i had a couple thoughts while driving a month ago:
(a) if utility functions are just as valid when transformed with a monotonically increasing function, of what use is the concept of diminishing marginal utility?
(b) diminishing marginal utility of income implies that lump-sum transfers can affect efficiency.
in retrospect, i'll address these now:
(a) wikipedia indeed says, "Ordinal utility functions are equivalent up to monotone transformations, while cardinal utilities are equivalent up to positive linear transformations." dmu requires the latter. positive linear transformations preserve second-order behavior. in general, a monotone transformation will not preserve second-order behavior.
(b) i still stand by this.
comments?
(a) if utility functions are just as valid when transformed with a monotonically increasing function, of what use is the concept of diminishing marginal utility?
(b) diminishing marginal utility of income implies that lump-sum transfers can affect efficiency.
in retrospect, i'll address these now:
(a) wikipedia indeed says, "Ordinal utility functions are equivalent up to monotone transformations, while cardinal utilities are equivalent up to positive linear transformations." dmu requires the latter. positive linear transformations preserve second-order behavior. in general, a monotone transformation will not preserve second-order behavior.
(b) i still stand by this.
comments?
economics is often defined as "the study of the allocation of scarce resources."
my new definition is "the study of costs."
here's why: take, for example, the firm's profit maximization model. nothing is scarce in this model. credit is perfect and unlimited! without costs, there would not be a solution. costs drive the results.
now consider the consumer's utility maximization problem. yes, income is scarce. but that is not interesting whatsoever. bill has $10, so bill purchases $10 of goods. who cares? what is interesting is how he allocates that money. that allocation is driven purely by costs.
i'm pushing this because my thesis is about willpower costs. costs, people!
my new definition is "the study of costs."
here's why: take, for example, the firm's profit maximization model. nothing is scarce in this model. credit is perfect and unlimited! without costs, there would not be a solution. costs drive the results.
now consider the consumer's utility maximization problem. yes, income is scarce. but that is not interesting whatsoever. bill has $10, so bill purchases $10 of goods. who cares? what is interesting is how he allocates that money. that allocation is driven purely by costs.
i'm pushing this because my thesis is about willpower costs. costs, people!
a) i think that is right. the only thing is that the wiki entry should probably read "Ordinal utility functions are equivalent up to <positive> monotone transformations, while cardinal utilities are equivalent up to positive linear transformations."
the negative transformation g(u(w))=-u(w) will not preserve ordinal ranking
b) as for b, i think that is basically the theoretical foundation for much of welfare economics. the underlying problem is that utility can not be measured cardinally. if we could measure individual's utility, then we could probably easily make adjustments that would result in 'most' of the people being better off. but who is to say that 15 million dollar yacht does not provide as much utility to the yacht owner as that to 1500 african orphans who can be fed for three years?
If you are interested, here is an article that uses relative utility http://homepages.wmich.edu/~bjr7864/Singer_famine.pdf
the negative transformation g(u(w))=-u(w) will not preserve ordinal ranking
b) as for b, i think that is basically the theoretical foundation for much of welfare economics. the underlying problem is that utility can not be measured cardinally. if we could measure individual's utility, then we could probably easily make adjustments that would result in 'most' of the people being better off. but who is to say that 15 million dollar yacht does not provide as much utility to the yacht owner as that to 1500 african orphans who can be fed for three years?
If you are interested, here is an article that uses relative utility http://homepages.wmich.edu/~bjr7864/Singer_famine.pdf
> what use is the concept of diminishing marginal utility?
i can't recall ever using the concept of diminishing marginal utility for anything in positive economics after high-school
i can't recall ever using the concept of diminishing marginal utility for anything in positive economics after high-school
fsmart > a) ... the only thing is that the wiki entry should probably read ...
yeah, i agree. i changed the wiki entry. :)
fsmart > b) as for b, i think that is basically the theoretical foundation for much of welfare economics.
so then why do many econ profs say, "it's efficient because it's a lump-sum transfer"? that seems necessary but not sufficient for efficiency-neutrality.
yeah, i agree. i changed the wiki entry. :)
fsmart > b) as for b, i think that is basically the theoretical foundation for much of welfare economics.
so then why do many econ profs say, "it's efficient because it's a lump-sum transfer"? that seems necessary but not sufficient for efficiency-neutrality.
>i can't recall ever using the concept of diminishing marginal utility for anything in positive economics after high-school
DMU is the critical assumption for the underlying theory behind expected utility risk aversion and much of the economic research done since 1960.
DMU is the critical assumption for the underlying theory behind expected utility risk aversion and much of the economic research done since 1960.