## Table of Contents

## 2

# Theory of Consumer Behaviour

### 2.1 Utility

#### 2.1.1 Cardinal Utility Analysis

##### Measures of Utility

##### Derivation of Demand Curve in the Case of a Single Commodity (Law of Diminishing Marginal Utility)

#### 2.1.2 Ordinal Utility Analysis

##### Shape of an Indifference Curve

##### Monotonic Preferences

##### Indifference Map

##### Features of Indifference Curve

### 2.2 The Consumer’s Budget

#### 2.2.1 Budget Set and Budget Line

#### EXAMPLE 2.1

##### Price Ratio and the Slope of the Budget Line

#### 2.2.2 Changes in the Budget Set

(x1, x2) such that p1x1 + p2x2 ≤ M′. Now the equation of the budget line is

### 2.3 Optimal Choice of the Consumer

##### Equality of the Marginal Rate of Substitution and the Ratio of the Prices

### 2.4 Demand

#### 2.4.1 Demand Curve and the Law of Demand

##### Functions

### EXAMPLE 1

### EXAMPLE 2

##### Graphical Representation of a Function

#### 2.4.2 Deriving a Demand Curve from Indifference Curves and Budget Constraints

##### Linear Demand

#### 2.4.3 Normal and Inferior Goods

#### 2.4.4 Substitutes and Complements

#### 2.4.5 Shifts in the Demand Curve

#### 2.4.6 Movements along the Demand Curve and Shifts in the Demand Curve

### 2.5 Market Demand

##### Adding up Two Linear Demand Curves

### 2.6 Elasticity of Demand

### Example 2.2

is estimated to be equal to one and the demand for the good is said to be Unitary-elastic at that price. Note that the demand for certain goods may be elastic, unitary elastic and inelastic at different prices. In fact, in the next section, elasticity along a linear demand curve is estimated at different prices and shown to vary at each point on a downward sloping demand curve.

#### 2.6.1 Elasticity along a Linear Demand Curve

Geometric Measure of Elasticity along a Linear Demand Curve

The elasticity of a linear demand curve can easily be measured geometrically. The elasticity of demand at any point on a straight line demand curve is given by the ratio of the lower segment and the upper segment of the demand curve at that point. To see why this is the case, consider the following figure which depicts a straight line demand curve, q = a – bp.

Suppose at price p0, the demand for the good is q0. Now consider a small change in the price. The new price is p1, and at that price, demand for the good is q1.

∆q = q1q0 = CD and ∆p = p1p0 = CE.

Therefore, eD = = × = × = ×

Since ECD and Bp0D are similar triangles, = . But =

eD = = .

Since, Bp0D and BOA are similar triangles, =

Thus, eD = .

The elasticity of demand at different points on a straight line demand curve can be derived by this method. Elasticity is 0 at the point where the demand curve meets the horizontal axis and it is ∝ at the point where the demand curve meets the vertical axis. At the midpoint of the demand curve, the elasticity is 1, at any point to the left of the midpoint, it is greater than 1 and at any point to the right, it is less than 1.

Note that along the horizontal axis p = 0, along the vertical axis q = 0 and at the midpoint of the demand curve p = .

##### Constant Elasticity Demand Curve

#### 2.6.2 Factors Determining Price Elasticity of Demand for a Good

#### 2.6.3 Elasticity and Expenditure

##### Rectangular Hyperbola

##### Relationship between Elasticity and change in Expenditure on a Good

= ∆p[q(1 +)] = ∆p[q(1 + eD)].