ECS2601 INTERMEDIATE MICROECONOMICS VERIFIED EXAM QUESTIONS
AND ANSWERS - LATEST VERSION 2026 /2027
Q: What is the definition of a preference relation in consumer theory?
ANSWER A preference relation is a binary relation on a consumer's
consumption set that indicates how a consumer ranks different bundles of
goods. It is typically assumed to be complete (any two bundles can be
compared), transitive (if A is preferred to B and B to C, then A is preferred to
C), and reflexive (any bundle is at least as good as itself).
Q: What is the difference between ordinal and cardinal utility?
ANSWER Ordinal utility only ranks bundles (e.g., Bundle A is preferred to
Bundle B) without measuring how much more it is preferred. Cardinal utility
assigns actual numerical values to utility, meaning the magnitude of the
difference matters. Modern consumer theory relies primarily on ordinal utility.
Q: What are the standard assumptions about consumer preferences?
ANSWER The standard assumptions are: (1) Completeness – the
consumer can compare any two bundles; (2) Transitivity – preferences are
consistent; (3) Reflexivity – every bundle is at least as good as itself; (4)
Continuity – small changes in bundles lead to small changes in preference;
(5) Monotonicity – more is better (non-satiation); (6) Convexity – averages
are preferred to extremes.
Q: What is a utility function and what does it represent?
ANSWER A utility function U(x₁, x₂) assigns a real number to every
consumption bundle such that bundles the consumer prefers receive higher
numbers. It represents the preference ordering of a consumer and allows
mathematical analysis of consumer choices.
Q: What is an indifference curve?
ANSWER An indifference curve is the set of all consumption bundles
among which the consumer is indifferent, i.e., all bundles yielding the same
level of utility. In a two-good world, it is typically downward-sloping, convex to
the origin, and indifference curves for different utility levels never cross.
Q: Why can indifference curves not intersect?
ANSWER If two indifference curves intersected at a point, transitivity would
be violated. At the intersection point, both curves represent the same utility
, level, but bundles on each curve away from that point represent different
utility levels. This creates a logical contradiction with the transitivity
assumption.
Q: What is the Marginal Rate of Substitution (MRS)?
ANSWER The MRS is the rate at which a consumer is willing to trade one
good for another while remaining on the same indifference curve (keeping
utility constant). It equals the negative slope of the indifference curve: MRS =
–(dx₂/dx₁) = MU₁/MU₂, where MU is marginal utility.
Q: What does a diminishing MRS imply about preferences?
ANSWER A diminishing MRS means the consumer is willing to give up
fewer and fewer units of good 2 for each additional unit of good 1 as they
consume more of good 1. This is reflected in the convex shape of
indifference curves and implies consumers prefer balanced bundles over
extreme ones.
Q: What is the difference between perfect substitutes and perfect
complements?
ANSWER Perfect substitutes have linear indifference curves (straight lines),
meaning the consumer is always willing to trade one good for the other at a
constant rate (MRS is constant). Perfect complements have L-shaped
indifference curves, meaning the goods must be consumed in fixed
proportions and additional units of one good alone provide no extra utility.
Q: What is a Cobb-Douglas utility function and what are its properties?
ANSWER The Cobb-Douglas utility function is U(x₁, x₂) = x₁ᵃx₂ᵇ where a, b
> 0. Its properties include: smooth, convex indifference curves; the MRS
equals (a/b)(x₂/x₁); it exhibits constant expenditure shares (the consumer
always spends a/(a+b) of income on good 1); and it is monotonically
increasing in both goods.
Q: What is a quasilinear utility function?
ANSWER A quasilinear utility function has the form U(x₁, x₂) = v(x₁) + x₂,
where x₂ appears linearly. Its indifference curves are parallel vertical
translations of one another. The MRS depends only on x₁ (not on x₂),
making demand for x₁ independent of income (no income effect for good 1).
Q: What is meant by 'monotonic transformation' of a utility function?
ANSWER A monotonic transformation is any increasing function f applied to
a utility function such that the new function f(U) represents the same
preference ordering. Since ordinal utility only ranks bundles, any monotonic
transformation preserves the ranking and therefore represents the same
preferences. For example, ln(U) is a monotonic transformation of U.
,Q: What is a budget constraint and how is it expressed mathematically?
ANSWER A budget constraint defines the set of affordable bundles given
prices and income. For two goods, it is: p₁x₁ + p₂x₂ ≤ m, where p₁ and p₂ are
prices, x₁ and x₂ are quantities, and m is income. The budget line is the
equality: p₁x₁ + p₂x₂ = m.
Q: What is the budget set?
ANSWER The budget set is the set of all consumption bundles that are
affordable at given prices and income. It is the area on or below the budget
line: {(x₁, x₂): p₁x₁ + p₂x₂ ≤ m, x₁ ≥ 0, x₂ ≥ 0}. The boundary of this set is the
budget line.
Q: How does the budget line change when income increases?
ANSWER When income increases (prices held constant), the budget line
shifts outward in a parallel fashion. Both intercepts (m/p₁ and m/p₂) increase
proportionally. The slope of the budget line (–p₁/p₂) remains unchanged
because the price ratio has not changed.
Q: How does the budget line change when the price of good 1
increases?
ANSWER When p₁ increases (income and p₂ held constant), the budget
line rotates inward around the vertical intercept (m/p₂). The horizontal
intercept (m/p₁) decreases, the vertical intercept remains unchanged, and
the slope (–p₁/p₂) becomes steeper (more negative).
Q: What is the slope of the budget line and what does it represent?
ANSWER The slope of the budget line is –p₁/p₂. It represents the market
rate of exchange between the two goods – how many units of good 2 must
be given up to purchase one more unit of good 1. It reflects the opportunity
cost of good 1 in terms of good 2.
Q: What is the consumer's optimization problem?
ANSWER The consumer's optimization problem is to choose a bundle (x₁*,
x₂*) that maximizes utility U(x₁, x₂) subject to the budget constraint p₁x₁ +
p₂x₂ = m. At the optimum (interior solution), the MRS equals the price ratio:
MU₁/MU₂ = p₁/p₂.
Q: What is the optimality condition for consumer choice?
ANSWER At the optimal interior solution, the slope of the indifference curve
equals the slope of the budget line: MRS = p₁/p₂, or equivalently MU₁/p₁ =
MU₂/p₂. This means the marginal utility per dollar spent is equal for both
goods. If MU₁/p₁ > MU₂/p₂, the consumer should buy more of good 1.
Q: What is a corner solution in consumer optimization?
, ANSWER A corner solution occurs when the optimal bundle involves
consuming zero of at least one good. This happens when the MRS never
equals the price ratio within the feasible region. For example, if at x₂ = 0 the
MRS > p₁/p₂, the consumer buys only good 1. Corner solutions are common
with perfect substitutes.
Q: What is revealed preference theory?
ANSWER Revealed preference theory, developed by Samuelson, infers
preferences from observed choices. If a consumer chooses bundle A when
bundle B is affordable, then A is revealed preferred to B. The Weak Axiom of
Revealed Preference (WARP) states: if A is directly revealed preferred to B,
then B cannot be directly revealed preferred to A.
Q: State the Weak Axiom of Revealed Preference (WARP).
ANSWER WARP states: if a consumer chooses bundle x when bundle y is
affordable (p·x ≤ p·y is false, meaning y costs at least as much), and later
bundle y is chosen, then x must not be affordable at the new prices.
Formally: if p·x ≥ p·y and x ≠ y, then p'·y > p'·x. It ensures internal
consistency of choices.
Q: What is the difference between a Giffen good and an inferior good?
ANSWER An inferior good is a good for which demand decreases as
income increases. A Giffen good is an inferior good whose demand actually
increases when its own price rises – a violation of the normal law of demand.
All Giffen goods are inferior goods, but not all inferior goods are Giffen
goods. Giffen goods require a very strong income effect that dominates the
substitution effect.
Q: What is a normal good?
ANSWER A normal good is a good for which demand increases as income
increases (holding prices constant). The income elasticity of demand is
positive. Most goods are normal goods. Examples include food, clothing, and
automobiles. The Engel curve for a normal good is upward sloping.
Q: What is the Engel curve?
ANSWER The Engel curve shows the relationship between a consumer's
income and their demand for a good, holding prices constant. For normal
goods, it is upward sloping (demand increases with income). For inferior
goods, it is downward sloping (demand decreases with income). For goods
with constant budget shares, the Engel curve is a straight line through the
origin.
Q: What is an offer curve (price-consumption curve)?
AND ANSWERS - LATEST VERSION 2026 /2027
Q: What is the definition of a preference relation in consumer theory?
ANSWER A preference relation is a binary relation on a consumer's
consumption set that indicates how a consumer ranks different bundles of
goods. It is typically assumed to be complete (any two bundles can be
compared), transitive (if A is preferred to B and B to C, then A is preferred to
C), and reflexive (any bundle is at least as good as itself).
Q: What is the difference between ordinal and cardinal utility?
ANSWER Ordinal utility only ranks bundles (e.g., Bundle A is preferred to
Bundle B) without measuring how much more it is preferred. Cardinal utility
assigns actual numerical values to utility, meaning the magnitude of the
difference matters. Modern consumer theory relies primarily on ordinal utility.
Q: What are the standard assumptions about consumer preferences?
ANSWER The standard assumptions are: (1) Completeness – the
consumer can compare any two bundles; (2) Transitivity – preferences are
consistent; (3) Reflexivity – every bundle is at least as good as itself; (4)
Continuity – small changes in bundles lead to small changes in preference;
(5) Monotonicity – more is better (non-satiation); (6) Convexity – averages
are preferred to extremes.
Q: What is a utility function and what does it represent?
ANSWER A utility function U(x₁, x₂) assigns a real number to every
consumption bundle such that bundles the consumer prefers receive higher
numbers. It represents the preference ordering of a consumer and allows
mathematical analysis of consumer choices.
Q: What is an indifference curve?
ANSWER An indifference curve is the set of all consumption bundles
among which the consumer is indifferent, i.e., all bundles yielding the same
level of utility. In a two-good world, it is typically downward-sloping, convex to
the origin, and indifference curves for different utility levels never cross.
Q: Why can indifference curves not intersect?
ANSWER If two indifference curves intersected at a point, transitivity would
be violated. At the intersection point, both curves represent the same utility
, level, but bundles on each curve away from that point represent different
utility levels. This creates a logical contradiction with the transitivity
assumption.
Q: What is the Marginal Rate of Substitution (MRS)?
ANSWER The MRS is the rate at which a consumer is willing to trade one
good for another while remaining on the same indifference curve (keeping
utility constant). It equals the negative slope of the indifference curve: MRS =
–(dx₂/dx₁) = MU₁/MU₂, where MU is marginal utility.
Q: What does a diminishing MRS imply about preferences?
ANSWER A diminishing MRS means the consumer is willing to give up
fewer and fewer units of good 2 for each additional unit of good 1 as they
consume more of good 1. This is reflected in the convex shape of
indifference curves and implies consumers prefer balanced bundles over
extreme ones.
Q: What is the difference between perfect substitutes and perfect
complements?
ANSWER Perfect substitutes have linear indifference curves (straight lines),
meaning the consumer is always willing to trade one good for the other at a
constant rate (MRS is constant). Perfect complements have L-shaped
indifference curves, meaning the goods must be consumed in fixed
proportions and additional units of one good alone provide no extra utility.
Q: What is a Cobb-Douglas utility function and what are its properties?
ANSWER The Cobb-Douglas utility function is U(x₁, x₂) = x₁ᵃx₂ᵇ where a, b
> 0. Its properties include: smooth, convex indifference curves; the MRS
equals (a/b)(x₂/x₁); it exhibits constant expenditure shares (the consumer
always spends a/(a+b) of income on good 1); and it is monotonically
increasing in both goods.
Q: What is a quasilinear utility function?
ANSWER A quasilinear utility function has the form U(x₁, x₂) = v(x₁) + x₂,
where x₂ appears linearly. Its indifference curves are parallel vertical
translations of one another. The MRS depends only on x₁ (not on x₂),
making demand for x₁ independent of income (no income effect for good 1).
Q: What is meant by 'monotonic transformation' of a utility function?
ANSWER A monotonic transformation is any increasing function f applied to
a utility function such that the new function f(U) represents the same
preference ordering. Since ordinal utility only ranks bundles, any monotonic
transformation preserves the ranking and therefore represents the same
preferences. For example, ln(U) is a monotonic transformation of U.
,Q: What is a budget constraint and how is it expressed mathematically?
ANSWER A budget constraint defines the set of affordable bundles given
prices and income. For two goods, it is: p₁x₁ + p₂x₂ ≤ m, where p₁ and p₂ are
prices, x₁ and x₂ are quantities, and m is income. The budget line is the
equality: p₁x₁ + p₂x₂ = m.
Q: What is the budget set?
ANSWER The budget set is the set of all consumption bundles that are
affordable at given prices and income. It is the area on or below the budget
line: {(x₁, x₂): p₁x₁ + p₂x₂ ≤ m, x₁ ≥ 0, x₂ ≥ 0}. The boundary of this set is the
budget line.
Q: How does the budget line change when income increases?
ANSWER When income increases (prices held constant), the budget line
shifts outward in a parallel fashion. Both intercepts (m/p₁ and m/p₂) increase
proportionally. The slope of the budget line (–p₁/p₂) remains unchanged
because the price ratio has not changed.
Q: How does the budget line change when the price of good 1
increases?
ANSWER When p₁ increases (income and p₂ held constant), the budget
line rotates inward around the vertical intercept (m/p₂). The horizontal
intercept (m/p₁) decreases, the vertical intercept remains unchanged, and
the slope (–p₁/p₂) becomes steeper (more negative).
Q: What is the slope of the budget line and what does it represent?
ANSWER The slope of the budget line is –p₁/p₂. It represents the market
rate of exchange between the two goods – how many units of good 2 must
be given up to purchase one more unit of good 1. It reflects the opportunity
cost of good 1 in terms of good 2.
Q: What is the consumer's optimization problem?
ANSWER The consumer's optimization problem is to choose a bundle (x₁*,
x₂*) that maximizes utility U(x₁, x₂) subject to the budget constraint p₁x₁ +
p₂x₂ = m. At the optimum (interior solution), the MRS equals the price ratio:
MU₁/MU₂ = p₁/p₂.
Q: What is the optimality condition for consumer choice?
ANSWER At the optimal interior solution, the slope of the indifference curve
equals the slope of the budget line: MRS = p₁/p₂, or equivalently MU₁/p₁ =
MU₂/p₂. This means the marginal utility per dollar spent is equal for both
goods. If MU₁/p₁ > MU₂/p₂, the consumer should buy more of good 1.
Q: What is a corner solution in consumer optimization?
, ANSWER A corner solution occurs when the optimal bundle involves
consuming zero of at least one good. This happens when the MRS never
equals the price ratio within the feasible region. For example, if at x₂ = 0 the
MRS > p₁/p₂, the consumer buys only good 1. Corner solutions are common
with perfect substitutes.
Q: What is revealed preference theory?
ANSWER Revealed preference theory, developed by Samuelson, infers
preferences from observed choices. If a consumer chooses bundle A when
bundle B is affordable, then A is revealed preferred to B. The Weak Axiom of
Revealed Preference (WARP) states: if A is directly revealed preferred to B,
then B cannot be directly revealed preferred to A.
Q: State the Weak Axiom of Revealed Preference (WARP).
ANSWER WARP states: if a consumer chooses bundle x when bundle y is
affordable (p·x ≤ p·y is false, meaning y costs at least as much), and later
bundle y is chosen, then x must not be affordable at the new prices.
Formally: if p·x ≥ p·y and x ≠ y, then p'·y > p'·x. It ensures internal
consistency of choices.
Q: What is the difference between a Giffen good and an inferior good?
ANSWER An inferior good is a good for which demand decreases as
income increases. A Giffen good is an inferior good whose demand actually
increases when its own price rises – a violation of the normal law of demand.
All Giffen goods are inferior goods, but not all inferior goods are Giffen
goods. Giffen goods require a very strong income effect that dominates the
substitution effect.
Q: What is a normal good?
ANSWER A normal good is a good for which demand increases as income
increases (holding prices constant). The income elasticity of demand is
positive. Most goods are normal goods. Examples include food, clothing, and
automobiles. The Engel curve for a normal good is upward sloping.
Q: What is the Engel curve?
ANSWER The Engel curve shows the relationship between a consumer's
income and their demand for a good, holding prices constant. For normal
goods, it is upward sloping (demand increases with income). For inferior
goods, it is downward sloping (demand decreases with income). For goods
with constant budget shares, the Engel curve is a straight line through the
origin.
Q: What is an offer curve (price-consumption curve)?
