Costs, Revenue and Profit

Subject: Economics
Topic: 3
Cambridge Code: 0455 / 2281

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Types of Costs

Fixed Costs

Fixed costs - Do not change with output

Characteristics:

• Constant regardless of production
• Must be paid even if output = 0
• Short-run concept

Examples:

• Rent on factory
• Salary of manager
• Insurance
• Depreciation

Variable Costs

Variable costs - Change with output level

Characteristics:

• Zero if output = 0
• Increase as production increases
• Directly related to output

Examples:

• Raw materials
• Hourly wages
• Utilities (electricity)
• Packaging

Total Costs

$\text{Total Cost (TC)} = \text{Fixed Costs (FC)} + \text{Variable Costs (VC)}$

Average Costs

Average Total Cost (AC): $AC = \frac{\text{Total Cost}}{\text{Quantity}}$

Average Fixed Cost (AFC): $AFC = \frac{\text{Fixed Cost}}{\text{Quantity}}$

Average Variable Cost (AVC): $AVC = \frac{\text{Variable Cost}}{\text{Quantity}}$

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Marginal Cost

Marginal Cost (MC) - Cost of producing one additional unit

$MC = \frac{\text{Change in TC}}{\text{Change in Quantity}}$

Example:

• Producing 10 units costs £100 total
• Producing 11 units costs £105 total
• MC of 11th unit = £105 - £100 = £5

Relationship to Average Cost

When MC < AC: AC decreasing (still getting cheaper per unit) When MC > AC: AC increasing (getting more expensive per unit) When MC = AC: AC at minimum

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Revenue

Revenue - Money received from selling products

Total Revenue

$\text{Total Revenue (TR)} = \text{Price} × \text{Quantity}$

Example: Sell 100 units at £5 each

• TR = £5 × 100 = £500

Average Revenue (Price)

$\text{Average Revenue} = \frac{\text{Total Revenue}}{\text{Quantity}} = \text{Price}$

Perfect competition: AR = Price (horizontal demand) Monopoly: AR = Price (but demand slopes down)

Marginal Revenue

Marginal Revenue (MR) - Revenue from selling one additional unit

$MR = \frac{\text{Change in TR}}{\text{Change in Quantity}}$

Perfect competition: MR = Price (constant) Imperfect competition: MR < Price (must lower price to sell more)

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Profit

Profit - Revenue minus all costs

$\text{Profit} = \text{Total Revenue} - \text{Total Cost}$

Profit Maximization

Condition: Marginal Revenue = Marginal Cost (MR = MC)

Logic:

• If MR > MC: Produce more (additional unit adds more revenue than cost)
• If MR < MC: Produce less (additional unit costs more than revenue adds)
• If MR = MC: Optimal output

Breaks Even

Break-even point - Revenue equals costs (Profit = 0)

$\text{Break-even Quantity} = \frac{\text{Total Fixed Costs}}{\text{Price - Average Variable Cost}}$

Importance:

• Minimum output to avoid loss
• Below this: Loss
• Above this: Profit

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Economies and Diseconomies of Scale

Economies of Scale

Economies of scale - AC decreases as output increases

Types:

Internal economies:

• Technical: Better equipment, specialization
• Financial: Lower interest rates, bulk buying
• Marketing: Advertising spread over more units
• Administrative: Share management costs

External economies:

• Suppliers locate nearby
• Skilled labor pool develops
• Infrastructure improves

Benefit: Large firms more competitive

Diseconomies of Scale

Diseconomies of scale - AC increases as output increases

Causes:

• Management coordination becomes difficult
• Communication breaks down
• Loss of control
• Worker alienation
• Inefficiency

Result: Optimal firm size exists (minimum AC)

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Productive and Allocative Efficiency

Productive Efficiency

Productive efficiency - Producing at minimum AC

$AC = \text{Minimum}$

Benefit:

• Using resources optimally
• No waste
• Maximum output from inputs

Allocative Efficiency

Allocative efficiency - Price = Marginal Cost

$P = MC$

Benefit:

• Resources allocated to highest valued uses
• Consumers pay for actual cost
• No under/overproduction

Perfect competition achieves both Monopoly achieves neither

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Cost and Revenue Analysis Example

Product: Coffee cups

Q	FC	VC	TC	AC	MC	P	TR	AR	MR	Profit
0	50	0	50	-	-	5	0	-	-	-50
1	50	2	52	52	2	5	5	5	5	-47
2	50	3	53	26.5	1	5	10	5	5	-43
3	50	5	55	18.3	2	5	15	5	5	-40
4	50	8	58	14.5	3	5	20	5	5	-38
5	50	12	62	12.4	4	5	25	5	5	-37

MR = MC at Q = 5, so profit maximizing output = 5 units

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Key Points

1. Fixed costs constant, variable costs change with output
2. TC = FC + VC
3. AC = TC/Q
4. MC is cost of one more unit
5. Profit = TR - TC
6. Profit maximized when MR = MC
7. Break-even when TR = TC
8. Economies of scale reduce AC
9. Productive efficiency at minimum AC
10. Allocative efficiency at P = MC

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Practice Questions

1. Calculate costs from data
2. Graph cost curves
3. Find profit maximizing quantity
4. Calculate break-even point
5. Analyze economies of scale
6. Compare efficiency types
7. Predict profit changes

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Revision Tips

• Know cost types clearly
• Practice cost calculations
• Understand MC relationship to AC
• Know profit maximization rule
• Practice break-even analysis
• Know efficiency concepts
• Practice graphing and analysis