Indifference map refers to a set of indifference curves corresponding to different income levels of satisfaction.

Budget line is a line showing different combinations of two goods which a consumer can attain at his given Income and Market price of the goods.

It is the sum total of the marginal utilities obtained from the consumption of successive units of a commodity.
TU=MU₁ +MU₂ +MU₃+ .....+MU_n or \(\Sigma MU\)

(i) Want satisfying power of a commodity is called utility.
(ii) It is measured in utils.

(i) Goods which are indispensable for the human being to exist in the world are called "necessaries" (for example food).
(ii) Goods which are not indispensable for life but to make our life easy, convenient and comfortable are called "comforts". (for example: TV)
(iii) Goods which are not very essential but are very costly are known as "Luxuries". (for example- Jewellery, Diamonds).

The slope of a linear demand curve is given as \(\frac{\Delta p}{\Delta q}\)
(i) While price elasticity of demand is given as
\(Ed=\frac{\Delta Q}{\Delta P}\times \frac{P}{Q}\)
(ii) Hence, we can write above equation
(iii) (i) as \(Ed=\frac{1}{Slope\ of\ Demand\ Curve}\times \frac{P}{Q}\)
\(Ed=\frac{1}{\frac PQ}\times \frac{P}{Q}\)
(iv) The above equation states that there exist an inverse relationship between slope of a linear demand curve and Price elasticity of demand.

(i) Cardinal utility of a commodity is measured in money terms.
(ii) Marshall assumes that there is definite relationship between expected satisfaction (utility) and realized satisfaction (actual).
(iii) Marginal utility of money is constant.
(iv) An absence of differences in income, taste, fashion etc.
(v) Independent goods and independent utilities.
(vi) Demand for a commodity depends on its price alone, it includes other determinants of demand.

Total utility	Marginal utility
Increases at a diminishing rate	Goes on diminishing
Reaches maximum	Becomes zero
Diminishes	Becomes negative

Characteristics
Wants are unlimited
(i) Wants are countless and various in kinds.
(ii) When one want is satisfied another want arises.
Wants become habits
(i) When a man starts reading newspaper in the morning it becomes a habit.
Wants are satiable
(i) We can satisfy particular wants at a given time.
(ii) When one feels hungry, he takes food and that want is satisfied.
Wants are alternative
(i) There are alternative ways to satisfy a particular want (eg) idly, dosa.
Wants are competitive
(i) There is competition among wants.
(ii) So we have to choose more urgent wants and satisfy them first.
Wants are complementary
(i) Satisfaction of a particular want requires the use of more than one commodity. (eg) car and petrol.
Wants are recurring
(i) Some wants occur again and again. For ex. if we feel hungry, we take food and satisfy our want.
(ii) But after some time we again feel hungry and want food.

a. Indifference Map:

Indifference Map is a group of indifference curves for two commodities showing different levels of satisfaction. In this indifference map, it should be clearly understood that a higher indifference curve denotes higher level of satisfaction and a lower indifference curve represents lower level of satisfaction. Being rational, the consumer will always choose a higher indifference curve to get maximum satisfaction, other things being equal.
b. Properties of an Indifference curve:
i. Indifference curves slope downwards to the right
ii. Indifference curves are convex to the origin
iii. No two indifference curves can ever cut each other.
i. All indifference curves slope downwards from left to right:

The downward slope of indifference curve must be attributed to the fact that the consumer in substituting good X by good Y, increases the amount of Y and reduces the amount of X. If the indifference curve were horizontal line running parallel to X axis then the combination which it represents is the same amount of Y but more and more of X. In that case, the satisfaction from the combination will not be equal. For the same reason, it can be said that indifference Curves will not be vertical.
ii. All indifference curves are convex to the origin:
This is because of the operation of a principle known as 'Diminishing Marginal Rate of Substitution'. The indifference curves are based on this principle. If they are concave to the origin, then it will mean that MRS is increasing. Indifference curve cannot be straight line except when the goods are perfect substitutes.
Marginal rate of substitution between X and Y refers to the amount of commodity Y to be offered in exchange for one unit of X commodity. The MRS goes on diminishing as consumer goes on substituting X for Y.
iii. No two indifference curves intersect each other:

The third assumption is that no two indifference curves can ever cut each other. But in the Figure we find two indifference curves do cut each other. Point A which is on indifference curve 2 represents a higher level of satisfaction to the consumer than at point B which is on indifference curve 1. But point C lies on both curves. That means, two levels of satisfaction A and B which are unequal have become equal. That cannot be accepted. So indifference curves can never cut each other. These are the three assumptions about the shape of an indifference curve.

Introduction:
(i) The law of demand explains the direction of change in demand due to change in price.
(ii) Elasticity of demand explains the rate of change in quantity demanded due to a given change in price.
Definition:
Elasticity of demand describes the degree of responsiveness of the quantity demand for a commodity to a change in its price - Stonier and Hague.
Types:

There are four methods of measuring price elasticity of demand.
Percentage Method:
It is known as ratio method.
\(\mathrm{e_p}=\frac{\Delta \mathrm{Q}}{\Delta \mathrm{P}} \times \frac{\mathrm{P}}{\mathrm{Q}} \text { or } \frac{\% \Delta \mathrm{Q}}{\% \Delta \mathrm{P}} \text { where } \frac{\% \Delta \mathrm{Q}}{\% \Delta \mathrm{P}}=\frac{\text { Percentage change in demand }}{\text { Percentage change in price }}\)
Total Outlay Method:
Marshall suggested that this is the simplest way to decide whether demand is elastic or inelastic.
Total Revenue (Outlay) = Price x Quantity sold

Point (or) Geometrical Method:
The point elasticity in a straight line or linear demand curve is the ratio of the segments of the line to the right and to the left of the particular point.
\(Point\ elasticity=\frac{Lower\ segment\ of\ the\ demand\ curve\ below\ the\ given\ point}{Upper\ segment\ of\ the\ demand\ curve\ above\ the\ given\ point}\)

(i) In terms of indifference curve analysis, the consumer achieves his optimum choice when he strikes a balance between what he wishes to buy and what he can buy.
(ii) According to indifference curve analysis, a consumer is in equilibrium at a point, where the slope of the indifference curve is equal to the slope of a budget line.
(iii) Condition of consumer's Equilibrium
\(MRS_{xy}=\frac{Px}{Py}\)
(iv) Here, MRS_xy = Marginal Rate of substitution between good x and y
(v) \(\frac{Px}{Py}\)= Price Ratio between good x and good y
(vi) \(MRS_{xy}=\frac{\Delta Y}{\Delta X}\) = Slope of indifference curve
(vii) At the point of equality between
\(MRS_{xy}=\frac{Px}{Py}=\) Indifference curve must be convex to the origin.
(viii) It implies that at the point of equilibrium, MRS must be diminishing.

Explanation:
(i) In the above diagram BL - is Budget line.
(ii) IC₁, IC₂, IC₃ = set of indifference curves.
(iii) Consumer is equilibrium at point 'e'. At this point, BL is tangent to IC₂ signifying that \(MRS_{xy}=\frac{Px}{Py}\)
(iv) Consumer will not be in equilibrium at point f and g because they belong to lower IC.