E_d = 0 (Perfectly inelastic demand)

Q = 50 units

Percentage fall in price = 25%

Price decreases and TE remains constant. It shows that there is unitary elastic demand, i.e. E_d = 1.

\(\Delta P = 9-10 =-1, \Delta Q = 18-18=0\)
Percentage Change in Quantity Demanded
= \(\frac{\Delta Q}{Q}\times 100\) 
= \(\frac{0}{18}\times100\) = 0 
Percentage change in Price
       = \(\frac{\Delta P}{P}\times 100=\frac{1}{100}\times 100 \)= Rs.10
\(E_d=\frac{Percentage \ \ Change \ \ in \ \ Quantity \ \ Demanded}{Percentage \ \ Change \ \ in \ \ Price}\)
\(=\frac{0}{10}=0\)
\( E_d=0\) (Perfectly inelastic demand)

Price Elasticity of Demand is a quantitative relationship between change in quantity demanded due to change in price. On the other hand, Income Elasticity of Demand is a quantitative instrument which measures the responsiveness of change in demand due to change in income of the consumer, it is calculated as:
\(E_y=\frac{Percentage \ \ Change \ \ in \ \ Demand}{Percentage \ \ Change \ \ in \ \ Income}\)
Where E_y = Income Elasticity of Demand.

Given, q = 10 - 2p
At p = 1
Quantity demanded, q = 10 - 2 x 1 = 10 - 2 - 8

Consumer's equilibrium with respect to purchase of one good is attained when
(i) the marginal utility of the good is equal to its of the good price.
(ii) MU should decrease with increase in consumption.
Example: Suppose a consumer is buying oranges and the price of each unit of orange is Rs.4. Hypothetical marginal utility schedule of orange is given as:

P_x=MU_x
It is evident from the schedule that the consumer will purchase 4 unts of oranges and reaches an equilibrium position. In this situation, the condition of consumer's equilibrium MU_x (in Rs) = P is satisfied. At this level of consumption, the marginal utility is equal to the price of orange, i.e., 4 = 4.

Equilibrium is struck, when \({MU_X\over P_X}=MU_M\)
If MU_X rises and P_X is constant the consumer will find his equilibrium only when consumption of commodity X is decreased. The above equation can be re-written as MU_X=P_X X MU_M. As P_X is constant and MU_M is rising, hence MU_X must, also rise for the consumer to be in equilibrium, hence consumption of good X must fall.

(i) The demand for commodoties having close substitutes is very elastic because if there is an increase in the price of the commodity, their people will start using substitute commodities.
(ii) Items such as toothpaste, needle will have an inelastic demand as consumers spend a small proportion of their income on such items. On the other hand, goods on which the consumers spend a large proportion of their income tend to have elastic demand.

Indifference curve is defined as the curve which represents all combinations  of two commodities which give same level of satisfaction to the consumer so that the consumer becomes indifferent towards these combinations.Following are the main properties of Indifference Curve:
(a) An Indifference Curve is always downward sloping:The indifference curve is negatively sloped or downward sloping from left to right which represents that in order to increase the consumption of commodity X, the consumer has to sacrifice commodity Y in order to remain at the same scale of preference or same level of satisfaction represented by the Indifference curve.
(b) An Indifference Curve is convex to origin: The nature and shape of  indifference curve is based on the concept of diminishing marginal rate of substitution. According to which the rate of sacrifice in terms of commodity Y in order to increase the consumption of commodity X decreases with every increase in unit of commodity X due to which an indifference curve is always made convex to origin . The marginal rate of substitution depends on relative marginal utilities derived from X and Y. When the consumer consumes more of X after sacrificing Y, when it leads to decrease in MU for X and increase in MU for Y due to which the consumer becomes willing to sacrifice lesser units of Y with every increase in consumption of X due to which MRS decreases and IC is convex to origin .
(c) Higher Indifference Curve represents higher scale of preference: Indifference  curve analysis is based on the assumption of monotonic preferences which represents that higher consumption of a commodity gives higher  level of satisfaction to the consumer. A higher indifference curve represents that the consumer is able to consume more units of the commodity and hence represents higher scale of preference to the consumer.

\(e_D={./.change\ in\ quantity demand\over ./. change\ in\ price}\)
\(-0.2={./.change\ in\ quantity demand\over 5}\)
% change in quantity demanded = -20 x 5 = -1%

\(E_d={\Delta q\over \Delta p}.{p\over q}\)
\(={3\over -1}.{5\over 12}={5\over -4}=(-)1.25\)

(i) Elastic demand.When the percentage change in quantity demanded is more than the percentage change in price, then the demand for the commodity is said to be elastic. The coefficient of price elasticity of demand in this case is greater than unity, i.e., e_D > 1, whereas when the percentage change in quantity demanded is less than the percentage change in price, then the demand for the commodity is said to be inelastic. The coefficient of price elasticity is less than unity, i.e., e_D < l.
(ii) Perfectly elastic demand.When the demand for a commodity rises or falls to any extent, without any change in its price, the demand for the commodity is said to be perfectly elastic. The coefficient of price elasticity of demand in this case is infinity, i.e., e _D = ∞. Whereas when the demand for a commodity does not change as a result of change in its price, the demand is said to be perfectly inelastic. It is also called zero elastic demand.The coefficient of price elasticity of demand in this case is zero, i.e., e_D = O.

Factors determining how many units of a good the consumer will buy are:
(a) Its Marginal Utility (b) Its Price
Consumer compares its marginal utility with its price. If marginal utility is more than price, he will continue to buy more, till the point is reached where marginal utility becomes equal to the price.
Following conditions must be satisfied for a consumer to be in equilibrium (getting maximum satisfaction)
(i) MU of a commodity = Price of the commodity, i.e., MU_x = P_x
(ii) MU should decrease with increase in consumption.

Consumer's equilibrium in case of two commodities x and y is attained when the ratio pf the marginal utilities of two goods and their prices is equal,
\(i.e., ={MU_X\over P_X}={MU_Y\over P_Y}\)
To attain consumer's equilibrium, two essential conditions to be met with:
(i) Marginal Utility of the last rupee of expenditure on each of the good is the same.
(ii) Marginal Utility of a good falls as more of it consumed.
The consumer's equilibrium condition on the basis of the above two conditions to be met with is:
\(i.e., ={MU_X\over P_X}={MU_Y\over P_Y}=MU\) of last rupee spent on each good.

(i) The demand for a commodity and unfavourable change in taste of the buyer are inversely related to each other. When there is an unfavourable change in taste of the buyer for the commodity, the demand for the commodity
falls at the same price and as a result the demand curve shifts to the left.The given diagram shows the effect In the diagram, demand curve of X is shown by the DD curve. With an unfavourable change in taste of the buyer for the commodity, the demand of good X, falls from OQ to OQo at the same price OP. The demand curve shifts leftward from DD to D₀D₀.

(ii) The demand for an inferior good and change in the income of the buyers are inversely related to each other. When there is a fall in the income of the buyer, the demand for the inferior good rises and as a result, the demand curve shifts to the right.The given diagram shows the effect.
In the diagram, demand curve of X (inferior good) is shown by DD curve. With a fall in the income of the buyer, the demand of inferior goods rises from OQ to OQ₁ at the same price OP. The demand curve shifts rightward from DD to D₁D₁.

Price elasticity of demand is the degree of responsiveness of the quantity demanded of a good to a change in its price. Following are the factors affecting price elasticity of demand:
(i) Availability of close substitutes for the commodity.A commodity will have elastic demand if there are close substitutes available, e.g., Pepsi, Coca-Cola, Frooti. A commodity having no substitutes, e.g., salt will have inelastic demand.
(ii) Nature of good.Generally, the demand for necessaries is inelastic and that for luxuries elastic.This is so because certain goods which are essential for life will be demanded at any price, whereas goods as luxuries can
be dispensed easily if they appear to be costly.
(iii) Uses of the commodity.If a commodity has only a few uses, e.g., butter, its demand is likely to be inelastic. If on the other hand, a commodity has many uses, its demand is likely to be elastic, e.g., milk.
(iv) l Share in total expenditure on the commodity.The demand for such commodities where a small part of the income spent is generally inelastic such as.commodities like needle, match box, button etc. On the other hand,the demand for such commodities where a significant part of income is spent, is very elastic, such as demand for woollen suit, other luxuries etc.
(v) Tastes and Preferences/Habits.If the consumers are habitual of some commodities, the demand for such commodities will be usually inelastic, because they will use them even if their prices go up. Asmoker generally does not smoke less when the price of cigarettes goes up.

Given that P_x = 3, P_y = 3 and Marginal Rate of Substitution = 3.Aconsumer is said to be in equilibrium when \(MRS={P_X\over P_Y}\)
By substituting the values, we find that \(3>{3\over3}\) i.e. \(MRS={P_X\over P_Y}\) in the given case, thus, the consumer is not in equilibrium because when \(MRS={P_X\over P_Y}\), it implies that the consumer is willing to pay more for unit of X, as compared
to what market demands. The consumer will buy more and more of X. As a result, MRS will fall due to the Law of Diminishing Marginal Utility.This will continue till \(MRS={P_X\over P_Y}\) and the consumer is again in equilibrium.