indifference curves and negative utility

  1. tenuous last message regarding circular indifference curves: “I talked to Mike about that. Circles was the immediate idea. Like a utility hill with contours.However the problem with that is that the other side of the hill represents dis-utility, whereas the side of the hill closer to the origin represents being less than satisfied. These two states cannot be equivalent. For example lets assume im at my utility hill with 10 bananas. 9 bananas and im not at the top, 11 bananas and im over-fed. But if we have circles that means that as far as utility is concerned 9 bananas is the same as 11, which is clearly not the same intuitively (at least for me). Underfed, and overfed are different experiences.So if it was a hill perhaps one side of the hill would be continuous, the other side would be a discontinuous drop into negative utility.

    So I dont think an indifference curve can ever take a nice shape. Realistic curves wouldn’t even be continuous, but discrete and they might look like piecewise functions not defined for all x. Simply because 10000000x whatever x is would represent disutility for many goods. Moreover the curves change with time. Pretty much utility theory seems like a dead end.

    It depends what we mean with utility, is utility an independent variable that every good gives us a little bit of (like energy). Or is utility a set of things? Or is utility a fancy word for describing dynamic behavior with some sort of end in mind?”

  2. ) I mean in all likelihood the utility function would not make a smooth surface. It probably wouldnt even be continuous assuming we are using discrete quantities of goods. I was saying the surface might look like a hill on one side, and a cliff on the other.
  3. quantities and circles
  4. if indifference curves (equi-total utility curves, level curves of the total utility surface) are circles then they must be insances of circles. here is  my resolution.  the indifference curve will be an ellipse (intuitively) for normal good/bad.  the major and minor axes (x=Qx, y=Qy) represent the critical quantities of each respective good/bad where marginal utility changes from positive to negative or vice versa depending on where you are on any respective elliptical indif curve. the intersection of each respective critical lines is the center of the elliptical indifference curve and together with the magnitude of the critical quantities, determines if it crosses any of the axes on the graph and also what quadrant(s) the elliptical inidfference curve will lie.  if the axes are both positive then the center of the ellipse will lie in the 1st quadrant. if they are both negative then they are in 3rd quadrant. if they are either negative/positive and positive/negative  then the centers of each ellipse will be in the 2nd and 4th quadrant respectively. if the magnitudes of the critical points are equal  (magnitude(Qx)= magnitude(Qy) ) then you will have a circular indifference curve somewhere on the cartesian plane.
  5. the top of the level surface may represent the maxium utility one can get from consuming those two goods. the budget constraint (a meta-self production capacity) is another dimension that allows you to move up the total utility surface (or what you call your “hill”)
  6. http://sites.csn.edu/istewart/mathweb/math127/ellipses/ellipses.htm
  7.   the first video was kind of done in haste after reading the first paragraph of the response im parsing here.
    “For example lets assume im at my utility hill with 10 bananas. 9 bananas and im not at the top, 11 bananas and im over-fed. But if we have circles that means that as far as utility is concerned 9 bananas is the same as 11, which is clearly not the same intuitively (at least for me). Underfed, and overfed are different experiences.”
    no contradiction here.  again, if it is ELLIPTICAL then this would only happen when the critical point that maximizes utility for the banana is 10.  once you cross the other side you are decreasing total utility.  dont understand why this is not the same intuitively.  underfed and overfed are different experiences with the same value/utility.  i think youre again reaching for a criticism here trying to conflate the statement 9=11 and f(9)=f(11) where f(x) is the total utility function. (more generally tenuous is saying (9,y)=(11,y) instead of f(9,y)=f(11,y) where f(x,y) is the total utility function).  this is either dishonest or ignorant. if your goal is to get out of a circular forest being x meters from the center have the same distance away from their respective closest “exit” point.
    “So if it was a hill perhaps one side of the hill would be continuous, the other side would be a discontinuous drop into negative utility.”
     first, remember this analysis was just an extention of how the continuous normal goods indifference curve presented in econ 101 accounts for negative utility.  this particular example does not mean this is the only type of indifference curve shape.
    as far as discontinuity (even when considering other indifference curves) it seems more intuitive that there are no discontinuities because it is a sum of an uncountably infinite amount of indifference curves.  units of goods are really continuous too. i can eat a half a banana or any proportion of that.  for every real number between two integers, i can consume that amount of banana (at least for the non-negative numbers), ensuring continuity.  bananas are sold and MORE IMPORTANTLY consumed by weight.  if you think weight is discrete… yeah. why arbitrarily choose the back side of the hill to be discontinuous?  even poison has gradual effects as you increase dosage.  temperature.  most if not everything seems proportional and continuous in nature. levels of nutrition and toxicity for bananas is not discrete since nutrition/toxicity is proportional to the amount consumed.    discrete units of goods are artificial.  buying isnt consuming. time you spend doing activities…

“It depends what we mean with utility, is utility an independent variable that every good gives us a little bit of (like energy). Or is utility a set of things? Or is utility a fancy word for describing dynamic behavior with some sort of end in mind?”

egoutism says utility/value is relative and objective.  it is the amount of usefulness an action provides in accomplishing the primary objective that evolution imposes upon any object in reality, namely to perpetuate instances of one’s meta-self.    

“I mean in all likelihood the utility function would not make a smooth surface. It probably wouldnt even be continuous assuming we are using discrete quantities of goods. I was saying the surface might look like a hill on one side, and a cliff on the other.”

taking ANY particular shape is virtually an impossibility.  like a probability distribution.  your shape is not only irrational or hard to explain why it would happen but even assuming they were equally reasoned would have the same probability as any specific shape. the goal is to describe the rough shape of a rational indifference curve.  not to describe all indifference curves of anything under any exceptional circumstance.

AT THE VERY LEAST MY ANALYSIS SHOWS THAT ELLIPTICAL AND CIRCULAR INDIFFERENCE CURVES ARE POSSIBLE SPECIAL CASES, NOT THE ONLY CASE.  it is just an example of an indifference curve. dont conflate this analysis to say that this specific shape applies to ALL indifference curves. 

https://mnmeconomics.wordpress.com/2012/01/18/shapes-of-indifference-curves/

 

it would somewhat make sense that for every quantity of any good there exists only 2 quantities of the other good that would correspond to the same indifference curve.  if there were more than two goods it violates the assumption of good and bad.  that would mean  a good oscillates between good and bad as you increase quantity monotonously. somewhat seems ridiculous if preferences are held constant ONLY FOR ANALYSIS.  one can easily vary preferences and make the curves do what you want them to do, but you must show that there is a dependent relation between quantity and preferences.  why would preferences change based upon quantity consumed?  its obvious you have the cart before the horse.  your sense of causality is ass-backwards. given a certain set of preferences, especially preference of evolution itself, determine the quantities and their utility.  if youre a determinists evolutionary preferences do not change with respect to a change in quantity consumed.

just take your example with bananas. if utility/value is relative and objective then were talking about nutrition here.  assuming each bite of the banana is the same good (no poisonous insect in a particular bite which necessarily makes it a different good or even bad), it doesnt make sense that if it provides the same nutrients per weight, that the objective utility of the nutrition wouldnt follow the weak law of diminishing marginal utility.

again, i dont think a criticism of continuity is applicable here as ive reasoned above.  the elliptical indifference curve is an abstraction.  they are cross sections of an infinitely dimensional (complex) euclidean space. the reason for the high level of abstraction is to isolate the dependence relationship between two variables, quantity and utility.  so it is somewhat saying the other variables held constant are independent upon quantity. but when the circle retraces quantity it only would be relevant if consumption of one good did not affect the other’s utility of the other, which is assumed in the “normal” goods as i started the analysis from.  so again, this is a special case of NORMAL goods.  there is a separate analysis of substitute, complementary, superior, and inferior goods.

 

https://en.wikipedia.org/wiki/Normal_good

does the analysis stop there? dont know, does the indifference curve have to be closed? can it spiral or take different shapes? obviously this is a more complex case that isnt necessarily assumed to be impossible its just theres no good reason to waste time analyzing strange cases.  its the law of diminishing marginal utility.  consider the easy more intuitive ones.  and when the time comes consider more complicated ones. but keen’s criticisms rely on a violation of ceteris paribus.

inverse error,  what alternative accounts for a radically different indifference curves that elminates the arguments for deadweight loss? and shows better explanation of the neo-classical or even neo-keynsian model?  there is not one that exists that has been shown to work over such a large time series like the analysis of the classical econ. if there were, profit seeking business men will adopt it in the long run.

 

 

 

 

 

 

 

 

 

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