ECS2601 Assignment
1 (COMPLETE
ANSWERS) Semester
1 2025 (655050) -
DUE 2 April 2025
For Assistance contact
Email:
,Question 1: Consumer Preferences, Utility Maximization, Elasticities, and Indifference
Curves
1.1 Assumptions about Consumer Preferences (4 marks)
In microeconomics, we make certain assumptions about how consumers make choices to build
models of demand. Two key assumptions are:
Completeness: This assumption states that a consumer can compare any two bundles of
goods and services and definitively state that they prefer one to the other, or are
indifferent between them. In real life, consider a consumer choosing between a new
smartphone (Bundle A) and a weekend getaway (Bundle B). The completeness
assumption implies that the consumer will be able to say one of three things: "I prefer the
smartphone to the getaway," or "I prefer the getaway to the smartphone," or "I am
indifferent between the smartphone and the getaway." Even if the decision is difficult, the
consumer is assumed to be able to make a comparison. For example, someone might
intensely debate whether they need a new phone more than a relaxing break, but
eventually, they will likely lean towards one or the other, or feel equally satisfied with
either.
Transitivity: This assumption states that if a consumer prefers bundle A to bundle B, and
prefers bundle B to bundle C, then they must also prefer bundle A to bundle C. This
ensures consistency in consumer preferences. Imagine a student choosing snacks. They
might prefer a chocolate bar (A) to a packet of crisps (B), and prefer the packet of crisps
(B) to an apple (C). The transitivity assumption implies that this student will also prefer
the chocolate bar (A) to the apple (C). If preferences were not transitive, a consumer
could theoretically end up in a perpetual cycle of switching between bundles without ever
reaching a most preferred option, which contradicts the idea of rational decision-making.
For instance, if they preferred A to B, B to C, and then C to A, their choices would be
inconsistent.
1.2 Critical Evaluation of Utility Maximization Condition (3 marks)
For a consumer to achieve maximum satisfaction, the marginal rate of substitution (MRS)
between two goods must equal the ratio of the prices of those goods. This condition arises from
the interaction of the consumer's preferences (represented by indifference curves) and their
budget constraint.
Indifference Curves and MRS: The MRS represents the rate at which a consumer is
willing to give up one good to obtain one more unit of another good while maintaining
the same level of utility. It is the absolute value of the slope of the indifference curve at a
given point. A diminishing MRS implies that as a consumer obtains more of one good,
they are willing to give up less of the other good to get an additional unit of the first
good. This reflects the idea that the marginal utility of a good decreases as we consume
more of it.
Budget Constraint and Price Ratio: The budget constraint represents all the
combinations of two goods that a consumer can afford given their income and the prices
, of the goods. The slope of the budget constraint is the negative ratio of the prices of the
two goods (-Pₓ/P<0xE1><0xB5><0x83>). This price ratio indicates the rate at which the
consumer can trade one good for the other in the market.
Maximizing Satisfaction: The consumer aims to reach the highest possible indifference
curve given their budget constraint. Graphically, this occurs at the point where the budget
constraint is tangent to an indifference curve. At this point of tangency, the slope of the
indifference curve (MRS) is equal to the slope of the budget constraint (the absolute
value of the price ratio).
Economic Intuition: If the MRS is greater than the price ratio
(MRSₓ<0xE1><0xB5><0x83> > Pₓ/P<0xE1><0xB5><0x83>), it means the consumer is
willing to give up more of good Y to get one more unit of good X than the market
requires. Therefore, they can increase their satisfaction by consuming more of good X
and less of good Y, moving to a higher indifference curve within their budget.
Conversely, if the MRS is less than the price ratio (MRSₓ<0xE1><0xB5><0x83> <
Pₓ/P<0xE1><0xB5><0x83>), the consumer is willing to give up less of good Y for one
more unit of good X than the market demands. They can increase satisfaction by
consuming less of good X and more of good Y.
Critical Evaluation: The condition MRS = Pₓ/P<0xE1><0xB5><0x83> represents an
equilibrium where the consumer's subjective valuation of the trade-off between the two
goods aligns with the market's objective valuation. Any deviation from this point implies
that the consumer can reallocate their spending to achieve a higher level of satisfaction.
This condition is crucial for understanding rational consumer choice in standard
microeconomic models. However, it relies on the assumptions of rational consumers with
well-defined and stable preferences, perfect information, and the ability to make marginal
adjustments in their consumption. In reality, consumers may face cognitive biases,
imperfect information, transaction costs, or emotional influences that lead to deviations
from this optimal condition. Nevertheless, it provides a powerful benchmark for
analyzing consumer behavior.
1.3 Comment on Elasticities (4 marks)
(a) Arc Elasticity of Demand: Arc elasticity of demand measures the responsiveness of quantity
demanded to a change in price over a range of prices (an arc of the demand curve), rather than at
a specific point. It is calculated using the average of the initial and final prices and quantities.
The formula is:
Arc Elasticity of Demand = [(Q2 - Q1) / ((Q2 + Q1) / 2)] / [(P2 - P1) / ((P2 + P1) / 2)]
Arc elasticity is useful when analyzing the impact of significant price changes, as point elasticity
can vary considerably along a non-linear demand curve. It provides an average elasticity over the
specified price range, giving a more representative measure of responsiveness for larger price
movements. However, because it uses averages, it might not perfectly reflect the elasticity at any
specific price within that range.
1 (COMPLETE
ANSWERS) Semester
1 2025 (655050) -
DUE 2 April 2025
For Assistance contact
Email:
,Question 1: Consumer Preferences, Utility Maximization, Elasticities, and Indifference
Curves
1.1 Assumptions about Consumer Preferences (4 marks)
In microeconomics, we make certain assumptions about how consumers make choices to build
models of demand. Two key assumptions are:
Completeness: This assumption states that a consumer can compare any two bundles of
goods and services and definitively state that they prefer one to the other, or are
indifferent between them. In real life, consider a consumer choosing between a new
smartphone (Bundle A) and a weekend getaway (Bundle B). The completeness
assumption implies that the consumer will be able to say one of three things: "I prefer the
smartphone to the getaway," or "I prefer the getaway to the smartphone," or "I am
indifferent between the smartphone and the getaway." Even if the decision is difficult, the
consumer is assumed to be able to make a comparison. For example, someone might
intensely debate whether they need a new phone more than a relaxing break, but
eventually, they will likely lean towards one or the other, or feel equally satisfied with
either.
Transitivity: This assumption states that if a consumer prefers bundle A to bundle B, and
prefers bundle B to bundle C, then they must also prefer bundle A to bundle C. This
ensures consistency in consumer preferences. Imagine a student choosing snacks. They
might prefer a chocolate bar (A) to a packet of crisps (B), and prefer the packet of crisps
(B) to an apple (C). The transitivity assumption implies that this student will also prefer
the chocolate bar (A) to the apple (C). If preferences were not transitive, a consumer
could theoretically end up in a perpetual cycle of switching between bundles without ever
reaching a most preferred option, which contradicts the idea of rational decision-making.
For instance, if they preferred A to B, B to C, and then C to A, their choices would be
inconsistent.
1.2 Critical Evaluation of Utility Maximization Condition (3 marks)
For a consumer to achieve maximum satisfaction, the marginal rate of substitution (MRS)
between two goods must equal the ratio of the prices of those goods. This condition arises from
the interaction of the consumer's preferences (represented by indifference curves) and their
budget constraint.
Indifference Curves and MRS: The MRS represents the rate at which a consumer is
willing to give up one good to obtain one more unit of another good while maintaining
the same level of utility. It is the absolute value of the slope of the indifference curve at a
given point. A diminishing MRS implies that as a consumer obtains more of one good,
they are willing to give up less of the other good to get an additional unit of the first
good. This reflects the idea that the marginal utility of a good decreases as we consume
more of it.
Budget Constraint and Price Ratio: The budget constraint represents all the
combinations of two goods that a consumer can afford given their income and the prices
, of the goods. The slope of the budget constraint is the negative ratio of the prices of the
two goods (-Pₓ/P<0xE1><0xB5><0x83>). This price ratio indicates the rate at which the
consumer can trade one good for the other in the market.
Maximizing Satisfaction: The consumer aims to reach the highest possible indifference
curve given their budget constraint. Graphically, this occurs at the point where the budget
constraint is tangent to an indifference curve. At this point of tangency, the slope of the
indifference curve (MRS) is equal to the slope of the budget constraint (the absolute
value of the price ratio).
Economic Intuition: If the MRS is greater than the price ratio
(MRSₓ<0xE1><0xB5><0x83> > Pₓ/P<0xE1><0xB5><0x83>), it means the consumer is
willing to give up more of good Y to get one more unit of good X than the market
requires. Therefore, they can increase their satisfaction by consuming more of good X
and less of good Y, moving to a higher indifference curve within their budget.
Conversely, if the MRS is less than the price ratio (MRSₓ<0xE1><0xB5><0x83> <
Pₓ/P<0xE1><0xB5><0x83>), the consumer is willing to give up less of good Y for one
more unit of good X than the market demands. They can increase satisfaction by
consuming less of good X and more of good Y.
Critical Evaluation: The condition MRS = Pₓ/P<0xE1><0xB5><0x83> represents an
equilibrium where the consumer's subjective valuation of the trade-off between the two
goods aligns with the market's objective valuation. Any deviation from this point implies
that the consumer can reallocate their spending to achieve a higher level of satisfaction.
This condition is crucial for understanding rational consumer choice in standard
microeconomic models. However, it relies on the assumptions of rational consumers with
well-defined and stable preferences, perfect information, and the ability to make marginal
adjustments in their consumption. In reality, consumers may face cognitive biases,
imperfect information, transaction costs, or emotional influences that lead to deviations
from this optimal condition. Nevertheless, it provides a powerful benchmark for
analyzing consumer behavior.
1.3 Comment on Elasticities (4 marks)
(a) Arc Elasticity of Demand: Arc elasticity of demand measures the responsiveness of quantity
demanded to a change in price over a range of prices (an arc of the demand curve), rather than at
a specific point. It is calculated using the average of the initial and final prices and quantities.
The formula is:
Arc Elasticity of Demand = [(Q2 - Q1) / ((Q2 + Q1) / 2)] / [(P2 - P1) / ((P2 + P1) / 2)]
Arc elasticity is useful when analyzing the impact of significant price changes, as point elasticity
can vary considerably along a non-linear demand curve. It provides an average elasticity over the
specified price range, giving a more representative measure of responsiveness for larger price
movements. However, because it uses averages, it might not perfectly reflect the elasticity at any
specific price within that range.
