27 Cards in this Set
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Venus is observed to orbit the sun every 0.62 years. What is the semi-major axis of Venus's orbit in AU?
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Kepler's Third law: (P/1 year)2 = (a/ 1AU)3
a = (p/1 year)2/3 AU
a = (0.62 years/1 year)2/3 AU = 0.73
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When Venus is at closest approach to Earth, it takes 270 seconds for radio waves to be transmitted to Venus, bounce off of Venus and return to Earth. Given this, compute how many meters are in an AU?
Venus is .73 AU away from the sun
Earth is 1 AU from the sun.
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First, compute the distance that the radio waves travel. Since Earth is 1 AU from the sun and Venus is .73 AU from the sun, when at closest approch to Earth, Venus is 1AU - .73 AU =.27 AU from Earth.
Distance=SpeedXTime; Radio waves travel at the speed of light: .54 AU = (3.0 x 108 m/s) …
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A new planet is discovered! Planet X is observed to orbit te sun every 300 years. What is the semi-major axis of Planet X's orbit in AU?
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Keplers Third Law:
a = (p/1 year)2/3 AU
a= (300 years/1 year)2/3 = 45 AU
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Fraction Chain Rule
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(a/b)/(c/d) = (ad)/(bc)
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Nested Fractions
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Turn whole numbers into fractions by dividing by 1 in order to apply the chain rule.
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complete
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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-off…
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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
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ordinal
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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)
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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
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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
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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
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Final Study Guide