<p>Two arguments to complement the existing answer:</p>

<ol>
<li><p>We need to have one price for which Bob is indifferent between buying the apple or not, otherwise his preferences are discontinuous, which does not make much sense normatively. That is, an infintesimal variation in the price would cause him to reverse his preferences.</p></li>
<li><p>Your logic is not entirely correct as Bob might also buy the apple for 1 dollar, as this action is not strictly dominated (he is indifferent). And whether he is indifferent at a price of 1 dollar or not is economically irrelevant, as it will not influence Bob's behavior in equilibrium. Suppose for instance that Sally is a monopolist who knows Bob's preferences and posts a price for the apple (a take-it-or-leave-it offer). Irrespective of whether Bob strictly or weakly prefers buying the apple for 1 dollar rather than not, the only equilibrium is the one in which Sally offers the apple for 1 dollar, and Bob accepts the offer (either because he is indifferent, or because he strictly prefers it).</p></li>
</ol>

CC BY-SA 4.0
2018-07-19T20:38:42.027Z
“That is, an infintesimal variation in the price would cause him to reverse his preferences.” In the current scheme, an infitesmal price variation could cause Bob to change his preference from “definitely buy” to indifferent. Is that not discontinuous? Could you explain why that is less of a problem that my proposed scheme? I’m not sure I fully understand yet.
Yatharth Agarwal
CC BY-SA 4.0
2018-07-19T20:41:11.377Z
“the only equilibrium is the one in which Sally offers the apple for 1 dollar, and Bob accepts the offer” If Bob is indifferent at that price, why would he _definitely_ accept? I may be lacking proper understanding of equilibrium here.
Yatharth Agarwal
CC BY-SA 4.0
2018-07-21T08:41:31.113Z
Kenny LJ answered regarding continuity. For the equilibrium argument, note two things. 1) The situation I described is indeed an equilibrium, because no one has a strict incentive to deviate. It is not an equilibrium in strictly dominant strategy because Bob is indifferent, but it is still an equilibrium because he is acting rationally. 2) It is the only equilibrium. If Sally posts a price larger than 1, Bob would definitely reject. If Sally posts a price smaller than 1 dollar, say $1-\epsilon$ ($\epsilon>0$), Bob would accept but Sally could instead choose a larger price like $1-\epsilon/2$.
Oliv
CC BY-SA 4.0
2018-07-21T08:42:30.233Z
And Bob would accept as well. Thus, the only way to solve the problem and make predictions on the transaction price is to accept the equilibrium in weakly dominant strategy that I described.
Oliv
CC BY-SA 4.0
2018-07-21T16:13:45.773Z
He won't "reverse preferences". He will have the same preferences, and under those preferences at 1.0000000000000000000001 he will certainly NOT buy, and at 0.9999999999999999999999999 he will certainly buy. That is a consistent preference. Probably the understanding is correct, but the way of saying it is not theoretically quite correct.
nathanwww
CC BY-SA 4.0
2018-07-22T09:46:04.787Z
@Oliv Aha, so the reason “Sally wants to sell for \$1, but Bob rejects” is because Sally would move to \$1-$\epsilon$, Bob would accept, and then Sally would continue pushing the price up!
Yatharth Agarwal
CC BY-SA 4.0
2018-07-19T06:55:35.517Z
2018-07-19T06:55:35.517Z
Oliv
<p>This is essentially  a request for clarification, but it is a bit long to be a comment. </p>

<p>Demand curves represent the amount that the consumer will definitely buy at each price (if it has the income). So the statement "the demand curve passes through the point $(1,1)$", means that the consumer will definitely buy one apple at one dollar price, (if he has one dollar). It will certainly also buy one apple (and maybe more), if the price is below one dollar (and he has the income).</p>

<p>It is not clear what the OP explores here, since Indifference curves are drawn in the goods space, or at least, in the "one good and income space". But the demand curve is drawn in the "good-price" space. We cannot superimpose the demand curve on the map of the indifference curves.  </p>

CC BY-SA 4.0
2018-07-19T20:43:07.773Z
I’m realizing I should not have said indifference curves; that has a different, specific meaning. I only meant to ask about demand-and-supply. I have edited my question.
Yatharth Agarwal
CC BY-SA 4.0
2018-07-19T20:58:52.410Z
@YatharthAgarwal The conceptual problem remains: points on the demand curve, like the (1,1) you use, do not reflect indifference between buying or not,  but a definite decision to buy.
Alecos Papadopoulos
CC BY-SA 4.0
2018-07-20T06:32:37.237Z
It seems the other answers agree that (1, 1) is a point of indifference. Would you be able to provide a source?
Yatharth Agarwal
CC BY-SA 4.0
2018-07-20T10:45:32.207Z
@YatharthAgarwal Please look up any microeconomics textbook on consumer theory. The demand curve is obtained as the solution to the utility maximization problem, i.e. it tells us what the consumer will actually _do_ in order to achieve utility maximization. There is no room for "indifference" at this point.
Alecos Papadopoulos
CC BY-SA 4.0
2018-07-19T10:14:39.943Z
2018-07-19T10:14:39.943Z
Alecos Papadopoulos
<p>If he obtains 1 util of value from an apple that costs 1 util, then he neither gains nor loses from purchasing the apple and consuming it.</p>

<p>He might buy it, or might not, and at that price will be indifferent as to whether he does.</p>

<p>Since the difference is literally infinitessimal, presumably convenience rather than theory will justify most decisions about whether to used an open or closed bound.</p>

<p>Compare this to a stock trading platform which may calculate to very small, but finite, differences in prices. Being finite, and not infinitessimal, it is strictly calculable whether a gain can be had. In which case specific features of reality would dictate the answer, and not convenience. </p>

<p>Textbook exercises may 'arbitrarily' be designed to require one or the other -- for practical applications, the difference simply is the type of inequality operator used in the programming.</p>

CC BY-SA 4.0
2018-07-21T16:23:59.137Z
2018-07-21T16:23:59.137Z
nathanwww
<p>In supply-and-demand curve, we draw curves of indifference. Say the demand goes through (1, \$1). Then Bob the Buyer is <em>indifferent</em> between spending \$1 for 1 apple or just keeping the \$1. If Sally the Seller had 1 apple to sell, then the equilibrium quantity sold would be 0 or 1—we cannot say. Seen differently, Bob will buy 1 apple if the price is in the interval [\$0, \$1) (and he <em>may</em> buy it if the price is exactly $1).</p>

<p>Would it not be simpler to use closed intervals? In our example, Bob will buy 1 apple is the price is in the interval [\$0, \$1]. The equilibrium quantity sold will <em>definitely</em> be \$0. Seen differently, the demand curve represents the maximum price buyers will pay, and the supply curve represents the minimum sellers will sell for.</p>

<p>It's (literally) an infitesmal of a difference, but it seems, at least for discrete situations like the above, it would be nice to say exactly what will happen.</p>

<p>Why don't we do that? There must be some elegant reason.</p>

<supply-and-demand>
Why not say the buyer will *definitely* buy at price X?
Yatharth Agarwal
# Why not say the buyer will *definitely* buy at price X?

(Asked by: username_0 on 2018-07-19)

In supply-and-demand curve, we draw curves of indifference. Say the demand goes through (1, \$1). Then Bob the Buyer is *indifferent* between spending \$1 for 1 apple or just keeping the \$1. If Sally the Seller had 1 apple to sell, then the equilibrium quantity sold would be 0 or 1—we cannot say. Seen differently, Bob will buy 1 apple if the price is in the interval [\$0, \$1) (and he *may* buy it if the price is exactly $1).

Would it not be simpler to use closed intervals? In our example, Bob will buy 1 apple is the price is in the interval [\$0, \$1]. The equilibrium quantity sold will *definitely* be \$0. Seen differently, the demand curve represents the maximum price buyers will pay, and the supply curve represents the minimum sellers will sell for.

It's (literally) an infitesmal of a difference, but it seems, at least for discrete situations like the above, it would be nice to say exactly what will happen.

Why don't we do that? There must be some elegant reason.

**Tags:** supply-and-demand

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## 3 answers

### Answer by username_1 on 2018-07-19. Score: 4

Two arguments to complement the existing answer:

1. We need to have one price for which Bob is indifferent between buying the apple or not, otherwise his preferences are discontinuous, which does not make much sense normatively. That is, an infintesimal variation in the price would cause him to reverse his preferences.
2. Your logic is not entirely correct as Bob might also buy the apple for 1 dollar, as this action is not strictly dominated (he is indifferent). And whether he is indifferent at a price of 1 dollar or not is economically irrelevant, as it will not influence Bob's behavior in equilibrium. Suppose for instance that Sally is a monopolist who knows Bob's preferences and posts a price for the apple (a take-it-or-leave-it offer). Irrespective of whether Bob strictly or weakly prefers buying the apple for 1 dollar rather than not, the only equilibrium is the one in which Sally offers the apple for 1 dollar, and Bob accepts the offer (either because he is indifferent, or because he strictly prefers it).

> **Comments:**
> **username_0**: “That is, an infintesimal variation in the price would cause him to reverse his preferences.” In the current scheme, an infitesmal price variation could cause Bob to change his preference from “definitely buy” to indifferent. Is that not discontinuous? Could you explain why that is less of a problem that my proposed scheme? I’m not sure I fully understand yet.  
> **username_0**: “the only equilibrium is the one in which Sally offers the apple for 1 dollar, and Bob accepts the offer” If Bob is indifferent at that price, why would he _definitely_ accept? I may be lacking proper understanding of equilibrium here.  
> **username_1**: Kenny LJ answered regarding continuity. For the equilibrium argument, note two things. 1) The situation I described is indeed an equilibrium, because no one has a strict incentive to deviate. It is not an equilibrium in strictly dominant strategy because Bob is indifferent, but it is still an equilibrium because he is acting rationally. 2) It is the only equilibrium. If Sally posts a price larger than 1, Bob would definitely reject. If Sally posts a price smaller than 1 dollar, say $1-\epsilon$ ($\epsilon>0$), Bob would accept but Sally could instead choose a larger price like $1-\epsilon/2$.  
> **username_1**: And Bob would accept as well. Thus, the only way to solve the problem and make predictions on the transaction price is to accept the equilibrium in weakly dominant strategy that I described.  
> **username_2**: He won't "reverse preferences". He will have the same preferences, and under those preferences at 1.0000000000000000000001 he will certainly NOT buy, and at 0.9999999999999999999999999 he will certainly buy. That is a consistent preference. Probably the understanding is correct, but the way of saying it is not theoretically quite correct.  
> **username_0**: @Oliv Aha, so the reason “Sally wants to sell for \$1, but Bob rejects” is because Sally would move to \$1-$\epsilon$, Bob would accept, and then Sally would continue pushing the price up!  

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### Answer by username_3 on 2018-07-19. Score: 1

This is essentially a request for clarification, but it is a bit long to be a comment.

Demand curves represent the amount that the consumer will definitely buy at each price (if it has the income). So the statement "the demand curve passes through the point $(1,1)$", means that the consumer will definitely buy one apple at one dollar price, (if he has one dollar). It will certainly also buy one apple (and maybe more), if the price is below one dollar (and he has the income).

It is not clear what the OP explores here, since Indifference curves are drawn in the goods space, or at least, in the "one good and income space". But the demand curve is drawn in the "good-price" space. We cannot superimpose the demand curve on the map of the indifference curves.

> **Comments:**
> **username_0**: I’m realizing I should not have said indifference curves; that has a different, specific meaning. I only meant to ask about demand-and-supply. I have edited my question.  
> **username_3**: @YatharthAgarwal The conceptual problem remains: points on the demand curve, like the (1,1) you use, do not reflect indifference between buying or not,  but a definite decision to buy.  
> **username_0**: It seems the other answers agree that (1, 1) is a point of indifference. Would you be able to provide a source?  
> **username_3**: @YatharthAgarwal Please look up any microeconomics textbook on consumer theory. The demand curve is obtained as the solution to the utility maximization problem, i.e. it tells us what the consumer will actually _do_ in order to achieve utility maximization. There is no room for "indifference" at this point.  

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### Answer by username_2 on 2018-07-21. Score: 0

If he obtains 1 util of value from an apple that costs 1 util, then he neither gains nor loses from purchasing the apple and consuming it.

He might buy it, or might not, and at that price will be indifferent as to whether he does.

Since the difference is literally infinitessimal, presumably convenience rather than theory will justify most decisions about whether to used an open or closed bound.

Compare this to a stock trading platform which may calculate to very small, but finite, differences in prices. Being finite, and not infinitessimal, it is strictly calculable whether a gain can be had. In which case specific features of reality would dictate the answer, and not convenience.

Textbook exercises may 'arbitrarily' be designed to require one or the other -- for practical applications, the difference simply is the type of inequality operator used in the programming.


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