14 Questions
What does the axiom of transitivity imply about indifference curves?
They can never cross each other
How does the assumption of monotonicity affect the shape of indifference curves?
They have negative slopes
What is the marginal rate of substitution (MRS) related to in microeconomics?
Slope of an indifference curve
How are well-behaved indifference curves described in microeconomics?
Flattening as x1 increases
What does a and b represent in the perfect-complement preferences utility function?
Positive numbers indicating consumption proportions
In the perfect complements model, what is the equation for the corner points?
ax1 = bx2
What does the Cobb-Douglas utility function look like for two goods x1 and x2?
u(x1,x2) = x1^c * x2^d
What transformation can be applied to the Cobb-Douglas utility function to make the exponents sum to 1?
Monotonic transformation
How is the marginal rate of substitution (MRS) defined?
The rate at which a consumer is willing to substitute a small amount of one good for another
What does the utility function u(x1,x2) = min{ax1,bx2} represent?
Perfect-complement preferences
What does the MRS measure according to the text?
The quantity of good 2 substituted for good 1
What is true about the Cobb-Douglas utility function transformation?
It preserves the relative ranking of bundles.
How can the consumer's willingness to substitute between goods x1 and x2 be calculated?
By determining the MRS at a given bundle of goods.
In terms of utility, how are perfect complements different from perfect substitutes?
They have identical utility functions.
Study Notes
Preferences
- Perfect substitutes: goods that can be substituted for each other at a constant rate
- Perfect complements: goods that are always consumed together in fixed proportions
- Example of perfect substitutes: two cups of coffee
- Example of perfect complements: left and right shoes
Utility Function
- Represents a preference relation that is complete, reflexive, transitive, and continuous
- Assigns a real number to each bundle of goods, ranking them in terms of preference
- Only the ordering of bundles matters, not the magnitude of the utility difference between them
- Referred to as ordinal utility
Indifference Curves
- Contain equally preferred bundles of goods
- Can be represented by a continuous utility function
- Convexity: averages are preferred to extremes, and indifference curves are convex (to the origin)
- Monotonicity: more of any commodity is always preferred, and indifference curves have negative slope
Marginal Rate of Substitution (MRS)
- Measures the rate at which a consumer is willing to substitute one good for another
- Calculated as the ratio of the change in good 2 to the change in good 1
- Approaches the slope of the indifference curve as the change in good 1 gets smaller
Perfect Substitutes
- Two goods are perfect substitutes if the consumer is willing to substitute one for the other at a constant rate
- Simplest case: one-to-one substitution
Cobb-Douglas Preferences
- Example of well-behaved indifference curves
- Formula: u(x1,x2) = ax1 + bx2
- Can be used to present algebraic examples of economic ideas
- Can be transformed into a utility function with exponents summing to 1
Utility Functions
- Can be used to measure the marginal rate of substitution (MRS)
- Can be transformed into a new utility function that preserves the preference ordering
Explore examples of special preferences and perfect complements in microeconomics, focusing on goods consumed together in fixed proportions. Dive into the concept of perfect substitutes and complements as discussed in Karoly M Kiss's Microeconomics Chapter 3-4.
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