Consumer's Equilibrium: Cardinal Approach

Consumer equilibrium using cardinal utility — single commodity (MU = Price) and two commodities (Law of Equi-Marginal Utility) with schedules and diagrams.

Notes

Consumer's Equilibrium: Cardinal Approach

Class 11 Micro Economics — Single commodity and two commodities equilibrium under cardinal utility analysis

What is Consumer's Equilibrium?

Consumer's Equilibrium refers to the situation when a consumer is having maximum satisfaction with limited income and has no tendency to change his way of existing expenditure.

Equilibrium means a state of rest — no change, maximum benefit. When a consumer buys goods, they pay a price; as they consume more, utility decreases due to the Law of Diminishing Marginal Utility; and their income also gets used up with each purchase. A rational consumer therefore tries to balance their expenditure in such a way that they attain maximum satisfaction with minimum expenditure.

Consumer equilibrium can be studied in two situations:

  • Single Commodity: Consumer consumes only one good
  • Two Commodities: Consumer consumes two goods (general case)

The Balance Scale — MU vs Price

MU (Benefit)Price (Cost)MU > Price
MU Benefit>Price Cost|Equilibrium

Single Commodity Equilibrium

When a consumer buys only one commodity, two factors determine equilibrium:

  • Price of the commodity
  • Expected utility (MU) from each unit

The consumer will be at equilibrium when:

Equilibrium Condition

$$\mathrm{MU}_x = P_x$$

Converting Utils to Money Terms

$$\text{MU in terms of Money} = \frac{\text{MU in utils}}{\text{MU of one rupee (MU}_M\text{)}}$$

Why MU = Px?

  • If MU > Px: The consumer gets more satisfaction than the price paid. They will buy more until MU falls (due to DMU) and becomes equal to price.
  • If MU < Px: The satisfaction is less than the price paid — a loss. The consumer will reduce consumption until MU rises to equal price.
  • When MU = Px: Maximum satisfaction achieved. No incentive to change.

Additional condition: MU must fall as consumption increases (implied by the Law of Diminishing Marginal Utility). Equilibrium is achieved only on the downward sloping portion of the MU curve.

Alternative Form

$$\frac{MU_x}{MU_M} = P_x \quad \text{or} \quad \frac{MU_x}{P_x} = MU_M$$

Interactive Equilibrium Graph

Drag the slider to change price
123456Units20151050-5Px = ₹10EQ = 3MU Curve
Price:10

Scenario

You're at a golgappa stall. Each plate costs ₹10. The MU from your current plate is shown on the graph above. Should you buy another plate?

UnitsPrice (₹)MU (utils)MU in ₹MU vs PriceRemark
1102020MU > PMU > P → Buy More
2101616MU > PMU > P → Buy More
3101010MU = P ✓MU = P → Equilibrium ✓
41044MU < PMU < P → Reduce
51000MU < PMU < P → Reduce
610-6-6MU < PMU < P → Reduce

Two Commodities Equilibrium

In reality, a consumer buys multiple commodities. The equilibrium condition extends to the Law of Equi-Marginal Utility — also known as:

Law of SubstitutionLaw of Maximum SatisfactionGossen's Second Law

Two conditions must be satisfied for equilibrium:

  1. Equi-Marginal Condition: The ratio of MU to price must be equal for all commodities, and equal to the marginal utility of money.
  2. MU falls as consumption increases: The Law of DMU must hold — equilibrium is achieved on the falling portion of the MU curve for each good.

Two Commodities Equilibrium Condition

$$\frac{MU_x}{P_x} = \frac{MU_y}{P_y} = MU_M$$

What if MU/P Ratios Are Not Equal?

  • If MUx/Px > MUy/Py: The consumer gets more marginal utility per rupee from X. They will buy more of X, which reduces MUx (Law of DMU), and less of Y, which increases MUy. This continues until both ratios equalize.
  • If MUx/Px < MUy/Py: The consumer gets more marginal utility per rupee from Y. They will buy more of Y, reducing MUy; and less of X, raising MUx. Again, the process continues until the ratios become equal.

Interactive Money Allocation Simulator

You have ₹5. Click a coin, then choose what to buy (Samosa or Cold Drink). Both cost ₹1 each.

Samosas (X)

0

Last MU: 0

Cold Drinks (Y)

0

Last MU: 0

Total Utility

0

utils

Optimal Rupee-by-Rupee Allocation

RupeeSpent OnMU GainedReason
1Samosa (X)20MUx (20) > MUy (16)
2Cold Drink (Y)16MUy (16) > MUx (14)
3Samosa (X)14MUx (14) > MUy (12)
4Cold Drink (Y)12MUy (12) = MUx (12), choose Y
5Samosa (X)12MUx (12) > MUy (8)

Limitation of Cardinal Approach

Utility is cardinally measurable in figures. However, utility is a feeling of mind — no standard measure exists. Utility cannot be expressed in exact units.

The cardinal utility approach assumes that satisfaction can be measured in exact numerical units called “utils” (1 util, 2 utils, etc.). But in reality, utility is a psychological and subjective concept — there is no instrument or scale that can objectively measure how much a person likes something. This is the most fundamental criticism of the cardinal approach, which led to the development of the ordinal utility approach (indifference curve analysis) by Hicks and Allen.

Key Takeaways

  • Consumer equilibrium: Maximum satisfaction with given income — no tendency to change expenditure pattern.
  • Single commodity: MUx = Px, with MU falling as consumption increases (Law of DMU).
  • Two commodities: MUx/Px = MUy/Py = MUm — the Law of Equi-Marginal Utility.
  • If MU/P ratios are unequal, the consumer reallocates expenditure — buy more where MU per rupee is higher.
  • Gossen's Second Law states: A rational consumer allocates income so that the last rupee spent on each good yields the same MU.