Sample Paper 2014-15 & 15-16 & 16-17 & 17-18
(Q1) Explain why an indifference curve is convex to the origin? (4)
Ans: An indifference curve is convex to the origin due to diminishing MRS .
Diminishing MRS means that the number of units of ‘Good Y’ that a consumer wants to substitute for one extra unit of ‘Good X’ goes on decreasing as the consumption of Good X increases.
As consumption of Good X increases, the willingness to pay for it diminishes (due to the law of diminishing marginal utility). This payment is in terms of the units of Good Y sacrificed. Thus, MRS diminishes along an indifference curve, which makes it convex to the origin.
(Q2) A consumer consumes only two goods. Explain the conditions that need to be satisfied for the consumer to be in equilibrium under indifference curve analysis. (6)
Ans: Let a consumer consume Good X and Good Y. A consumer attains equilibrium when:
1)MRSXY = Px / Py
2)MRSXY must be decreasing due to the law of diminishing marginal utility. (1)
MRSXY is the number of units of Good Y a consumer in willing to sacrifice for an extra unit of Good X.
Px / Py is the ratio of prices that prevail in the market and gives the actual units of Good Y that need to be sacrificed to obtain an extra unit of Good X in the market. (1)
Suppose MRSXY < Px / Py
• It means that the consumer is willing to sacrifice less of Good Y than is actually required in the market for as extra unit of Good X.
• The consumer loses and reduces the consumption of Good X.
• As consumption of Good X decreases, its marginal utility increases.
• Thus, MRSXY increases.
• The process continues till MRSXY = Px /Py
(Q3) ‘Higher indifference curve represents higher level of satisfaction to the consumer’. Explain the statement, also state the underlying assumption related to this property of indifference curve.
Ans: Higher indifference curve represents higher level of satisfaction, in other words any combination that lie on a higher indifference curve i.e. away from origin represents higher level of satisfaction.
Combination B > A
( OX2,OY1 > OX1,OY1 )
The underlying assumption here is the assumption of monotonic preference which represents that a consumer will prefer a combination which contains more of at least one and no less of the other. (2+1+1)
(Q4) Show diagrammatically the conditions for consumer’s equilibrium, in Hicksian analysis of demand. (6M)
Ans: In the Hicksian / Indifference Curve analysis, a consumer attains equilibrium when
(a) Budget line is tangential to the Indifference curve at a unique combination of two goods. i.e,
Slope of Indifference Curve = Slope of Budget line
MRSxy = (-) Px / Py
(b) Indifference Curve is strictly convex to origin at the point of tangency i.e., MRSxy must be diminishing Explanation with diagram
(Q5) A consumer has total money income of 250 to be spent on two goods X and Y with prices
of 25 and 10 per unit respectively. On the basis of the information given, answer the following questions:
(a) Give the equation of the budget line for the consumer.
(b) What is the value of slope of the budget line ?
(c) How many units can the consumer buy if he is to spend all his money income on good X ?
(d) How does the budget line change if there is a fall in price of good Y ? (4)
(a) PxQx + PyQy = M that is 25Qx + 10Qy = 250
(b) Slope of Budget Line = (-) Px/Py = (-) 25/10 = (-) 2.5
(c) If Qy is to be Zero , Qx = M / Px = 250 / 25 = 10 units
(d) If Py falls the consumer will be able to buy more of good Y in the same money income pushing the Y-intercept of the Budget Line away from origin, keeping the X-intercept constant. (shifts outwards)
(Q6) Identify which of the following is not true for the Indifference Curves. Give valid reasons for choice of your answer:
a) Lower indifference curve represents lower level of satisfaction.
b) Two regular convex to origin indifference curves can intersect each other.
c) Indifference curve must be convex to origin at the point of tangency with the budget line at the consumer’s equilibrium.
d) Indifference curves are drawn under the ordinal approach to consumer equilibrium.
Ans: Out of the given options, (B) is incorrect. Indifference Curves have a property that two ICs cannot intersect. Suppose, there are any two ICs intersecting each other. As per the figure
A =C ( on IC1) & B= C (on IC2)
But if we see the peculiarity of point C (the point of intersection), this would result into absurd situation of A = B = C , which is not possible, as they are violating the assumption of monotonic preference & thus basic definition of the Indifference Curve (1 + 3)
CBSE paper 2014 & CBSE 2015
(Q1) Define indifference curve. (1M)
Ans: It is the locus of points that represent different combination of two goods that give the same satisfaction to the consumer.
(Q2) Define Budget set
Ans: Budget set consists of all the bundles of the goods which at given prices cost less than or equal to the given income of the consumer.
(Q3) What is meant by monotonic preferences. (1M)
Ans: Monotonic preferences refers to a situation when consumption increases total utility also increases alongwith.
(Q4) Define Budget line
Ans: Budget line is the locus of points, each point representing a bundle of the two goods which cost the consumer exactly his income.
(Q5) Define Indifference map
Ans: The set of indifference curves of a consumer is called indifference map.
(Q6) Explain the concept of ‘Marginal Rate of Substitution’ with the help of a numerical example. Also explain its behaviour along an indifference curve. (6M)
Ans: Marginal Rate of Substitution (MRS) means the rate at which a consumer is willing to sacrifice quantity of one good to obtain one more unit of the other good. Let the two goods consumed be A and B. (1M)
Suppose the following combinations of these two goods have the same utility level for him : (3M)
Good A Good B MRS
1 8 -
2 4 4B : 1A
3 1 3B : 1A
The consumer is willing to sacrifice 4B to obtain second unit of A . For the third unit of A , he is willing to sacrifice less because marginal utility of A decreases as he consumes more of A. (2M)
(Q7) A consumer consumes only two goods . If the price of the goods falls , the indifference curve
(a) Shift upwards
(b) Shifts downards
(c) Can shift both upwards or downwards
(d) does not shift
(Q8) If marginal rate of substitution is constant throughout, the indifference curve will be : (choose the correct alternative) (D)
(a) parallel to the X-axis
(b) downward sloping concave
(c) downward sloping convex
(d) downward sloping straight line
Ans: (d) Downward sloping straight line.
Ans: (b) Downward sloping concave.
(Q9) A consumer consumes only two goods. If price of one of the goods falls, the indifference curve: (choose the correct alternative) (F)
(a) shifts upwards
(b) shifts downwards
(c) can shift both upwards or downwards
(d) does not shift
(Q10) If Marginal Rate of Substitution is increasing throughout, the Indifference Curve will be : (Choose the correct alternative) (1 M)
(a) Downward slopping convex
(b) Downward sloping concave
(c) Downward sloping straight line
(d) Upward sloping convex
(Q11) Give equation of budget line. (D)
Ans: p1x1 + p2x2 = m
(Q12) Give equation of budget set. (D)
Ans: p1x1 + p2x2 < m
(Q13) Define utility
Ans: Utility refers to satisfaction from the consumption of goods.
(Q14) What do you mean by ordinal utility
Ans: Ordinal utility is the utility expressed in ranks.
(Q15) A consumer consumes only two goods X and Y, both priced at Rs. 2 per unit. If the consumer chooses a combination of the two goods with Marginal Rate of Substitution equal to 2, is the consumer in equilibrium ? Why or why not ? What will a rational consumer do in this situation ? Explain.
Ans: Given Px = 2 , Py = 2 and MRS = 2, A consumer is said to be in equilibrium when MRS = Px/Py
Substituting the values we find that
2 > 2/2 i.e. MRS > Px/Py
Therefore, consumer is not in equilibrium. (3M)
It means that consumer is willing to pay more for one more unit of X as compared to what the 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 = Px / Py and consumer is in equilibrium.
(Q1) Explain three properties of indifference curves. (6M)
(Q2) Explain the conditions of consumer’s equilibrium using indifference curve analysis (6)
(Q3) A consumer consumes only two goods X and Y. The Marginal Rate of Substitution is 1. Prices of X and Y are ‘ 3 and ‘ 4 per unit respectively. Is the consumer in equilibrium ? What will be further reaction of the consumer ? Give reason.
(Q1) Define indifference curve. (1M)
Ans: curve joining all points representing such bundles of two goods among which the consumer is indifferent is called an indifference curve.
(Q2) Explain with the help of a numercial example, the meaning of diminishing marginal rate of substitution. (4M)
Ans:When a consumer substitutes one good for one unit of another good, the rate at which this substitution takes place is called the (marginal rate of substitution As the substitution goes on, the marginal rate of substituition declines. (2M)
Combination of substitution Units of X Units of Y Marginal rate of g
good X and good Y
A 1 8 --
B 2 4 4Y : 1X
C 3 2 2Y : 1X
D 4 1 1Y : 1X (2M)
(Q3) Explain the meaning of ‘Budget set’ and ‘Budget line’. (3M)
Ans: Budget set refers to the set of possible combinations of two goods which the consumer can afford with his income at given prices. (11/2M)
From the Budget set if only such bundles are taken on which total expenditure equals total income and plotted on a graph, we get a line called the budget line. (11/2M)
(Q3) Why is an indifference curve negatively sloped ? Explain (3)
(Q4) Explain the meaning of budget line. What can cause a change in it ? Explain.
(Q5) Why is budget line a straight line ? Explain.
(Q1)What is Indifference Curve ? State three properties of indifference curves.
Ans: The three properties of ICs are
1) An IC slopes downwards from left to right :: It is because to consume more quantity of one good, some quantity of the other good must be reduced for the consumer to remain on t he same IC
2) An IC is convex towards origin :: It is because MRS declines as more is consumed of one good, because of operation of law of diminishing marginal utility.
3) An IC to the right represents higher level of satisfaction :: It is because an IC to the right shows more units of goods consumed and more units of goods consumed are assumed to have more satisfaction.
(Q2) Explain the conditions of consumer’s equilibrium using Indifference Curve Analysis (6M)
(Q3) Write a budget line equation of a consumer if the two goods purchased by the consumer, Good X and Good Y are priced at Rs.10 and Rs. 5 respectively and the consumer’s income is Rs.100.
Ans: Budget Line equation: m = PxQx + PyQy ; where m=income 1
Accordingly: 100 = 10Qx + 5Qy 3
(Q4) Define marginal rate of substitution. Explain its behaviour along an indifference curve (4M)
Ans: Marginal Rate of Substitution is defined as ‘the rate at which a consumer is willing to sacrifice units of a good to obtain one more unit of the other good. 1
Marginal Rate of Substitution diminishes as the consumer moves downward along the same indifference curve. It shows that consumer is willing to sacrifice lesser units of a Good Y, in order to gain one additional unit of Good X. This happens due to the operation of law of diminishing marginal utility.
(Q5) What is a budget line? State its properties. (extra)
Ans: Budget line is a line that shows different possible combinations of the two goods that can be purchased by a consumer, given his money income and market prices of goods.
(1)Budget line is downward sloping :: Budget line has a negative slope i.e – Px / P y. The negative slope of budget line indicates that the consumer can buy extra units of one commodity (say x) only by sacrificing some units of the other commodity (say y).
(2) Budget line is a straight line. Another property of budget is that it is a straight line implying that slope of budget line is constant. The slope is constant due to two assumptions (a) Consumer has a fixed income and (b) Prices of two goods are given.