Cost & Revenue: Types, Short/Long Run, Profit Maximization

TAKEAWAYS:

• Costs are divided into fixed (do not change with output) and variable (change with output), and their averages/marginals are key tools for decision-making.
• Revenue is split into total, average, and marginal revenue, with marginal revenue showing how extra output affects total revenue.
• In the short run, at least one factor of production is fixed; in the long run, all factors are variable.
• Firms maximize profit where MR = MC (marginal revenue equals marginal cost).
• Shutdown rule: A firm should stop production if price < average variable cost (P < AVC).
• Break-even point occurs where total revenue equals total cost (TR = TC), and firms earn normal profit.

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1. Introduction to Costs

Costs are the expenses a business incurs to produce goods and services. They can be classified into two main types:

1.1 Fixed Costs (FC)

• Definition: Costs that do not change with the level of production in the short run.
• Examples:
  • Rent of factory
  • Salaries of permanent workers
  • Insurance premiums
  • Interest on loans
• Graph: Fixed costs remain constant regardless of output.

A horizontal line showing FC = $100 at all output levels (0 to 10 units) (Image: The original uploader was Yunzhong Hou at English Wikibooks., CC BY-SA 2.0, via Wikimedia Commons)

#### **1.2 Variable Costs (VC)**
- **Definition**: Costs that **change** with the level of production.
- **Examples**:
- Raw materials
- Wages of temporary workers
- Electricity bills
- Packaging costs
- **Graph**: Variable costs **increase** as output increases.

#### **1.3 Total Cost (TC)**
- **Definition**: The **sum of fixed and variable costs** at any level of production.
$$TC=FC+VC$$
- **Example**:
If FC = $100 and VC = $200 at 5 units of output, then:
$$TC=100+200=\$300$$

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### **2. Average and Marginal Costs**

```figure
{"type":"curves","lines":[{"label":"AFC","fn":true,"expr":"100/x","from":[1,100],"to":[10,10]},{"label":"AVC","fn":true,"expr":"0.1*x^2 - 2*x + 50","from":[1,48],"to":[10,130]},{"label":"ATC","fn":true,"expr":"0.1*x^2 - x + 150","from":[1,158],"to":[10,140]},{"label":"MC","fn":true,"expr":"0.2*x - 2","from":[1,-1.8],"to":[10,0.2]}],"points":[{"x":5,"y":20,"label":"AFC min"},{"x":5,"y":47.5,"label":"MC = ATC (Q=5)"},{"x":5,"y":125,"label":"ATC min"}],"xlabel":"Quantity (Units)","ylabel":"Cost ($/unit)","caption":"Cost curves showing AFC declining, AVC and MC U-shaped, and MC intersecting ATC at its minimum"}

2.1 Average Fixed Cost (AFC)

• Definition: Fixed cost per unit of output. $$AFC=\frac{FC}{Q}$$
• Graph: AFC falls as output increases (spreading effect).

2.2 Average Variable Cost (AVC)

• Definition: Variable cost per unit of output. $$AVC=\frac{VC}{Q}$$
• Graph: AVC first falls, then rises (due to diminishing returns).

2.3 Average Total Cost (ATC)

• Definition: Total cost per unit of output. $$ATC=\frac{TC}{Q}=AFC+AVC$$
• Graph: ATC is U-shaped (sum of AFC and AVC).

2.4 Marginal Cost (MC)

• Definition: The additional cost of producing one more unit. $$MC=\frac{\Delta TC}{\Delta Q}$$
• Graph: MC cuts ATC at its minimum point.

Why does MC cut ATC at its minimum?

• When MC < ATC, ATC falls.
• When MC > ATC, ATC rises.
• At the minimum point of ATC, MC = ATC.

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3. Short Run vs. Long Run Costs

Why does the long run matter?

• Firms can adjust all inputs (e.g., expand factory, hire more workers, adopt new tech).
• Long-run ATC curve is flatter than short-run ATC (due to economies of scale).

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4. Revenue Concepts

Revenue is the total income a firm earns from selling goods/services.

4.1 Total Revenue (TR)

• Definition: Total money received from selling all units. $$TR=P\times Q$$
• Example: If a firm sells 10 units at $5 each: $$TR=5\times 10=\$50$$

4.2 Average Revenue (AR)

• Definition: Revenue per unit sold. $$AR=\frac{TR}{Q}=P$$
• Graph: AR is a horizontal line in perfect competition (price taker).

4.3 Marginal Revenue (MR)

• Definition: The additional revenue from selling one more unit. $$MR=\frac{\Delta TR}{\Delta Q}$$
• Graph:
  • In perfect competition, MR = AR = Price (horizontal line).
  • In monopoly, MR falls as more units are sold (downward-sloping).

Key Difference:

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5. Profit Maximization

Firms aim to maximize profit, which is: $$\text{Profit}=TR-TC$$ Rule for Profit Maximization: A firm maximizes profit where: $$MR=MC$$ Why?

• If MR > MC, producing more increases profit.
• If MR < MC, producing less increases profit.
• At MR = MC, profit is maximized.

Example:

Analysis:

• At Q=3, MR (10) = MC (10) → Profit is maximized ($13).
• At Q=2, MR (15) > MC (7) → Increase output.
• At Q=4, MR (5) < MC (13) → Decrease output.

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6. Shutdown Rule

A firm should stop production if: $$P<AVC$$ Why?

• If price is below AVC, the firm loses more by producing than by shutting down.
• It can cover variable costs and part of fixed costs by shutting down.

Example:

• If AVC = $4 and P = $3, the firm should shut down (losing $1 per unit).
• If AVC = $4 and P = $5, the firm should continue (making $1 per unit).

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7. Break-Even Point

The break-even point is where: $$TR=TC\text{or}AR=ATC$$ At this point:

• The firm covers all costs but earns zero economic profit.
• It is the minimum point where the firm can operate without loss.

Graphical Representation:

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Exam Tip: How to Score Full Marks

1. Understand the difference between short run and long run – Always mention whether the question is about short-run or long-run costs.
2. Draw cost curves correctly – Label FC, VC, TC, MC, ATC, AVC properly. Show MC cutting ATC at its minimum.
3. Apply MR = MC rule – Always check if the question asks for profit maximization and solve using this rule.
4. Shutdown vs. Continue – Remember:
   • If P > AVC, continue producing.
   • If P < AVC, shut down.
5. Numerical Problems – Practice calculating TC, ATC, MC, TR, MR, and profit from given data.
6. Real-World Examples – Relate concepts to Nepalese businesses (e.g., tea factories, hydropower projects).

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NEB Board-Style Questions (Practice)

Short Answer Questions

1. Define:

   • (a) Fixed Cost
   • (b) Marginal Cost
   • (c) Break-Even Point

2. Distinguish between:

   • (a) Short-run and Long-run costs
   • (b) Average Revenue and Marginal Revenue

3. Why is the MC curve U-shaped?

Long Answer Questions

4. Explain the relationship between MC and ATC with a diagram. Why does MC cut ATC at its minimum point?

5. A firm has the following cost data:

   Q	FC	VC
   1	50	20
   2	50	35
   3	50	55
   4	50	80

   • Calculate TC, ATC, AVC, and MC for each output level.
   • At what quantity does the firm maximize profit if the market price is $25?

6. What is the shutdown rule? When should a firm continue production despite making losses?

Diagram-Based Questions

7. Draw a cost curve showing FC, VC, TC, MC, ATC, and AVC. Label the minimum points of ATC and AVC.

8. Draw a graph to show the break-even point. What happens if the firm produces beyond this point?

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Good luck with your NEB exam preparation! 🚀