Friday, August 29, 2014
A Non-Convexity Example
Maybe there are examples of people preferring extreme values over certain ranges of consumption of a good to averages in between. I think education is a good example, because there are discrete cutoffs in the value (derived in terms of future salary or policy restrictions) at various cutoffs in the quantity of education "consumed" (invested in?). These cutoffs take place at about the 10th year (policy restriction on dropping out below age 16), 12th year (high school diploma), and 16th year (bachelor's degree). Since there is a "jump" in the market value of education at the diploma and degree levels, a consumer might prefer both 12 years and 16 years of education to some convex combinations in between (13 or 15 years education and correspondingly more consumption of "other goods"). Here is an example of what the resulting indifference curve might then look like:
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I have another example for non-convexity,let's say,I want to have a pet,a cat costs as much as a dog,and further that my budget suffices for one cat or one dog.Suppose that I view either animal as equally valuable.In this case, I would purchase either one cat or one dog.It is obvious that I don't want to purchase half of a cat and half of a dog!Thus, my preferences are non-convex:I prefers having either animal to having any strictly convex combination of both.
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