Microeconomics Notes – Utility, Consumer Choice, Production & Costs

Total Utility, Marginal Utility & Consumer Choice

• Definitions

  • Utility = satisfaction from consuming goods/services.

  • Total Utility (TU) = cumulative satisfaction from all units of a product consumed.

  • Marginal Utility (MU) = extra satisfaction from one additional unit of a product.

• Utility Schedule (Alison – Bottled drinks)

  Bottles	TU	MU
  0	0	–
  1	30	30
  2	50	20
  3	65	15
  4	75	10
  5	83	8
  6	89	6
  7	93	4
  8	96	3
  9	98	2
  10	99	1

  • Graphically: TU rises at a decreasing rate; MU curve slopes downward.

• Law of Diminishing Marginal Utility

  • As total consumption increases over a given time period, the MU from each extra unit falls.

• Consumer’s Objective

  • Maximize total utility subject to: income, market prices, rational preferences, two-product assumption (X & Y).

  • Key rule: equate MU per last dollar across goods.
    \frac{MUX}{PX}=\frac{MUY}{PY}

Numerical Utility-Maximization Example

• Income = \$10, Products: Apples (X, PX=\$1) & Oranges (Y, PY=\$2).

• MU table (per unit):
  | Unit | MUX | MUX/PX | MUY | MUY/PY |
  |------|------|----------|------|----------|
  |1|10|10|24|12|
  |2|8|8|20|10|
  |3|7|7|18|9|
  |4|6|6|16|8|
  |5|5|5|12|6|
  |6|4|4|6|3|
  |7|3|3|4|2|

• Decision sequence (always buy highest MU/$ first): Y₁ → Y₂ → Y₃ → X₁ → X₂.

  • Expenditure: 2+2+2+1+1 = \$8 (stop when next best MU/$ is < existing).

  • Final purchase bundle achieves equality MUX/PX = MUY/PY = 8, leaving \$2 unspent or used on next-best equal utilities.

Demand Curve from Utility Maximization

• If P_Y drops from \$2 to \$1:

  • New MU/$ table (divide MU by 1): values double for oranges.

  • Consumer buys more oranges (up to 6 units in slide).

• Implied individual demand for Y:

  • PY=\$2 → QY=4 (obtained earlier).

  • PY=\$1 → QY=6.

• Market demand = horizontal summation of all individual demand curves.

• Consumer Surplus (CS): Area under demand but above price.

  • Graphically: triangle/trapezoid between price line & demand curve.

Substitution & Income Effects of Price Change

• Real income = purchasing power of money income.

• Two distinct effects when a price changes:

  1. Substitution Effect (SE) – movement along indifference curve caused by change in relative price, holding utility (real income) constant.

  2. Income Effect (IE) – parallel shift to a new indifference curve from the change in purchasing power, holding relative prices constant.

• Formal statements

  • SE: quantity demanded of a good rises when its relative price falls & vice-versa.

  • IE:

  • For normal goods: real-income ↑ → quantity demanded ↑.

  • For inferior goods: real-income ↑ → quantity demanded ↓.

Demand-Curve Slopes through SE & IE

1. Normal Good (price ↓):

   • SE ↑

   • IE ↑

   • Total: quantity ↑, therefore demand is negatively sloped.

2. Inferior Good (price ↓):

   • SE ↑

   • IE ↓

   • If SE > |IE| → overall ↑ (still downward-sloping).

   • If |IE| > SE → overall ↓ → upward-sloping (Giffen good).

   • Upward-sloping demand implies Giffen behaviour.

Labor-Supply Application

• Wage = price of leisure.

• Wage ↑ raises relative price of leisure (SE → work more).

• Wage ↑ raises real income (IE → desire more leisure, work less)

• Net labour-supply response depends on the relative sizes of SE vs IE.

Firms, Costs & Profits

• Production function Q=f(L,K) shows max output from inputs Labor & Capital.

• Economic profit \pi = TR - (Explicit\;costs + Implicit\;costs).

  • Accounting profit ignores implicit costs.

• Example (Ruth's Soup):

  • TR = 2000, Explicit = 1160 → Accounting Profit = 840.

  • Implicit = 265 → Economic Profit = 575.

Short-Run Production Concepts

• Total Product (TP), Average Product AP=TP/L, Marginal Product MP = \Delta TP/\Delta L.

• Law of Diminishing MP: Adding more of a variable factor to fixed input eventually lowers MP.

• Graph: MP intersects AP at AP’s maximum; TP flattens as MP ↓.

Short-Run Cost Concepts

• Total Cost TC = TFC + TVC.

  • TFC doesn’t vary with output.

  • TVC rises with output.

• Averages: ATC=TC/Q, AFC=TFC/Q (declines continuously), AVC=TVC/Q.

• Marginal Cost MC=\Delta TC/\Delta Q ; equals marginal variable cost.

• U-Shapes explained:

  • As long as AP rising, AVC falling; once AP falls, AVC rises (mirror with MP & MC).

• Variable-factor price ↑ → MC & ATC shift upward; fixed-factor price ↑ shifts ATC but not MC.

Long-Run Cost & Scale

• All inputs are variable; firms choose cost-minimizing input mix.

• Cost-minimization condition:
  \frac{MPK}{PK}=\frac{MPL}{PL} \quad \text{or} \quad \frac{MPK}{MPL}=\frac{PK}{PL}

• Principle of Substitution: if PL rises relative to PK, firms substitute K for L.

Long-Run Average Cost (LRAC)

• Obtained from envelope of all possible Short-Run ATCs (SRATCs).

• Typical "saucer-shape":

  1. Economies of scale (downward) up to Q_M.

  2. Minimum Efficient Scale (MES) at Q_M where LRAC minimum.

  3. Diseconomies of scale beyond Q_M.

• Relation to returns to scale:

  • Increasing RTS ⇒ Economies of scale; Constant ⇒ flat LRAC; Decreasing RTS ⇒ Diseconomies.

Market Structures & Perfect Competition

• Market power = ability to influence market price.

• Four structures (in ascending power): Perfect Competition → Monopolistic Competition → Oligopoly → Monopoly.

Conditions for Perfect Competition

• Many buyers & sellers; homogeneous product; perfect information; price-taking firms; free entry/exit.

• Firm faces horizontal demand at market price p despite industry’s downward-sloping demand.

Revenue under Perfect Competition

• TR = p \times Q

• AR = TR/Q = p

• MR = \Delta TR/\Delta Q = p
  ⇒ For competitive firm: p = AR = MR.

Short-Run Production Decision

1. Produce or Shut Down?

   • If p < AVC_{min} → Shut down (loss = TFC).

   • If p \ge AVC_{min} → Produce where MC = p.

2. Output Choice

   • Profit-maximization: choose Q where MC = MR = p (as long as p ≥ AVC).

• Shut-Down Price: price at minimum AVC; below this, firm’s best option is zero output.

Key Numerical & Graphical References

• Alison’s TU/MU table shows diminishing MU.

• Apple–Orange MU/$ tables demonstrate utility-max rule & derivation of individual demand.

• Demand curves plotted at p=\$1 & p=\$2 for oranges (Q=6 vs 4).

• Labor-supply indifference diagrams: SE & IE decomposition.

• TP, MP, AP graphs: point of diminishing MP, AP peak correspond to cost minima (AVC & MC).

• Cost curve diagrams show MC intersecting AVC & ATC at minima and SRATC envelope tangent to LRAC.

Ethical / Practical Notes

• Consumer surplus measures benefit to buyers; policy changes (taxes, subsidies) can be evaluated via changes in CS.

• Firms’ cost minimization affects resource allocation: substitution principle explains technological adoption (e.g., automation when labor costly).

• Understanding SE & IE aids welfare analysis of taxation or welfare programs (work incentives).