Understand indifference curves, calculate Marginal Rate of Substitution (MRS), and apply properties of indifference maps.
Hook explaining the shift from Cardinal to Ordinal utility.
In real life, we rarely express our satisfaction with numbers. You don't put on a jacket and say, "This gives me exactly 50 units of utility!"
Instead, you just know whether you prefer it over another jacket. This practical approach is the foundation of Ordinal Utility Analysis, which argues that consumers evaluate options by simply ranking their alternative consumption bundles.
Calculating MRS as the ratio of mangoes sacrificed to bananas gained.
Problem. A consumer's preferences are plotted on an indifference curve. You are given two consumption bundles of bananas () and mangoes () that provide the exact same level of satisfaction.
Calculate the Marginal Rate of Substitution (MRS) as the consumer moves from Bundle A to Bundle B.
Given Data:
Calculating MRS for perfect substitutes using Table 2.3.
Let us calculate the Marginal Rate of Substitution (MRS) for a consumer who is indifferent between 5-rupee notes and 5-rupee coins. According to the example, if the consumer moves from Combination A (1 note, 8 coins) to Combination B (2 notes, 7 coins), they gain 1 note and give up exactly 1 coin. The formula for MRS is the absolute value of the change in coins divided by the change in notes. Therefore, the MRS for this step is calculated as , which is expressed as the ratio . Moving from Combination B to C (3 notes, 6 coins), the consumer again sacrifices exactly 1 coin for 1 additional note, yielding an MRS of . Because the marginal rate of substitution does not diminish but remains constant throughout, we consider these two commodities to be . Consequently, the indifference curve depicting these combinations will simply be a straight line.
Formal definition of MRS.
What it means
The amount of Good Y a consumer must forego to obtain one extra unit of Good X, keeping total utility constant.
Why absolute value?
Because is negative, the absolute bars ensure is expressed as a positive magnitude.
Visuals of standard convex ICs and straight-line ICs for perfect substitutes.
Left: Standard convex curve (Diminishing MRS). Right: Straight line for perfect substitutes (Constant MRS).
Explanation of the three main features and monotonic preferences.
Indifference curves have four strict mathematical properties that define how rational consumers make choices. Let's break them down.