for profit maximization): MC = MR with MC rising

Profit Scenarios: Normal vs Abnormal Profit

If TR > TC at the profit-maximizing output: abnormal/supernormal profit
If TR = TC at the profit-maximizing output: normal profit (breakeven in the long run for perfectly competitive firms)
If TR < TC at the profit-maximizing output: loss

Practical Relationships and Quick Facts (from transcript and standard theory)

In perfect competition: AR = MR = Price; MC intersects ATC and AVC at their minima; long-run equilibrium leads to zero economic profit
In imperfect competition: AR > MR; MR slope is twice AR slope in linear cases; revenue maximization occurs where MR = 0, implying unit elastic demand for revenue-maximizing output (in the context of certain revenue-maximization problems)
Elasticity intuition: At high prices, demand is more elastic; at low prices, demand is more inelastic; revenue-maximizing output tends to occur where elasticity is unitary (|ε| = 1) under certain revenue-maximizing conditions

Worked Numerical Practice (illustrative only)

Example 1: Simple TC to find MC, AVC, and AC
- Suppose TC(Q) = FC + VC(Q) with FC = 500 and VC(Q) = 20Q + 2Q^2
- Then TC(Q) = 500 + 20Q + 2Q^2
- AVC(Q) = VC/Q = (20Q + 2Q^2)/Q = 20 + 2Q
- MC(Q) = dTC/dQ = 20 + 4Q
- ATC(Q) = TC/Q = (500 + 20Q + 2Q^2)/Q = 500/Q + 20 + 2Q
- Fixed cost: FC = 500 (nonzero in SR)
- Long run analogue would set FC = 0 and use only VC-based expressions
Example 2: Profit-maximizing rule under perfect competition
- If MR = P = 25, and MC(Q) = 5 + Q, solve MR = MC: 25 = 5 + Q ⇒ Q* = 20
- Check that MC is rising at Q = 20 to confirm a minimum of profit loss or maximum of profit
Example 3: Revenue-maximizing output under a simple TR function
- If TR(Q) = P \, Q with P constant, MR = AR = P; revenue-maximizing output would be where MR = 0 if TR is concave; otherwise not typical in standard linear TR models; in many contexts revenue maximization occurs where elasticity is unitary

Exam Preparation Prompts (based on transcript content)

Explain the difference between fixed cost, variable cost, and semi-variable cost with examples
Describe why AFC falls with increasing output and why AVC becomes U-shaped
Define TC, ATC, AVC, AFC, and MC; explain their relationships and typical shapes
Explain the long-run vs short-run distinction; why LRAC is the envelope of SRAC curves; define MES
Distinguish internal and external economies of scale; provide examples for technical, commercial, financial, risk-bearing, and external economies
Describe the law of variable proportions and how it leads to increasing then diminishing marginal returns in the short run
Explain the concept of revenue, average revenue, and marginal revenue under perfect competition vs imperfect competition; discuss AR and MR slopes and their relationships
State the profit-maximizing conditions under the two approaches (TC-based and MR = MC); explain why MC should be rising at the optimum
Provide a small numerical exercise: given a TC function, compute FC, VC, MC, AVC, ATC; identify SR vs LR; determine MES and potential profits
Explain why short-run average costs can be higher than long-run average costs and what this implies for decision-making

Quick recap of key relationships (for quick reference)

TC(Q) = FC + VC(Q)
AFC(Q) =
rac{FC}{Q}; ATC(Q) =
rac{TC(Q)}{Q} = AFC(Q) + AVC(Q)
AVC(Q) =
rac{VC(Q)}{Q}; MC(Q) =
rac{dTC}{dQ} or
rac{ΔTC}{ΔQ}
In SR: FC > 0; LR: FC = 0
MC intersects AVC at its minimum and MC intersects ATC at its minimum (under standard U-shaped curves)
Profit maximization: MR = MC with MC rising; alternatively maximize TR − TC
Perfect competition: AR = MR = Price; MR is constant; LR equilibrium yields zero economic profit in the long run
Imperfect competition: AR > MR; MR slope is steeper; profit maximization still at MR = MC, with different MR behavior
Revenue maximization often linked to unit elastic demand (|ε| = 1) at the TR maximum point in certain contexts