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The graph above represents a typical Cobb-Douglas utility function given by . Higher level of utility is presented by a higher utility function such that , meaning the consumer is better off at .
Recall that total derivative of a function is given by
Axioms of Preferences
– We are talking about goods and not bads >> More is better!
– Consider two bundles X and Y. If Y has at least as much of both goods, and more of one, then
– Averages are better than extremes (or at least not worse)
– An average of two bundles on the same indifference curve will be (at least weakly) preferred
– The consumer can always compare/rank bundles.
– If X is preferred to Y, and there is a third bundle Z which lies within a small radius of Y, then X will be preferred to Z.
Marginal Rate of Substitution
- So the slope of an indifference curve is equal to the ratio of marginal utilities (will become important later).
- If indifference curves are convex, so that the MRS is diminishing:
–We can notice a few things about the function. As , conversely as . What happens to the MRS in this case? As a consumer moves along the
–As we get more q1 each additional unit is worth less to us (so U_1 goes down).
–As we get less q2 each additional unit is worth more to us (so U_2 goes up).
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