Economic substitution

[wanderer27]

I'm trying to get this figured out.

If item X increases in price (or is shorter supply - same thing) and there is a suitable substitute Y, will item Y be purchased to totally fill the shortfall of item X?

For example, say 10 Apples and 6 Pears are normally purchased, but only 6 Apples (due to price or whatever) are feasible for purchase. Would a substitute purchase of 6 Apples and 10 Pears be a correct relationship, or would there be less Pears due to some kind of substitution penalty?

Intuitively I'm kind of thinking that there may be some kind of substitution penalty, but from what I've seen Googling it infers a 100% substitution fill rate.

If there is a substitution penalty how would that be calculated?

 

[daishi5]

There is not enough information to know how he would substitute in your question. The buyer is limited by the money he has, and he buys as much as he can to make himself happy. A pear and apply each provide a certain amount of happiness, but cost a certain amount. Once you know how much happiness he gets per dollar for each item, you can figure out substitution, but I don't know where you get the 100% substitution rate.

Edit, I think I may know the answer to the original question now that I reread it. Only in one very unlikely scenario would he be able to totally fill the shortfall. Almost always (just one example I can think of is an exception) he will not be able to fill the shortfall. The only exception are perfect substitutes. (IE he doesn't care between X and Y) And the substitutes must be priced so that he can just as much happiness from X as he did from Y for the same amount of money. I don't think you should care about the perfect substitutes so much in this, at least from what you are asking I think it is not a concern.

 

[wanderer27]

Yeah, after thinking some more about it I should have mentioned that the initial price was the same for each item.

Unfortunately I also came up with a few more twists, of which you kind of brushed upon.

One is (as you hit on), that the Apples aren't a full substitute for Pears. If you need Apples for a pie (or two) you could use Pears, but it's not quite the same.

Another is that maybe I really like Apples a lot more than Pears (for example).

The last (which you also ran across) is that with fewer Apples, the demand (and hence price) for Pears would likely increase.

In my mind, these three expand on the substitution penalty.
The first would be a functionality penalty, the second a preference penalty, and the last a (likely) price penalty.

Adding these in, reconciling this seems like it going to be a lot tougher.
Since I am trying to apply this to the food side of things, it may not be an easy thing to do (I'm looking at food shortage / surplus, and those may be even more variables to consider).

 

[piasabird]

The answer may be yes and may be no.

However, if you look at items like the I-phone you may see a demand for the original high-quality product.

 

[Fayd]

There is not enough information to know how he would substitute in your question. The buyer is limited by the money he has, and he buys as much as he can to make himself happy. A pear and apply each provide a certain amount of happiness, but cost a certain amount. Once you know how much happiness he gets per dollar for each item, you can figure out substitution, but I don't know where you get the 100% substitution rate.

Edit, I think I may know the answer to the original question now that I reread it. Only in one very unlikely scenario would he be able to totally fill the shortfall. Almost always (just one example I can think of is an exception) he will not be able to fill the shortfall. The only exception are perfect substitutes. (IE he doesn't care between X and Y) And the substitutes must be priced so that he can just as much happiness from X as he did from Y for the same amount of money. I don't think you should care about the perfect substitutes so much in this, at least from what you are asking I think it is not a concern.

have to think about the marginal benefits of each.

if he's buying x apples, then chances are that's the most he's willing to buy with that amount of money. IE, spending the right amount to make him the most happy.

the question doesnt include all info. and if that is it, i would argue with the teacher.

 

[Fayd]

Yeah, after thinking some more about it I should have mentioned that the initial price was the same for each item.

Unfortunately I also came up with a few more twists, of which you kind of brushed upon.

One is (as you hit on), that the Apples aren't a full substitute for Pears. If you need Apples for a pie (or two) you could use Pears, but it's not quite the same.

Another is that maybe I really like Apples a lot more than Pears (for example).

The last (which you also ran across) is that with fewer Apples, the demand (and hence price) for Pears would likely increase.

In my mind, these three expand on the substitution penalty.
The first would be a functionality penalty, the second a preference penalty, and the last a (likely) price penalty.

Adding these in, reconciling this seems like it going to be a lot tougher.
Since I am trying to apply this to the food side of things, it may not be an easy thing to do (I'm looking at food shortage / surplus, and those may be even more variables to consider).

there's a lot more points of confusion as well. :/

 

[wanderer27]

the question doesnt include all info. and if that is it, i would argue with the teacher.

In this case I'll have to argue with myself, as this is a self directed project

 

[daishi5]

This really depends on how you are approaching this, because this seems like a "thought experiment." For example, a single consumer is usually assumed to have no impact on price from a micro point of view. If I choose to purchase 6 more apples tomorrow, the price of apples will not go up. However for some entities of sufficient size, or for multiple consumers, they can. If all the apple juice companies increase their purchases of apples by 60% then yes prices go up. So, remember the assumption that you can increase your purchase volume without an increase in per unit price is only valid for very small consumers in large markets.

Next there is marginal utility. I don't know your knowledge level, but marginal utility means how much you value each additional item, it almost always decreases as you purchase more items. (increasing marginal value is an exception that is rare, but I believe it can happen, but I cannot think of any examples).

However, I need to point out, that there is only one very rare situation that I can think of where a price increase would not result in a decrease in utility. There is almost always a substitution penalty when it is due to a price increase.

 

[MStele]

Some people here are overcomplicating this I think. IMO this is a simple lesson about opportunity cost. He didn't specify whether the lack of apples is due to the elasticity of the price or demand, but in either case the consumer must make a decision. If they buy the extra pears, then the opportunity cost would be the money they would kept in their pockets had they not. If they don't buy the extra pears, then then OC would be enjoyment of the fruit.

There is always a %100 percent substitution rate, because if they don't buy the pears then the leftover money would be the substitution for the apples that it was meant to purchase. This may not be what the OP was asking about, but given the scenerio this is what makes sense to me. Every purchase we make has a connected opportunity cost tied to it, because in every case something is sacrificed for something else.

 

[daishi5]

Back to the original question, if the amount of apples he can purchase goes down, can he make up the shortfall by substituting pears?

A few basics, we assume the consumer knows what he likes, knows the total cost of everything, and the consumer tries to get the most out of his money.

With these assumptions, we consider the 10 apples 6 pears, bundle to be his 'most preferred' bundle. In other words, this is the best he could get with his money. The only way he could fully substitute pears for apples in the case of a price increase is if he A. considers apples to be just as good as pears, and B. there is no price difference. This means, that before the price change, 16 apples or 16 pears, or any other total of apples + pears that adds up to 16 is just as good. It also means that he just choose 10 apples, 6 pears by complete randomness, because he does not see any difference between apples and pears. If the price of apples goes up, he will buy 16 pears. Because 16 pears was already considered just as good as 10 apples, 6 pears, his utility (happiness) did not change. This also requires that there is no decreasing marginal utility for pears or apples, at least below a total of 16.

This is the only example I can think of where he could make up the shortfall of a price increase. But, this example requires several circumstances that are just not normal, perfect substitutes, no decreasing marginal utility within our possible bundles, and no increase in the price of pears due to the increase in price of a substitute*. So, the answer is, no, he cannot make up the loss of happiness from less apples by buying more pears, unless we have a very rare set of circumstances.

*Note: His purchase of more pears should not increase the price, however if everyone considers pears a substitute for apples, when apples price goes up, a large number of people buy more pears, and that shifts the supply curve, causing the price of pears to increase. Ugh, I completely forgot, substitutes by definition increase in price together, so unless only a very few people consider apples and pears substitutes, then the price increase in apples will decrease their utility, this just makes the rare case where he does not end up worse off even rarer (or non-existant).

 

[daishi5]

Some people here are overcomplicating this I think. IMO this is a simple lesson about opportunity cost. He didn't specify whether the lack of apples is due to the elasticity of the price or demand, but in either case the consumer must make a decision. If they buy the extra pears, then the opportunity cost would be the money they would kept in their pockets had they not. If they don't buy the extra pears, then then OC would be enjoyment of the fruit.

There is always a %100 percent substitution rate, because if they don't buy the pears then the leftover money would be the substitution for the apples that it was meant to purchase. This may not be what the OP was asking about, but given the scenerio this is what makes sense to me. Every purchase we make has a connected opportunity cost tied to it, because in every case something is sacrificed for something else.

I could be right, and I could be confused. I don't see where his question relates to opportunity costs. In the OP, he asks if the ability to purchase X is reduced, can the shortfall be made up by the substitute Y. To the basic question, the answer is no. A price increase reduces the amount he can purchase, a price increase in X also increases Y because Y is a substitute (definition of substitute). Our consumer is limited by the amount of money he has, he must either buy less quantity, or have less money left over after his purchase. He cannot have the same amount of happiness from his product and leftover money after the price increase.

I tried to construct a scenario where that would not happen, but it requires so many circumstances that are not realistic that it is really just stretching for an exception.

I have no idea where this idea of 100% substitution is coming from, maybe I am answering the wrong question? Could you please explain this in more detail, because I would hate to be misleading the OP due to a misunderstanding.

 

[wanderer27]

Actually you are all on the right track for what I'm trying to figure out.

The example I gave is just a small piece of the picture I'm looking at, but I'm trying to keep things as simple as possible to keep the confusion to a minimum.
This is probably making it a bit more difficult to define, because in the back of my mind these other factors are coming into to play.

As we bounce this around, some of these other factors are coming in (functionality, preference, price, utilization/opportunity).


Here is just one of the 100% substitution references I've looked at (Substitution Effect):

http://en.wikipedia.org/wiki/Consumer_theory

I think part of my problem with the above reference is that the graph is dimensionless and therefore it adds support that less X means more Y, and vice versa.

There are several other references though that do explicitly support the 100% substitution, however they're not in reference food supply


Okay, I guess I need to expand on things a little without making it too complex.

As my starting point I'm looking at a very unique (and unrealistic) situation.
The initial condition is that there is just enough food to satisfy the needs/demands for 'normal' conditions.
The situation where the Substitution Effect comes into play is when there is a shortage of one good, but a surplus of another.

For the purpose of trying to determine if there is a substitution penalty, let's say that the surplus quantity is sufficient to make up for the shortage quantity.
Under 'normal' conditions, 100 units of each food good is required. In this example the shortage good is 50 and the surplus good is 150. The 50 unit good would have a price increase, and I'm thinking the 150 unit good would probably be cheaper.

Now what I'm looking at, is just because there are a sufficient number of total units available, will all of the surplus be consumed to make up the shortfall, or would the choice of going a 'little' hungry come into play due to a substitution penalty (functionality, preference, price, etc.) ?

 

[daishi5]

Ok, now I see the problem. The answer is, we don't know.

I have a final paper to finish, but I will come back to this in more detail tomorrow. This will take a little bit of time, because what you are asking is actually a couple of questions combined.

However, if you don't mind, could you give me a basic idea of what your education and knowledge level is in economics? I don't want to waste your time explaining basic assumptions if you know them, and I don't want to skip the important basics if you are trying to learn on your own and may have missed some of them.

 

[wanderer27]

Ok, now I see the problem. The answer is, we don't know.

I have a final paper to finish, but I will come back to this in more detail tomorrow. This will take a little bit of time, because what you are asking is actually a couple of questions combined.

However, if you don't mind, could you give me a basic idea of what your education and knowledge level is in economics? I don't want to waste your time explaining basic assumptions if you know them, and I don't want to skip the important basics if you are trying to learn on your own and may have missed some of them.

I've had some Economic courses in College many years ago (forgotten most of it). I've read several articles across the Internet within the past several months as a little brush up and in researching what I'm looking at.

It's probably not a bad idea to go into whatever detail you think may be needed. There are probably some others on board that may have an interest in this as well (we've got a fair number of hits on this thread already).


Like I mentioned earlier, this is just a portion of what I'm working on. I think I have most of it squared away. The Substitution issue is really causing to think and I'm having difficulty reconciling it's impact/behavior though.

This probably sounds twisted, but what I'm working on is a crude/primitive Economic Model. I'm trying to keep it as simple as possible right now, but it's already caused me to go off on quite a few tangents to develop other portions of it.

It's not going to reflect real world Economics - Super Computers and Teams of Economic Scientists can't even do that. I've read studies showing price variations based on a surplus/shortage that differ per item and are not linear, and that information is not even available for a great majority of goods. I do have some techniques that I think will emulate that type of behavior though for my purposes.

I have a rough skeleton already, but there's more to add (front end and back end). I need to get other issues resolved first though (Substitution) because I don't want to have to go back and redo everything in case my understanding is wrong.

 

[daishi5]

Ok, well for starters before I go in depth, you are trying to simulate too many things at once. Normally, you would consider first the price movement and impact of the shortage of X. Prices would go up, and there would be shortages if there were not enough substitutes. Then, after you know product's Xs supply shift has caused a price increase and a shortage, you would look at the change in product Y, its supply shift that causes a price decrease and an oversupply.

The basic economic models of things like consumer theory, and the indifference curves are most clear when you change one variable at a time. You can change multiple things, but most often you end up with an answer that is basically maybe A, maybe B.

If you are trying to create an economic model for a simulation, things can actually become much easier, because you can choose what things you want to simplify. For example, life becomes a lot easier without marginal rates of utility. In your example, it might be possible that the marginal rate of pears looks something like (Y= -X^2+49x) Y being the benefit, or utility each person gains from pears, and X is the number of pears. In this simple example, you get a lot of benefit from 1 pear, and after 7, you actually become worse off, maybe the person is so sick of pears they throw up or something else weird like that.




(Very strange, I just wrote a paper arguing we should use more bio-fuels because the substitute effect would allow the bio-fuels to help stabilize food prices around the world, and actually prevent starvation)

 

[wanderer27]

I've been reading some more, and I'm starting to think that taking Utility into consideration may help to answer the Substitution effect/penalty I'm thinking about.

As you mention, increasing the amount of one particular good seems to indicate that the demand for it drops with increased consumption. At a certain point it may become more preferable to do without additional amounts, even if the shortage of another good hasn't been fully compensated for.

This is what I'm looking for. Now I have to figure out how best to model this 'drop off' curve.

I'm really looking at things highly compartmentalized at this point, so incorporating the curve shouldn't be too big of an issue.

 

[DominionSeraph]

Nobody's gonna starve to death with food available.
If you're hungry enough, you'll eat it.