Is it considered theoretically impossible for the demand curve to be perfectly vertical or horizontal (infinite elasticity or inelasticity)?
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BlackNumero: This is the source of your problem. The construction of the demand curve is completely unrelated to the construction of the supply curve. At a price of $5, you will buy 15 packs. Not 1 OR 2 OR 3 ....OR 14 OR 15, but 15. There is no horizontal line from 1 to 15, but simply a dot at 15. If you go there and want 15 but they only have 10, then in Supply and Demand analysis a shortage will occur and the seller will raise the price from $5 to whatever will clear the market. Using your type of analysis then all Supply and Demand curves would be step functions with a line starting at 1 to the new quantity, and then a line below it to the greater quantity, and so on and so forth.
This is the source of your problem. The construction of the demand curve is completely unrelated to the construction of the supply curve. At a price of $5, you will buy 15 packs. Not 1 OR 2 OR 3 ....OR 14 OR 15, but 15. There is no horizontal line from 1 to 15, but simply a dot at 15. If you go there and want 15 but they only have 10, then in Supply and Demand analysis a shortage will occur and the seller will raise the price from $5 to whatever will clear the market. Using your type of analysis then all Supply and Demand curves would be step functions with a line starting at 1 to the new quantity, and then a line below it to the greater quantity, and so on and so forth.
Well, in my example, I am the only person buying the cigarettes and I am so sensitive to price changes I would stop buying them if the price went above $5 per pack. So that doesn't sound like the smart thing for the producer to do. I really don't see how this is a case of a shortage. I am not willing to pay more for more cigarettes and he is not willing to sell more for the price I am willing to pay. This sounds like a case of equilibrium to me.
Now, in my example I was not saying the construction of the demand curve relies on the construction of the supply curve, I was only creating an example to explain why I wouldn't neccessarily always buy 15 cigarettes but that I would be willing to buy more than zero. In other words, I was creating the example to illustrate why there would not be a gap between 0 and 15. You keep asserting that there would not be a line between 0 and 15, but you don't explain why. I am willing to buy 1 pack at $5 per pack, a second, a third, etc. That should be represented.
Let me know if I am not picking up on something. BBL! Heading to a concert.
Ambition is a dream with a V8 engine - Elvis Presley
Student: Well, in my example, I am the only person buying the cigarettes and I am so sensitive to price changes I would stop buying them if the price went above $5 per pack. So that doesn't sound like the smart thing for the producer to do. I really don't see how this is a case of a shortage. I am not willing to pay more for more cigarettes and he is not willing to sell more for the price I am willing to pay. This sounds like a case of equilibrium to me. Now, in my example I was not saying the construction of the demand curve relies on the construction of the supply curve, I was only creating an example to explain why I wouldn't neccessarily always buy 15 cigarettes but that I would be willing to buy more than zero. In other words, I was creating the example to illustrate why there would not be a gap between 0 and 15. You keep asserting that there would not be a line between 0 and 15, but you don't explain why. I am willing to buy 1 pack at $5 per pack, a second, a third, etc. That should be represented. Let me know if I am not picking up on something. BBL! Heading to a concert.
If at $5 you would demand 15, then between that and whatever price you would buy zero at there would be a price for the quantity demanded of 14,13,12,...to 2 and 1. Each of those is a different discrete quantity of a "good" (our subjective valuation of a pack of cigarettes), and so for each discrete unit there will be a different price, no matter how small. Meaning that it would diagonally slope upwards to the left, and there would be no horizontal demand curve.
If for some reason you were still inclined to say that it was "15 packages of cigarettes or nothing", then the only thing I would be able to say is that you subjectively value 15 packages of cigarettes as "1 unit" of a good (cigarettes), and then on the graph/value scale let each unit proceed like that (so 2 units would be 30 packages of cigarettes, and 45, and 60 and so on, almost like we measure 24 bottles of water as 1 unit when it is all packaged up).So then, to complicate matters further, the supply schedule and the demand schedule would not be for the same good (The seller's cigarette "unit" is less than your unit and thus would not be the same subjective valuation as 15 cigarette "unit" in your eyes), meaning we would have to either make a new supply or a new demand schedule. So then, if we were to make a new supply schedule and at a price of $5 he wouldn't supply one unit (15), then no exchange occurs.
A surplus is when quantity supplied is greater than quantity demanded. A shortage is when quantity demanded is greater than quantity supplied. Equilibrium is when quantity demanded is equal to quantity supplied. Using the first example (My first paragraph) a shortage was met and then depending on the seller's actions equilibrium could be met as well. Using the second example (second paragraph) would depend entirely on the new value scale.
I am saying you cannot have a horizontal line from 0 to 15 because at one price you can only have one quantity demanded. You may demand 15 but still only buy 8 cigarettes because that is all the owner has. In that case, quantity demanded is greater than quantity supplied, and just like in any normal supply/demand analysis the seller will raise prices in order to decrease quantity demanded and increase quantity supplied until quantity demanded is equal to quantity supplied (he will try to at least, before the market is upset by new changes).
From what I understand between the two opposing views is that Student believes that if you restrict the domain then demand may be horizontal over that domain, not beyond it. Black tends not to subscribe to this because the demand curve is completely separate from the supply curve and that there is no connectivity between the demand curve, only plotted points in response to price. Therefore, if a price doesn’t exist 1/8 of on penny, then a quantity doesn’t exist. There is a hole in the domain. Given this, and if I am following the arguments correctly, are we then to conclude that there is no marginal, incremental shifts in the demand curve? Or thus, is marginal shifts a function of money denominations. For example, there is no marginal shift in demand as you move from the price of .01 cents to .02 cents because there is no denomination to distinguish. Thus, marginal shifts jump from .01 to .02 cents.
Finally, if we eliminate the possibility vertical and horizontal demand curves, do we eliminate the possibility of Giffien Goods (goods with inverted demand curves)?
Wrong thread
BlackNumero: If at $5 you would demand 15, then between that and whatever price you would buy zero at there would be a price for the quantity demanded of 14,13,12,...to 2 and 1. Each of those is a different discrete quantity of a "good" (our subjective valuation of a pack of cigarettes), and so for each discrete unit there will be a different price, no matter how small. Meaning that it would diagonally slope upwards to the left, and there would be no horizontal demand curve.
In other words, you simply do not think there ever be a person like the one in my example. Why? I'm not sure, because you only assert that it must be so. I suggest that you can read a horizontal demand curve as saying I will buy up to X amount at a given price. You simply insist "no that isn't how it works." But again you don't really explain why.
I think we may have to amiably agree to disagree on this one. :) Thanks for the convo!
I'm with Student. First, let's establish the coordinates as some of the confusion probably comes from definitions. Let's define the demand function as Q = f(P) where Q (vertical axis) is the quantity demanded at a certain price P (horizontal axis). (Economists prefer to switch things around and plot the inverse demand function P = g(Q), instead, where P is on the vertical and Q on the horizontal axis, which to me looks backward as logically Q depends on P). If the market consists of a single consumer who is not willing to pay more than $5 for a pack of cigarettes (no matter what), the Q = f(P) function will be horizontal at level Q=0 for all P>$5. If he is willing to buy any non-zero amount Q1 at $5 or below, then the function will have a vertical section (step) at P=$5. For simplicity, and without any loss of generality, if this consumer only needed one pack of cigarettes (Q=1) for which he's not willing to pay more than $5, the Q = f(P) function would be horizontal at a level of Q = 1 for $0 < P <= $5 and horizontal again at a level of Q = 0 for $5 < P < infinity, with a vertical step from Q=1 to Q=0 at P = $5. This demand function consists of horizontal and vertical sections, only.
Another potential source of confusion comes from modeling discrete-space reality with continuous-space theoretical models. In reality, neither price differences (P1-P2) nor quantity differences (Q1-Q2) can be infinitely small. In other words, in reality we must have P1-P2 >= $0.01 and Q1-Q2 >= 1 making Q = f(P) a discrete function, while in theory Q = f(P) is continuous. The signal processing implications of switching from discrete-space to continuous-space and back are beyond the realm of this thread, but suffice it to say that step-functions, zero-slope, and infinite-slope sections of functions have different meanings in each space.
Z
Student: In other words, you simply do not think there ever be a person like the one in my example. Why? I'm not sure, because you only assert that it must be so.
In other words, you simply do not think there ever be a person like the one in my example. Why? I'm not sure, because you only assert that it must be so.
I have explained this continuously throughout the discussion. For each discrete unit, from a given price where you would not demand anything to a given price where you would not buy anymore (vertical downward), there must be a price. I am asserting that because in the supply/demand analysis we are dealing with continuous demand functions, and so for every one independent variable (Price) there can be only one dependent variable (Quantity).In a horizontal demand curve, you have more than one dependent variable for every independent variable, and in mathematical methodology, you do not have a function and thus no demand curve (Meant for Z1235 as well).
To quote Armentano in Antitrust and Monopoly, anatomy of a policy failure p. 23 :
"Another objection to the horizontal demand curve is that in strict mathematical terms, the curve is not a "function". In the mathematics methodology, a functional relationship between two variables always implies that for every value of the independent variable there exists one, and only one, value for the dependent variable. In economics models, although the familiar axes have been reversed, "price" is clearly the independent variable and "quantity demanded" is the dependent variable. Yet a perfectly elastic demand curve implies that there are an infinite number of values for the dependent variable ("quantity demanded") associated with any one independent variable ("price"). Clearly, then, the perfectly elastic line in a competition (assuming for the moment that it could exist) is not a demand function."
I am also asserting this because of, more importantly, how value scales are created. In Austrian economics, the concept of demand and supply are deduced from marginal utility, which is deduced from the action axiom. Because humans use means to achieve ends, the means to satisfy our wants are goods, when we have another "unit" of a good it is placed lower on our value scale (one unit has satisfied our first wants, and so a second would satisfy lower wants), it gives us a lower, or diminished utility (meaning it ranks lower on our ordinal value scale); so as the supply of a good increases, its utility decreases. And so, for every discrete unit of a good, from a given price where you would not demand anything to a given price where you would not buy anymore, there must be a price. And what constitutes the "discrete unit" has been discussed in my previous post (either a unit is 1 pack of cigarettes or 15).
MES p.21
"It is evident that things are valued as means in accordancewith their ability to attain ends valued as more or less urgent.Each physical unit of a means (direct or indirect) that enters intohuman action is valued separately. Thus, the actor is interestedin evaluating only those units of means that enter, or that heconsiders will enter, into his concrete action. Actors choosebetween, and evaluate, not “coal” or “butter” in general, butspecific units of coal or butter. In choosing between acquiringcows or horses, the actor does not choose between the class ofcows and the class of horses, but between specific units ofthem—e.g., two cows versus three horses. Each unit that entersinto concrete action is graded and evaluated separately. Onlywhen several units together enter into human action are all ofthem evaluated together."
Student: I suggest that you can read a horizontal demand curve as saying I will buy up to X amount at a given price. You simply insist "no that isn't how it works." But again you don't really explain why. I think we may have to amiably agree to disagree on this one. :) Thanks for the convo!
I suggest that you can read a horizontal demand curve as saying I will buy up to X amount at a given price. You simply insist "no that isn't how it works." But again you don't really explain why.
Aside from talking about the implications of a horizontal demand curve (hopefully I touched upon this enough above), if we read a point as “up to 15…20, etc etc”, then we would have to read every point like that. Then, as I said earlier, every demand curve would look like a step function with a new line at each point going from zero to whatever the quantity is. Illustrated,
P
7|. 6|. 5|. 4| . 3|___________. 2|________________. 1|_______________________. 0 _________________________________Q
1 2 3 4 5
Which would not look like any normal demand curve at all. There is no way that this could be made any clearer.
BlackNumero: "...so as the supply of a good increases, so does its utility."
"...so as the supply of a good increases, so does its utility."
BlackNumero:
This seems the opposite of the law of marginal utility ??
"It would be preposterous to assert apodictically that science will never succeed in developing a praxeological aprioristic doctrine of political organization..." (Mises, UF, p.98)
Adam Knott: BlackNumero: "...so as the supply of a good increases, so does its utility." BlackNumero: This seems the opposite of the law of marginal utility ??
What an embarrassing find! I thought I reviewed my post. Much obliged.
Student: In other words, you simply do not think there ever be a person like the one in my example. Why? I'm not sure, because you only assert that it must be so. I suggest that you can read a horizontal demand curve as saying I will buy up to X amount at a given price. You simply insist "no that isn't how it works." But again you don't really explain why. I think we may have to amiably agree to disagree on this one. :) Thanks for the convo!
Here is why. The law of diminishing marginal utility says that each additional unit is less valuable than the previous unit. If this value can be expressed in price, then for each additional unit, he will demand a price less than that of the previous unit. Therefore the demand curve would be downward sloping.
If on the other hand, he demands exactly 5 units, and will not settle for less (either it's all or nothing), than those 5 units would be considered one serviceable unit of one good. Each additional 5 units composing one good would be less valuable than the previous 5 units, so he would demand a lesser price for the extra 5.
Because each unit is valued less than the previous unit, the seller through price discrimination could take advantage of the fact and charge the buyer the maximum price the buyer would pay for the 1st unit, and then provide "discounts" at successively lower prices for each additional unit.
But fortunately, for the buyer, the seller usually does not have access to that information, since it only exists in the buyer's mind, so instead the seller would charge a flat price for those units.
. . .
However, there is one exception to this principle.
If the prices were expressed in whole numbers, such that the price units cannot be divided any further, then it is very possible for the buyer to demand an additional unit at the exact same price as the previous unit.
Indeed, in this situation, the demand curve could be horizontal with zero slope.
For example, the buyer will not pay one red cent above $5.00 per unit for all 5 units. If the seller charges $5.01, then the buyer will demand a quantity of 0 units. Price discrimination is not possible, since the buy would demand a maximum price of $5.00 for each additional unit.
To better illustrate the concept, instead of the buyer paying for the units in dollars, he pays for the units in eggs. Price would then be expressed in terms of eggs.
For the 1st unit, the buyer is willing to pay a maximum price of 5 eggs. For the 2nd unit, even though 2nd unit is less valuable than the 1st unit, he is still willing to pay a maximum price of 5 eggs. This is true for each additional unit, up to 5 units, such that the maximum price for each additional unit is 5 eggs.
How is it possible that buyer will buy the 2nd unit at the exact same price at the 1st unit? Isn't the 2nd unit less valuable than the 1st unit? Isn't this contrary to the law of diminishing marginal utility?
Fundamentally, this scenario is completely consistent with the concept of diminishing marginal utility. Here is why.
For the 1st unit, its marginal value is greater than that of the 1st five eggs in the buyer's possession, so the buyer makes a trade with the seller for the 1st unit.
For the 2nd unit, its marginal value is less than that of the 1st unit. Because the buyer's supply of eggs would decrease, the marginal value of the 2nd 5 eggs would be greater than that of the 1st five eggs.
However, even though the marginal value of the 2nd unit has decreased, while the marginal value of the 2nd 5 eggs has increased, the marginal value of the 2nd unit is still greater than that of the 2nd 5 eggs. Therefore an exchange between the buyer and seller will happen.
For the 3rd unit, the marginal value of the 3rd unit is still greater than the marginal value of the 3rd 5 eggs. Thus an exchange happens. The same is true for the 4th and 5th unit.
But at the 6th unit, the marginal value of the 6th unit (whose value decreased) is less than the marginal value of the 6th 5 eggs (whose value increased). Thus an exchange will not happen.
Let's try this example at the other end of the demand curve. For the 5th unit, the buyer is willing to pay a maximum of 5 eggs. For the 4th unit, even though its value is greater than that of the 5th units, the buyer will pay a maximum of 5 eggs.
But if the 4th unit is more valuable than the 5th unit, shouldn't the buyer pay a higher price at 6 eggs? He can. But his demand preferences dictate that the marginal utility of 6 eggs is greater than that of the 4th unit, and the marginal utility of 5 eggs is less than that of the 4th unit.
In other words:
MU 5 eggs < MU 4th unit < MU 6 eggs
Therefore the buyer will exchange 5 eggs for the 4th unit, but will not exchange 6 eggs for the 4th unit. Expressed in expanded form to include the 5th unit:
MU 5 eggs < MU 5th unit < MU 4th unit < MU 6 eggs
But what if the buyer wants to buy 5 units, but there are only 3 units at the store? Marginal utility analysis provides an answer.
Provided that the marginal utility of the nth unit is greater than the marginal utility of the nth eggs, the buyer will keep buying additional units until either the store supply runs out, or until the marginal utility of the nth unit is less than the marginal utility of the nth eggs.
Because the marginal utility of the 1st, 2nd, and 3rd units are respectively greater than the marginal utility of the 1st, 2nd, and 3rd 5 eggs, the buyer will buy up all three units. He may wish to buy two more additional units, but he will settle for less, because he still experiences a psychic gain for the three units.
But what would happen if the seller lowers the price of the units from 5 eggs to 4 eggs?
Let's say the buyer's demand schedule states he will buy the 6th and 7th unit at a maximum of 4 eggs, and will not buy the 8th unit above 4 eggs.
In other words, the marginal utility of the 6th and 7th unit is greater than that of the 6th and 7th 4 eggs. But the marginal utility of the 8th unit is less than the 8th 4 eggs.
Then based on the demand schedule, the buyer will buy an additional 2 units, on top of the 5 units, for a total of 7 units. He will not buy the 8th unit.
Now contrasts this if all 5 units were treated as one serviceable good at a price of 5 eggs per unit. Then the buyer will only buy in multiples of 5 units each (5, 10, 15, etc.).
In this scenario, with one serviceable good of 5 units, it would be impossible for the buyer to buy 7 units
But with the above marginal utility analysis, it can be demonstrated how it is possible for the buyer demand the 1st to 5th units at 5 eggs each, then the 6th to 7th units at 4 eggs each.
There would be no need to resort to a serviceable good greater than 1 unit.
Keep in mind, this only works for prices as whole numbers. Take this analysis, and substitute 1 egg for $1.00.
Let's say the buyer is unwilling to pay one red cent above $5.00 for 5 units. Then at 5.01 he will buy zero units. However, he did not say he was unwilling to pay an extra amount above $5.00 but less than $5.01. For all we know he may value the 1st unit at $5.009 and the 2nd unit at $5.008.
Therefore with dividable units, the demand curve can still be expressed as a downward slope.
BlackNumero: Thinking of it differently, any demand curve that has horizontal parts cannot be a demand function either. There has to be an independent variable (price) and with only one dependent variable (quantity demanded) in order for something to be a function. With a horizontal demand curve, there is more than one dependent variable for the independent variable($5) and so it cannot be a function.
Thinking of it differently, any demand curve that has horizontal parts cannot be a demand function either. There has to be an independent variable (price) and with only one dependent variable (quantity demanded) in order for something to be a function. With a horizontal demand curve, there is more than one dependent variable for the independent variable($5) and so it cannot be a function.
If the problem is that the demand curve cannot be a function, because it has a one to many solution on one or the other axis, then instead we can call it a demand relation.
But because the demand curve ceases to be function, it does not necessarily negate the possibility of a horizontal demand.
BlackNumero: Aside from talking about the implications of a horizontal demand curve (hopefully I touched upon this enough above), if we read a point as “up to 15…20, etc etc”, then we would have to read every point like that. Then, as I said earlier, every demand curve would look like a step function with a new line at each point going from zero to whatever the quantity is. Illustrated, P 7|. 6|. 5|. 4| . 3|___________. 2|________________. 1|_______________________. 0 _________________________________Q 1 2 3 4 5
There is no need to start each and every line at zero quantity. That would be redundant. Instead, the demand can be expressed like this:
Think Blue: If the problem is that the demand curve cannot be a function, because it has a one to many solution on one or the other axis, then instead we can call it a demand relation. But because the demand curve ceases to be function, it does not necessarily negate the possibility of a horizontal demand.
Your not really negating whether a demand curve is actually a function or not, it seems as though you are just calling it something different. Although Austrians technically say you can't have a demand function because demand curves cannot be continuous (infinitesimal steps, humans can only buy things in discrete units 1,2,3,4, 5, etc), in neoclassical terminology economic curves are differentiable functions.But like I said before, a horizontal line in S/D analysis can't be a function (can't have more than one dependent for every independent)
Think Blue: BlackNumero: Aside from talking about the implications of a horizontal demand curve (hopefully I touched upon this enough above), if we read a point as “up to 15…20, etc etc”, then we would have to read every point like that. Then, as I said earlier, every demand curve would look like a step function with a new line at each point going from zero to whatever the quantity is. Illustrated, P 7|. 6|. 5|. 4| . 3|___________. 2|________________. 1|_______________________. 0 _________________________________Q 1 2 3 4 5 There is no need to start each and every line at zero quantity. That would be redundant. Instead, the demand can be expressed like this:
I'd rather not get into a debate about how to draw wrong demand curves, but I was trying to refer to Student's point if you a point symbolizes you demand up to a specific quantity, then at every price you could demand anything from 0 to X (X being max quantity at that price).
I'm not trying to agree with this viewpoint (as I have repeatedly expressed), but I was just trying to draw a demand curve using Student's applications. You could clean it up and make into a regular step function, but that wasn't the point I was trying to get across and I wanted it to be redundant to stay "true" to his horizontal demand curve.
BlackNumero: Your not really negating whether a demand curve is actually a function or not, it seems as though you are just calling it something different. Although Austrians technically say you can't have a demand function because demand curves cannot be continuous (infinitesimal steps, humans can only buy things in discrete units 1,2,3,4, 5, etc), in neoclassical terminology economic curves are differentiable functions.But like I said before, a horizontal line in S/D analysis can't be a function (can't have more than one dependent for every independent)
I would think whether the demand curve is a function or not would be tangential to the actual matter in question. [1]
The real question is, is it possible for one reservation price to have many quantities? [2]
From what I understand, Student would say yes, and you would say no.
I would say in general no, but yes with a very narrow exception (goods priced at whole number prices, as I explained above). [3]
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[1] In neoclassical thinking, the demand curve can be a function, but it does not have to be. It is recognized that some parts would be differentiable, while others not, particularly if the line is vertical, or there are kinks or gaps. In strictly mathematical terms, every function is a relation, but not all relations are functions. In a sense, all demand curves are relations, even though not all are functions.
[2] By reservation price, I mean the maximum price a consumer is willing to pay for each particular quantity.
[3] For example, the 1st unit reservation price is 5 eggs, and the 2nd unit reservation price is 5 eggs, with exactly 1 unit considered the equally serviceable good.