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Economics/Significane of The Last Unit Available

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Question
Dear Professor,   

I was wondering why do books always write something like: the maximum price that someone is willing to pay for the last unit available is... What is the intuition behind this. I was thinking that since it is the last unit, people may or may not pay the same price as the previous units sold? So, by stating the price that someone is willing to pay for the last unit... we get to be sure that that is the highest price that someone is willing to pay even though it is the last unit available for that instance? I apologize if my explanation seem vague or ambiguous. Thank you for your time professor.  

Sincerely,
Justin

Answer
Hi Justin,
Thank you for posing this question. Take it for sure, Justin, that this is a topic which almost everybody at first exposure finds a trifle too tricky and confusing. One might as well get confounded when most books only throw around terms and terse statements with not much consideration as to whether readers are comfortable enough to capture the idea to the hilt. As such, I won’t be surprised if this notion pops up as something wacky to a perceptive student like you. The reason is this is an abstract topic, although this embodies the real-life behavior patterns of rational consumers. The idea behind it is sound and simple, but the reification in ordinary language may sound mystifying if not spelled out in clear terms.
As you have a good background, I hope the following explanation will give you a clear picture of the mutually splicing strands of reasoning that go to build this all-important concept of microeconomic theory.

PRICE AND UTILITY
Price is what a consumer is willing to pay for a commodity which gives him satisfaction. Something which doesn’t give him satisfaction is of no interest to the consumer, and so he doesn’t care to pay anything for it. This satisfaction that he derives from consumption of a commodity is called “utility.”

The next point is how much utility he derives and how much he should pay. If he gets high utility, he is prepared to pay a high price; if he gets low utility, he is prepared to pay only a low price; if he get no utility, he is not prepared to pay any price. You can visualize it this way: Suppose you are badly in need of a place in a new city. You are prepared to pay a high price for a one-room apartment, if you can’t get by one at a lower price.

Suppose then that you already have a one-room flat and feel another room could give you more comfort. If the price of a two-room flat (call it rental), which has to be higher than that of a one-room flat, is sufficiently less than twice the price of a one-room flat such that you can afford that and feel that is worth it, you go for that. Otherwise, you are not in such pressing need as you were when you first set your foot on that city, and you can pull on even without an extra room. So you have now an edge. So you may go for the extra room only if the price/room is lower. The extra rent you are prepared to pay for extra (the second) room is the extra price you pay for living, and the extra satisfaction you get from the second room is the “marginal utility.” If you don’t need another room, a third room would yield only zero marginal utility. You don’t pay for the third room. But, mind it, you nonetheless pay for the first room and the second room.

Similarly, suppose you are making more money and would want to enjoy more luxury in a three-room apartment. You are willing to pay for the third room, but even lower than that for the second room because the third room you may do away with.  Maybe this way you go on acquiring room after room, paying lower and lower per-room price, say finally having a five-room flat. You simply don’t need the extra sixth room even if it were available –it would simply remain shut. You are therefore not at all willing to pay for the sixth room.

If you plot the points, rental up the vertical axis and room along the horizontal axis, and pass a smooth line through all these points, then you will discover you end up with a downsloping curve. This is called demand curve.

Now the question is: Does total utility fall as one consumes more? No. Total utility is the amount of satisfaction a person derives from consuming some specific quantity –e.g., 5 units –of a commodity. Marginal utility is the additional or extra satisfaction a consumer realizes from one additional or extra unit of that product.

MAXIMUM PRICE THAT SOMEONE IS WILLING TO PAY FOR THE LAST UNIT AVAILABLE
What’s the intuition behind the above-captioned statement? When you have put this question, you have also correctly surmised that “people may or may not pay the same price as the previous units sold.” There are two lines that can be taken.

First, suppose we say people pay the same price as the previous units. Then we have just a semantic problem. This –take a hard look at it, Justin –this is NOT the last unit in strict sense of economic terminology. This “so-called last unit” is in fact included in the units previously bought, because you are deriving the same level of satisfaction –or else, why should you pay the same price? It is immaterial whether yesterday I bought 1 lb. of milk and today another 1 lb. If I combine the two temporal points “yesterday” and “today,” I am in fact buying 2lbs. at the same price. Suppose yesterday –or, for that matter, today –my demand for milk is more or less met, but I won’t mind more only if I could get the extra at a lower price.
Similar reasoning you may have if you let time stand still. At one time you buy two chocolate bars, and then one more chocolate bar, at the same price. This may be construed as “one unit of chocolate bar,” a unit consisting of three pieces. [“Unit” is how we take it, “one bar” or “three bars” –for example 1 litre of gas and one gallon of gas, each is “a unit,” but the latter is more than four times the former.] Your marginal utility for the three bars is the same. So we resolve the question whether a buyer pays for the last unit based on the marginal utility of that unit.

Second, suppose the retailer tells you that you will get a discount if you buy more than a specific amount. You will calculate you benefit mentally, and will decide whether to go for extra amount. If you don’t, you have already had your marginal unit, and you don’t go for that which has zero marginal utility for you. If you do, you pay additionally less for a unit that gives you lower marginal utility than does the previous unit.

WHAT SOMEONE IS WILLING TO PAY FOR THE LAST UNIT: IS THAT THE HIGHEST PRICE HE IS WILLING TO PAY FOR THAT UNIT?
This part of your question gets solved as soon as you take it that when a consumer is “willing to pay the highest price,” he in fact wants to pay a lower price but, because of the sellers asking, he can’t offer any price below that price. So that’s what he can pay as his highest, also because he “demands” this commodity at that price. Should the price go higher, he wouldn’t buy that. He buys a particular amount –a unit, so to say –at that price. Should price go down, and should he still want that extra bit, he might go for that: his marginal utility for that extra is less, and so he pays less.

CONCLUSION
Utility is the benefit or satisfaction a person receives from consuming a commodity. The law of diminishing marginal utility indicates that gains in satisfaction become smaller as successive units of a specific product are consumed. This provides a simple rationale for the law of demand. The demand curve is a locus of points. Each point shows the “maximum price” a consumer is willing to pay for the specific unit. This “maximum price” varies as additional or extra units are purchased, since extra units yield successively lower levels of satisfaction.
I hope this would make your points clear. You may impart geometric analysis to this concept. I know you are good at that and can sure enough get an even better idea.
Best of luck.

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Eklimur Raza

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It appears some students in this website are confused about elasticity of demand and the slope of the demand curve when they are trying to figure out why rectangular hyperbola comes up in case of unitary demand curve. First, they don't know that RH can be depicted in a positive quadrant of price,quantity plane. Secondly, they make the mistake that the slope of RH is constant at -1. Two points could help them: first, e=1 at each and every point of the RH, because the tangent at any point shows lower segment=upper segment (another geometric definition of e); yet slopes at different points,dQ/dP, are different; second, e is not slope but [(Slope)(P/Q)]in absolute terms. Caveat: only if we measure (log P) along the horizontal axis and (log Q) up the vertical axis, can we then say slope equals elasticity --in which case RH on P,Q plane is transformed into a straight-line demand curve [with slope= -tan 45 deg] on (log Q),(logP) plane, and e= -d(log Q)/d(log P). [By the way, logs are not used in college textbooks --although that is helpful in econometric estimation of elasticity viewed as an exponent of P, when demand equation is transformed into log-linear form.] I have not found the geometrical explanation I have given in any textbook followed in undergraduate and college classes in Canada (including the book followed in a university where I taught for a short time and in the book followed in George Brown College, Toronto, where I teach.

Experience

About 11 years' teaching economics and business studies, and also English, history and elementary French.Practical experience in a development bank, working with international donor agencies like the World Bank and the ADB. Experience in free-lance journalism, including Canada's "National Post."

Organizations
I teach micro- and macroeconomics at George Brown College (continuing education), Toronto, ON, Canada.

Publications
Many articles and editorials, on different subjects, in English newspapers. Recently an applied Major Research Paper, based on a synthesis of the Solow growth model and the Lewis two-sector model, has be accepted by Ryerson University, Toronto. Professors Thomas Barbiero and Eric Cam, Ryerson University, accepted the paper.

Education/Credentials
Master degree in Interantional Economics and Finance and diploma with honours in Business Administration from Canada.

Awards and Honors
Received First Prize in an inter-university Literary Contest.

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