Ch3. Consumer Theory — Utility, Indifference Curves & Budget Constraints

Utility

Utility: the satisfaction a consumer derives
  from consuming a good or service

Total Utility (TU):
  Total satisfaction from consuming a given quantity
  TU rises as consumption rises, but at a
  decreasing rate

Marginal Utility (MU):
  Additional utility from consuming one more unit
  MU = ΔTU / ΔQ

Law of Diminishing Marginal Utility:
  As consumption of a good increases,
  each additional unit yields less satisfaction
  (the first slice of pizza > the fifth slice)

The Equal-Marginal-Utility-Per-Dollar Rule

Consumer's Optimal Choice Condition:
  MUx / Px = MUy / Py

Interpretation:
  The last dollar spent on each good
  must yield equal marginal utility

Example:
  MUx/Px = 3, MUy/Py = 2
  → Buy more X and less Y
  → Equilibrium reached when MUx/Px = MUy/Py

Indifference Curves

Indifference Curve: all combinations of
  goods X and Y that yield the same level
  of utility

Four Properties:
  ① Downward sloping: more X requires
    less Y to maintain the same utility
  ② Convex to the origin: reflects
    diminishing marginal rate of substitution
  ③ Cannot cross: would violate transitivity
  ④ Higher curve = higher utility level

Marginal Rate of Substitution (MRS):
  MRS = MUx / MUy = |ΔY/ΔX|
    (the slope of the indifference curve)
  = units of Y the consumer will give up
    for one more unit of X

Diminishing MRS:
  As X increases, the consumer values
  additional X less → MRS falls
  (this is why the curve bows toward the origin)

Budget Constraint

Budget Line: all combinations of X and Y
  affordable given income (M) and prices

M = Px·X + Py·Y
→ Y = M/Py − (Px/Py)·X

Slope = −Px/Py (relative price ratio)

Budget Line Shifts:
  Income increases: parallel shift outward
  Px falls: X-intercept increases (pivots right)

Consumer Equilibrium

Consumer Equilibrium:
  The point where the budget line is tangent
  to the highest attainable indifference curve

Tangency Condition:
  MRS = Px/Py
  MUx/MUy = Px/Py
  → MUx/Px = MUy/Py (same as the equal-MU rule)

Price Change Effects:
  Substitution Effect: relative price change
    → consumer substitutes toward cheaper good
  Income Effect: real income change
    → affects overall consumption level

Normal Good: income effect positive
  → price falls → consumption rises
Inferior Good: income effect negative
  → price falls → consumption rises
  (substitution effect dominates)
Giffen Good: income effect negative > substitution effect
  → price falls → consumption FALLS
  (demand curve slopes upward — rare)

Equal-Marginal-Utility-Per-Dollar Rule ★★★★★ : MUx/Px = MUy/Py. When the last dollar spent on every good yields equal utility, the consumer has maximized satisfaction. Memory hook: utility maximized = equal bang per buck

Four Properties of Indifference Curves ★★★★★ : Downward sloping, convex to origin, cannot cross, higher = more utility. Slope = MRS = MUx/MUy. Memory hook: indifference curve = downslope + convex + no crossing

Giffen Good Condition ★★★★☆ : An inferior good whose (negative) income effect outweighs the substitution effect. Price falls → quantity demanded falls. Violates the law of demand. Memory hook: Giffen = inferior + income effect beats substitution

Practice Questions

Q. MUx = 12, Px = 4, MUy = 6, Py = 2. Is the consumer at equilibrium?

MUx/Px = 12/4 = 3; MUy/Py = 6/2 = 3. The ratios are equal — the consumer is already at equilibrium. No reallocation is necessary.

Q. Why is the indifference curve convex to the origin?

Because of diminishing MRS. As the consumer acquires more of X, the marginal utility of X falls and the marginal utility of Y rises → MRS = MUx/MUy decreases → the curve becomes flatter as we move right, creating the convex (bowed-in) shape.