Production & Cost Analysis: Short/Long Run, Cost Curves & Efficiency

Key Definitions

1. Production Function

The relationship between inputs (factors of production) and output, holding technology constant. $$Q=f(L,K,M)$$ where:

• $Q$ = Total output
• $L$ = Labor
• $K$ = Capital
• $M$ = Materials

2. Cost Classification

Short-Run vs. Long-Run Costs

Short Run

• At least one input is fixed (e.g., factory size).
• Law of Variable Proportions: As labor increases, output rises but at a diminishing rate.

flowchart TD
    A["Labor Input"] --> B["Output"]
    B --> C[Increasing Returns
"0-2 workers (TP ↑↑)"]
    C --> D[Diminishing Returns
"3+ workers (TP ↑↓)"]
    D --> E[Negative Returns
"4+ workers (TP ↓)"]
    A -->|"Note"| F["Law of Variable Proportions"]

Long Run

• All inputs are variable (e.g., expanding factory).
• Returns to Scale: How output changes when all inputs scale proportionally.

flowchart TD
    A["Scale Inputs Proportionally"] --> B["Returns to Scale"]
    B --> C[Constant Returns
"Q = k×inputs (e.g., k=2)"]
    B --> D[Increasing Returns
"Q > k×inputs (e.g., Q=3× inputs)"]
    B --> E[Diminishing Returns
"Q < k×inputs (e.g., Q=1.5× inputs)"]
    C -->|"Example"| F["Nepal’s tea production"]

Cost Curves (Short Run)

1. Total Cost (TC) Curve

• Shape: Steeply rising after a point due to diminishing marginal returns.
• Example: Daraz’s order processing cost.

2. Average Cost (AC) Curve

• U-shaped due to economies/diseconomies of scale.

3. Marginal Cost (MC) Curve

• Intersection with AC: MC = AC at the minimum point of AC.

Long-Run Cost Curves

1. Long-Run Average Cost (LAC) Curve

• Envelope of SRAC curves (shows the lowest possible AC for each output).

2. Economies of Scale

• Internal: Cost savings from larger production (e.g., NEPSE’s bulk trading).
• External: Industry-wide efficiencies (e.g., Kathmandu’s shared logistics for Daraz/Pathao).

Profit Maximization

Marginal Revenue (MR) = Marginal Cost (MC) Rule

• Monopolist: Produce where $MR=MC$.
• Perfect Competition: Price = MC (no market power).

Real-World Applications

1. Daraz’s Order Queue

• Short-run: Fixed warehouse space (FC) + variable delivery costs (VC).
• Long-run: Expands warehouse (LAC curve shifts down).

2. NTC’s Call Charges

• AC curve: Starts high (small users) → drops (bulk users) → rises (peak hours).

3. Bank Loans

• MC = Interest rate for each loan. Banks lend until $MC=MR$.

Exam Tip

• Always show curves (TC, AC, MC, LAC) with labeled axes.
• Compare short/long run: Use Daraz/NTC as examples.
• Profit maximization: Link $MR=MC$ to real firms (Ncell, Pathao).
• Avoid memorization: Focus on why curves are U-shaped or why MC intersects AC at its minimum.

Worked Example (Nepal Bank Loan) Given:

• Fixed cost (FC) = ₹10,000
• VC per loan = ₹500
• Borrowers: 10, 20, 30

Key Insight: AC falls until Q=20 (economies of scale), then rises (diseconomies).