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ECON 410: Notes
complete |
a decision can be made
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symmetric
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an individual is indifferent
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transitive
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preference is "consistent"
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local nonsatiation
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no bliss points
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monotonicity
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more is better
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strict convexity
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a preference for diversity
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continuity
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no unexpected shifts in preferences
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Indifference curves
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The graphical set of all bundles of goods that an individual views equally desirable.
-Specific to the individual
-complete summary of "tastes"
-indifference map is a combo of indifference curves
-CANNOT be upward sloping
-infinite and non crossing
-Curvature tells about trade-offs individuals are willing to make
-Bowed in |
Perfect compliments
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-Goods that a consumer is interested in in consuming only in fixed proportions
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Perfect substitutes
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-Goods that a consumer is indifferent as to which to consume.
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Marginal Rate of Substitution 1
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The max amount of good 2 the individual would be willing to give up to get one more Good 1
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Marginal Rate of Substitution (2)
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The minimum amount of Good 2 the individual would need to receive to give up one more good 1
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Marginal Rate of Substitution (3)
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(the negative) of the derivative of the indifference curve, x2=f(x1)
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Utility function
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a mathematical function that represents an individuals preferences in a very particular way (ITS JUST A LABEL)
-Increasing utility function exists if and only if preferences are rational and monotonic |
ordinal |
no way of comparison
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cardinal
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one that tells us the relative ranking of the two things and tells us how much
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Monotonic Transformations
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1. Adding a constant
2. Multiplying by a positive constant
3. Assuming each is positive, raising to a positive power
4.Ln/Exponential
*(if the derivative of a transformation is positive, it is monotonic) |
Cobb-douglas
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Holds the property that at low levels of each good they are complementary, High levels of each, they are more substitutable
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Constatn Elasticity of Substitution (CES) utility function
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A chameleon function that can "mimic" other utility functions/
p=1 if a perfect substitute
p-->0 it becomes a Cobb-Douglas utility function
p-->-Infiniti if becomes a perfect compliment utility function |
budget set
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set of all bundles from which an individual can choose
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Constrained Optimization
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1. If preferences are monotonic, then my optimal point will be on the budget line or else monotonicity is violated
2. If preferences are rational, convex, and monotonic, then if I am consuming both goods, my optimal point will be on the budget line and will be at a point |
Diminishing Marginal Rate of subsitution
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Strictly convex preferences display a diminishing marginal rate of substitution. In other words, the more of a good an individual has compared to the other good to offset a decrease in another good.
CONVEXITY DRIVES EVERYTHING |