Cost Theory: Short-run vs. Long-run, Revenue, Profit Maximization

Key Concepts in Cost Theory

1. Cost Classification: Short-run vs. Long-run

Costs are classified based on the time period and flexibility of factors of production.

Short-run Costs

• Fixed Costs (FC): Costs that do not change with output (e.g., rent, salaries, insurance).
  • Example: A Daraz warehouse’s monthly rent remains the same regardless of how many orders are processed.
• Variable Costs (VC): Costs that change with output (e.g., raw materials, wages of temporary workers).
  • Example: Ncell’s cost of additional SIM cards increases as more subscribers join.
• Total Cost (TC): Sum of fixed and variable costs. $$TC=FC+VC$$

Long-run Costs

• All costs are variable because all factors (including plant size) can be adjusted.
• No fixed costs exist in the long run.

classDiagram
    class Costs {
        +Fixed Costs (FC)
        +Variable Costs (VC)
        +Total Cost (TC = FC + VC)
    }
    class ShortRun {
        <<includes>>
        FC: Unchangeable
        VC: Changeable
    }
    class LongRun {
        <<includes>>
        All costs variable
        No fixed costs
    }
    Costs --> ShortRun
    Costs --> LongRun

2. Cost Curves

A. Per Unit Costs

B. Relationship Between Cost Curves

• MC cuts AC at its minimum (this is the profit-maximizing rule).
• AVC is the lower envelope of AC (AC = AFC + AVC).
• AFC always declines as output increases.

graph LR
    A["MC"] -->|"Cuts at minimum"| B["AC"]
    B -->|"Composed of"| C["AFC + AVC"]
    C --> D["AFC: Declines"]
    C --> E["AVC: U-shaped"]

3. Revenue Concepts

4. Profit Maximization

Rule 1: MR = MC (Short-run)

• A firm maximizes profit where Marginal Revenue (MR) = Marginal Cost (MC).
• Worked Example: Daraz’s Profit-Maximizing Quantity
  • Suppose Daraz sells a product at Rs. 500.
  • At Q=50 units, MR = Rs. 500, MC = Rs. 400 → Profit increases (MR > MC).
  • At Q=60 units, MR = Rs. 500, MC = Rs. 550 → Profit decreases (MR < MC).
  • Optimal Q = 55 units (where MR = MC).

Rule 2: AC < AR (Long-run Survival)

• In the long run, firms must cover all costs (AC ≤ AR).
• If AC > AR, the firm shuts down (e.g., a failing e-commerce startup).

MC and MR intersecting at Q=55, with AC below AR at this point. (Image: 2012. Theory And Applications Of Microeconomics. [Place of p, CC BY-SA 4.0, via Wikimedia Commons)

5. Short-run vs. Long-run Decisions

In the Real World

1. Daraz’s Order Fulfillment

   • Daraz uses marginal cost analysis to decide how many orders to process.
   • If the cost of delivering one more order (MC) exceeds the revenue per order (MR), it stops expanding deliveries.
   • Example: During Dashain sales, Daraz may increase delivery fees if MC rises due to higher fuel costs.

2. Ncell’s Pricing Strategy

   • Ncell applies average cost pricing to set call rates.
   • If AC per minute is Rs. 2, it charges Rs. 2.50 to ensure profitability.
   • During promotions, it may lower AR but ensures MR > MC to attract customers.

3. Bank Loan Interest Rates

   • Banks calculate marginal cost of lending (additional cost per loan).
   • If MC of a loan = Rs. 50,000, but AR (interest) = Rs. 60,000, the bank profits.
   • Example: NMB Bank sets loan rates based on AC + profit margin.

Exam Tip

1. Memorize the Profit-Maximizing Rule: MR = MC (short-run) and AC ≤ AR (long-run).
2. Draw Cost Curves Correctly:
   • MC cuts AC at its minimum.
   • AFC declines continuously.
   • AVC is U-shaped.
3. Apply to Real Firms:
   • Use Daraz, Ncell, or bank examples in numerical problems.
   • Always label axes (Q, Cost, Revenue) in graphs.
4. Common Mistakes to Avoid:
   • Confusing short-run (fixed costs) with long-run (all variable).
   • Forgetting that shutdown rule is $P\ge AVC$ (not AC).
5. Numerical Questions:
   • If given TC = 100 + 5Q, derive:
     • FC = 100
     • VC = 5Q
     • MC = 5
     • AC = 100/Q + 5

Final Note: Cost theory is the backbone of pricing and production decisions. Master the relationships between MC, AC, and MR, and you’ll ace both theory and numerical questions in your exams!