Utility (Copy)

7.1.1 Definition and Calculation of Total Utility and Marginal Utility

• Utility
  • The satisfaction or benefit derived from consuming a good or service.
  • Measured in utils (a notional unit of satisfaction – not a real-world measurement).
  • Subjective: varies between individuals based on preferences, tastes, and circumstances.
• Total Utility (TU)
  • The total amount of satisfaction gained from consuming a certain quantity of a good or service.
  • TU increases as more units are consumed, but usually at a decreasing rate due to diminishing marginal utility.
  • Formula:
    TU = Σ(MU from each unit)
• Marginal Utility (MU)
  • The extra satisfaction from consuming one additional unit of a good or service.
  • Formula:
    MU = ΔTU ÷ ΔQ
    where ΔTU = change in total utility, ΔQ = change in quantity consumed.
• Example Table:

• Interpretation:
  • TU rises as more units are consumed until the 6th unit.
  • At the 7th unit, MU = 0 → TU reaches maximum.
  • Beyond the 7th unit, MU becomes negative → TU falls (disutility).
• Diagram:
  • Total Utility Curve: upward-sloping at first, flattening, then declining.
  • Marginal Utility Curve: downward-sloping, intersects MU = 0 at maximum TU.

7.1.2 Diminishing Marginal Utility

• Law of Diminishing Marginal Utility (DMU):
  • As more units of a good are consumed, the additional satisfaction from each successive unit eventually decreases.
  • Example:
    • 1st slice of pizza: very satisfying
    • 2nd slice: still satisfying, but less than the first
    • 5th slice: minimal satisfaction
    • 8th slice: possible discomfort (negative MU)
• Economic Implications:
  • Explains the downward slope of the individual demand curve.
  • Consumers only buy additional units if the price is low enough to match their lower MU.
• Graph:
  • MU curve slopes downward and may become negative.
  • Price consumers are willing to pay falls as Q increases.

7.1.3 Equi-Marginal Principle

• Definition:
  • Consumers maximise total utility when allocating income so that the last unit of money spent on each good yields the same marginal utility per unit of currency.
• Condition:
  MUx / Px = MUy / Py = MUz / Pz … = MUn / Pn

  where:

  • MUx = marginal utility of good X
  • Px = price of good X
  • Applies to all goods purchased
• Example:
  • Suppose:
    • MU of apples = 20 utils, price of apples = $2 → MU/P = 10
    • MU of bananas = 15 utils, price of bananas = $1 → MU/P = 15
  • The consumer should buy more bananas and fewer apples until MU/P is equalised.
• Diagram:
  • Budget constraint + indifference curves can also illustrate utility maximisation.

7.1.4 Derivation of an Individual Demand Curve

• Link between MU and Price:
  • A rational consumer will only buy a unit if MU ≥ price.
  • As quantity consumed increases, MU falls → lower price needed to buy more units.
• Step-by-Step Derivation:
  1. Plot MU against quantity.
  2. Assume MU is measured in monetary terms (via willingness to pay).
  3. MU curve becomes the demand curve.
• Example:

• Diagram:
  • MU curve (in $ terms) is the same as the individual demand curve.
  • Downward sloping due to diminishing MU.

7.1.5 Limitations of Marginal Utility Theory and Assumptions of Rational Behaviour

• Main Assumptions:
  1. Consumers are rational and aim to maximise utility.
  2. Utility can be measured in cardinal units (utils).
  3. MU of money remains constant regardless of income spent.
  4. Consumption of goods is independent (MU of one good unaffected by consumption of another).
• Limitations:
  1. Utility Measurement Issue: Utility is subjective, cannot be objectively measured in utils.
  2. Irrational Behaviour: Behavioural economics shows biases, habits, and emotions affect decisions.
  3. Interdependence of Goods: Complementary/substitute goods mean MU is not independent.
  4. Changing MU of Money: Spending large amounts may reduce the value of remaining money.
  5. Incomplete Information: Consumers may not know all prices or options.
• Real-World Relevance:
  • Marginal utility theory is useful for explaining downward-sloping demand, but unrealistic in its pure form.
  • Modern approaches use ordinal utility (ranking preferences) and indifference curve analysis.

1. Total Utility and Marginal Utility Curves

Total Utility (TU)
↑
|                         _______
|                       /
|                    __/
|                 __/
|              __/
|           __/
|        __/
|     __/
|  __/
|_/_________________________________→ Quantity (Q)

Marginal Utility (MU)
↑
| 20  *   
| 18    *   
| 16      *  
| 12        *  
| 8           *   
| 4             *   
| 0               *   
| -2                *
|___________________________________→ Quantity (Q)

• TU rises then plateaus, MU falls, hits zero, then negative.

2. Diminishing Marginal Utility

Marginal Utility (MU)
↑
| 20  *   
| 15    *   
| 10      *   
| 5         *   
| 0           *   
| -5            *   
|_____________________________→ Quantity (Q)

• MU decreases as quantity increases, can become negative.

3. Equi-Marginal Principle (MU/P for Two Goods X and Y)

Marginal Utility per $ (MU/P)
↑
| 15  *       *   
| 12    *    *    
| 9       * *      
| 6         *      
| 3          *     
|________________________→ Quantity Purchased

   * Blue = MUx/Px
   * Orange = MUy/Py

The consumer reallocates spending until MUx/Px = MUy/Py.

4. Derivation of Individual Demand Curve from Marginal Utility

Price / MU ($)
↑
| 10  *   
| 8     *  
| 6       *  
| 4         *  
| 2           *  
|________________________→ Quantity (Q)

- Downward sloping curve shows price consumer willing to pay falls as Q increases.