Utility Flashcards
What is ordinal utility and why is it important?
Ordinal utility assigns numbers to consumption bundles to rank preferences without measuring the exact differences in satisfaction. It only matters whether one bundle is preferred over another, not by how much. This approach allows economists to describe consumer choices based on preference orderings rather than exact utility values.
What are monotonic transformations in utility functions?
A monotonic transformation changes the utility numbers while preserving the order of preferences. Examples include multiplying by a positive number, adding a constant, or raising to an odd power. Such transformations keep the preference rankings the same, meaning the utility function still represents the same consumer preferences.
What is cardinal utility, and why do economists prefer ordinal utility over it?
Cardinal utility assigns meaningful magnitudes to utility differences, implying one bundle is twice as preferred as another. However, it’s difficult to measure these differences accurately and doesn’t add value in predicting choices, as only the order of preferences matters. Thus, economists favor ordinal utility for its simplicity and effectiveness in describing consumer behavior.
What are perfect substitutes, and how is their utility function defined?
Perfect substitutes are goods that can replace each other at a constant rate. For example, red and blue pencils where only the total number matters. Their utility function is typically linear, such as u(x₁, x₂) = a x₁ + b x₂, where a and b represent the value of each good to the consumer. The slope of indifference curves is -a/b.
What are perfect complements, and how is their utility function defined?
Perfect complements are goods consumed together in fixed proportions, like left and right shoes. The utility function is u(x₁, x₂) = min{a x₁, b x₂}, where a and b indicate the required proportions. Indifference curves are L-shaped, reflecting that additional units of one good only add utility if paired with the other good in the specified ratio.
What are quasilinear preferences and their utility function?
Quasilinear preferences have indifference curves that are vertical shifts of each other, meaning utility is linear in one good but possibly nonlinear in another. The utility function is u(x₁, x₂) = v(x₁) + x₂, where v(x₁) is a function of good 1. Examples include u(x₁, x₂) = √x₁ + x₂ or u(x₁, x₂) = ln(x₁) + x₂.
What are quasilinear preferences and their utility function?
Quasilinear preferences have indifference curves that are vertical shifts of each other, meaning utility is linear in one good but possibly nonlinear in another. The utility function is u(x₁, x₂) = v(x₁) + x₂, where v(x₁) is a function of good 1. Examples include u(x₁, x₂) = √x₁ + x₂ or u(x₁, x₂) = ln(x₁) + x₂.
What are Cobb-Douglas preferences and their utility function?
Cobb-Douglas preferences are a common utility form where both goods are valuable but in different amounts. The utility function is u(x₁, x₂) = x₁ᶜx₂ᵈ, where c and d are positive constants representing the importance of each good. Indifference curves are smooth and convex, making this form useful for many economic models.
What is marginal utility and how is it calculated?
Marginal utility (MU) is the additional satisfaction from consuming an extra unit of a good. It is calculated as:
MU
1
=
Δx
1
ΔU
=
Δx
1
u(x
1
+Δx
1
,x
2
)−u(x
1
,x
2
)
Similarly, MU₂ is for good 2. It measures how utility changes with a small increase in the quantity of a specific good, holding other goods constant.
Scaling the utility function by multiplying it by a positive number changes the marginal utility by the same factor. For example, if utility is doubled, marginal utility also doubles. However, the preference order remains unchanged, meaning the behavioral implications of marginal utility do not change with scaling
What is the Marginal Rate of Substitution (MRS) and how is it calculated?
MRS is the rate at which a consumer is willing to substitute one good for another while keeping utility constant. It is calculated as:
𝑀𝑅𝑆=− ( 2𝑀𝑈1/ 2𝑀𝑈2 )
This ratio represents the slope of the indifference curve, showing how much of good 2 a consumer is willing to give up for an additional unit of good 1.
How is utility used to analyze commuting choices in transportation economics?
Utility functions model consumers’ choices between transportation modes (e.g., driving vs. taking the bus) based on factors like travel time, waiting time, and cost. By estimating utility functions from observed choices, economists can predict preferences and evaluate the benefits of transportation improvements, such as reducing travel time or costs.
How is utility used to analyze commuting choices in transportation economics?
Utility functions model consumers’ choices between transportation modes (e.g., driving vs. taking the bus) based on factors like travel time, waiting time, and cost. By estimating utility functions from observed choices, economists can predict preferences and evaluate the benefits of transportation improvements, such as reducing travel time or costs.
