<p><strong>TLDR</strong> Perfect substitutes is a very theoretical utility function class; consumers with such preferences generally go 'all or nothing'. Because of this, your rationale describes a very rare equilibrium, generally not found in the real world. Also, this function class is hardly used in empirical models.</p>
<hr />
<ol>
<li><p>(An example.) Suppose I need a door wedge for my office. It should be durable, and it should have specific dimensions, but other than these I don't care about its properties. An iron door door wedge and a titanium one would be 1:1 substitutes for me. If people felt like me, the only case when the store could sell some units of both types was if they were priced identically. Yet titanium is much more expensive, so a profit maximizing store should actually not offer both types, because the profit on each unit sold is much higher for the iron type if they are priced identically.</p>
</li>
<li><p>(Theory.) As we saw in the example above, firms profitmaximizing decisions are not dictated solely by consumer tastes, costs also factor in. Even if the cost structure was identical, it is possible to construct a model where due to economies of scale only one type is sold.</p>
</li>
<li><p>(Empirics.) You can't really measure preferences, you can only measure revealed preferences. In the empirical models where they try look at quantity price pairs, they do not assume perfect substitutes, as that would imply sudden jumps in quantities demanded (at most price combinations all but one of the goods would sell 0 units), resulting in poor fit. So you do not see this behavior in the real world, except in extreme cases, where the store would not realistically expect to sell a product and hence they would probably not stock it either.</p>
</li>
</ol>

CC BY-SA 4.0
2024-06-01T18:45:23.740Z
2024-06-02T17:16:59.737Z
2024-06-02T17:16:59.737Z
Giskard
<p>Let's say we have a retail firm, which sells various products. I am interested in general pricing strategy, so we could abstract from competition between firms.</p>
<p>Among these products, the firm also sells <span class="math-container">$n$</span> products that consumers consider to be perfect substitutes (assume the firm has reliable estimates of tastes; i.e., parameters <span class="math-container">$a_j$</span> of utility function) . We can imagine the individual consumer's utility function such as:</p>
<p><span class="math-container">$$U(\boldsymbol{x}) = a_1 x_1 + a_2 x_2 + \dots + a_n x_n$$</span></p>
<p><strong>Is it optimal for a firm to set the price in accordance with tastes?</strong></p>
<p>For instance, <span class="math-container">$a_2 = 2 \cdot a_1 \implies P_2 = 2 \cdot P_1$</span>? Alternatively, if tastes are the same, then we should expect all prices to be the same (when the firm has complete information that these products are perfect substitutes)?</p>
<hr />
<p>My rationale is such that the firm should price them relevant to their tastes. If the firm sets the same price and tastes of one product are significantly above tastes of other products, all consumers would just buy it and the firm could increase the price for this exact product. <strong>Is this correct? And would we see it in the real world?</strong></p>

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2024-06-01T13:12:32.290Z
Please post separate questions separately.
Giskard
CC BY-SA 4.0
2024-06-01T13:13:16.460Z
"*If multiple products have the same price, are these likely to be perfect substitutes with equal tastes?*" ...like a cow and a reasonably expensive bike?
Giskard
CC BY-SA 4.0
2024-06-01T13:15:44.033Z
A house vs. a Tomahawk missile might also be similarly priced, but would only qualify as 1:1 substitutes for a very small set of people with very peculiar tastes.
Giskard
CC BY-SA 4.0
2024-06-01T15:12:51.867Z
@Giskard Yeah, that was stupid, I see... I adjusted the question appropriately.
Athaeneus
CC BY-SA 4.0
2024-06-01T16:36:38.627Z
@Athaeneus I can’t exactly understand the scope of your question. You are dealing with a firm that is a price setter, that is not in a perfect  competitive market. Microeconomics deals with optimal choice of price/quantity of production in its models. Of course, a firm sets its prices according to the tastes of consumers.  Where are these tastes? They are included in the demand functions the firm faces, as demand comes from utility maximization.
BakerStreet
CC BY-SA 4.0
2024-06-01T16:39:14.983Z
Maybe, your idea colud be very good, as you can try to build a microeconomic model with your utility function and considering the features of the firm and the type of market.
BakerStreet
CC BY-SA 4.0
2024-06-01T17:53:39.007Z
@BakerStreet I was trying to go for a universal set-up, with all problems associated with it. By that I mean, what would be the optimal pricing of perfect substitutes regardless of company's type. If that is not possible to determine, I would think of price-setter's (monopolist's) optimal strategy. I can understand how monopolists would set a price per one product, but then there is the question how would they do it for multiple products (which are perfect substitutes) simultaneously... Since consumers cannot distinguish perfect substitutes I think it collapses into the one-good problem.
Athaeneus
CC BY-SA 4.0
2024-06-01T18:01:23.390Z
Concurrently... In the real world, we can see multiple (almost) perfect substitutes being offered simultaneously in a shop and usually these have the same price (e.g., certain drinks with just different flavors). The tastes $\boldsymbol{a}$ enter the consumer's utility and thus are reflected in the demand. If these tastes differ significantly among these products, some of them will be bought less. If these are bought less, it would be best for a firm not to make them and focus only on the tastiest ones, unless the less tasty products have smaller costs. It may go the way of separ/pooling eq...
Athaeneus
CC BY-SA 4.0
2024-06-01T21:00:27.170Z
If I understand correctly what you said, at first sight, yes, you are right, it will collapse in a one good model, as the two goods are indistinguishable (if, as Gyskard says, other aspects, as costs, are the same). Formally, actually we have identical demand functions, even if we have different coefficients $a_1$ and $a_2$ in the utility function. In fact, we can just rescale the units of measurement of one of the two goods to have identical coefficients in the utility function (indifference curves of slope $-1$)
BakerStreet
<microeconomics><price>
What prices do firms impose on perfect substitutes?
Athaeneus
# What prices do firms impose on perfect substitutes?

(Asked by: username_0 on 2024-05-15)

Let's say we have a retail firm, which sells various products. I am interested in general pricing strategy, so we could abstract from competition between firms.

Among these products, the firm also sells $n$ products that consumers consider to be perfect substitutes (assume the firm has reliable estimates of tastes; i.e., parameters $a\_j$ of utility function) . We can imagine the individual consumer's utility function such as:

$$U(\boldsymbol{x}) = a\_1 x\_1 + a\_2 x\_2 + \dots + a\_n x\_n$$

**Is it optimal for a firm to set the price in accordance with tastes?**

For instance, $a\_2 = 2 \cdot a\_1 \implies P\_2 = 2 \cdot P\_1$? Alternatively, if tastes are the same, then we should expect all prices to be the same (when the firm has complete information that these products are perfect substitutes)?

---

My rationale is such that the firm should price them relevant to their tastes. If the firm sets the same price and tastes of one product are significantly above tastes of other products, all consumers would just buy it and the firm could increase the price for this exact product. **Is this correct? And would we see it in the real world?**

**Tags:** microeconomics, price
> **Comments:**
> **username_1**: Please post separate questions separately.  
> **username_1**: "*If multiple products have the same price, are these likely to be perfect substitutes with equal tastes?*" ...like a cow and a reasonably expensive bike?  
> **username_1**: A house vs. a Tomahawk missile might also be similarly priced, but would only qualify as 1:1 substitutes for a very small set of people with very peculiar tastes.  
> **username_0**: @Giskard Yeah, that was stupid, I see... I adjusted the question appropriately.  
> **username_2**: @Athaeneus I can’t exactly understand the scope of your question. You are dealing with a firm that is a price setter, that is not in a perfect  competitive market. Microeconomics deals with optimal choice of price/quantity of production in its models. Of course, a firm sets its prices according to the tastes of consumers.  Where are these tastes? They are included in the demand functions the firm faces, as demand comes from utility maximization.  
> **username_2**: Maybe, your idea colud be very good, as you can try to build a microeconomic model with your utility function and considering the features of the firm and the type of market.  
> **username_0**: @BakerStreet I was trying to go for a universal set-up, with all problems associated with it. By that I mean, what would be the optimal pricing of perfect substitutes regardless of company's type. If that is not possible to determine, I would think of price-setter's (monopolist's) optimal strategy. I can understand how monopolists would set a price per one product, but then there is the question how would they do it for multiple products (which are perfect substitutes) simultaneously... Since consumers cannot distinguish perfect substitutes I think it collapses into the one-good problem.  
> **username_0**: Concurrently... In the real world, we can see multiple (almost) perfect substitutes being offered simultaneously in a shop and usually these have the same price (e.g., certain drinks with just different flavors). The tastes $\boldsymbol{a}$ enter the consumer's utility and thus are reflected in the demand. If these tastes differ significantly among these products, some of them will be bought less. If these are bought less, it would be best for a firm not to make them and focus only on the tastiest ones, unless the less tasty products have smaller costs. It may go the way of separ/pooling eq...  
> **username_2**: If I understand correctly what you said, at first sight, yes, you are right, it will collapse in a one good model, as the two goods are indistinguishable (if, as Gyskard says, other aspects, as costs, are the same). Formally, actually we have identical demand functions, even if we have different coefficients $a_1$ and $a_2$ in the utility function. In fact, we can just rescale the units of measurement of one of the two goods to have identical coefficients in the utility function (indifference curves of slope $-1$)  

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## 1 answers

### Answer by username_1 on 2024-06-01. Score: 1

**TLDR** Perfect substitutes is a very theoretical utility function class; consumers with such preferences generally go 'all or nothing'. Because of this, your rationale describes a very rare equilibrium, generally not found in the real world. Also, this function class is hardly used in empirical models.

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1. (An example.) Suppose I need a door wedge for my office. It should be durable, and it should have specific dimensions, but other than these I don't care about its properties. An iron door door wedge and a titanium one would be 1:1 substitutes for me. If people felt like me, the only case when the store could sell some units of both types was if they were priced identically. Yet titanium is much more expensive, so a profit maximizing store should actually not offer both types, because the profit on each unit sold is much higher for the iron type if they are priced identically.
2. (Theory.) As we saw in the example above, firms profitmaximizing decisions are not dictated solely by consumer tastes, costs also factor in. Even if the cost structure was identical, it is possible to construct a model where due to economies of scale only one type is sold.
3. (Empirics.) You can't really measure preferences, you can only measure revealed preferences. In the empirical models where they try look at quantity price pairs, they do not assume perfect substitutes, as that would imply sudden jumps in quantities demanded (at most price combinations all but one of the goods would sell 0 units), resulting in poor fit. So you do not see this behavior in the real world, except in extreme cases, where the store would not realistically expect to sell a product and hence they would probably not stock it either.


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