<p>First, you need a clear definition of what is a substitute and what is a complement (as there are various definitions out there).</p>
<p>I do not know how most economists would answer, but I would model your example in the following way.</p>
<p>Utility depends on three things: eating mango <span class="math-container">$m_e$</span>, eating pineapple <span class="math-container">$a_e$</span> (ananas as us europeans like to say) and eating poké <span class="math-container">$p$</span>. Poke is made out of mango <span class="math-container">$m_p$</span> and pineaple <span class="math-container">$a_p$</span>, using say a production function <span class="math-container">$p = f(m_p, a_p)$</span>.</p>
<p>Then utility would look like <span class="math-container">$u(m_e, a_e, f(m_p, a_p))$</span>.</p>
<p>In such case, <span class="math-container">$m_e$</span> and <span class="math-container">$a_e$</span> could be substitutes but <span class="math-container">$m_p$</span> and <span class="math-container">$a_p$</span> could be complements (in the production of <span class="math-container">$p$</span>).</p>
<p>The ``reduced form&quot; utility function then looks like
<span class="math-container">$$
U(m,a) = \max_{m_e, a_e, m_p, a_p} u(m_e, a_e, f(m_p, a_p)) \text{ s.t. } m = m_e + m_p \text{ and } a = a_e + a_p.
$$</span>
Whether <span class="math-container">$m$</span> and <span class="math-container">$a$</span> are substitutes or complements in <span class="math-container">$U$</span> will then depend on how they are (optimally) allocated over their different uses.</p>

CC BY-SA 4.0
2024-03-06T15:44:05.240Z
Yeah, this is a very good answer, but I would then argue that $m_e$ and $m_p$ are, in fact, two different goods from the perspective of the consumer, that are just indistingushable to an outsider's perspective.
Athaeneus
CC BY-SA 4.0
2024-03-06T13:09:51.467Z
2024-03-06T13:09:51.467Z
tdm
<p>I have read the following claim:</p>
<blockquote>
<p>Sometimes the relationship between products can be
both substitute and complement; that is, two products may
be complements for one purpose but substitutes for another.  (Shocker et al. 2004)</p>
</blockquote>
<p><strong>How would an economist respond?</strong></p>
<p>To me, this makes sense and simultaneously does not. I agree, two goods can be either substitutes or complements depending on a specific context (i.e., when preferences change). But, on the other hand, I would argue that they cannot be both at the same time. Contexts may change in time, so of course in one setup I could perceive goods as substitutes and in another time, I could perceive them as complements.</p>
<p>What if I buy 2 pieces of the same good but with two different reasons in mind (i want to buy mango and ananas together for tomorrow's poké, but also I buy one mango instead of ananas for pure eating today)? Would we say that it averages out? Are two goods in this context both substitutes and complements?</p>
<p>The classic CES function does not allow for this to happen, and as that seems to me to be the best definition of substitutes and complements (since it is derived from tastes, not prices), I am inclined to stick with this definition.</p>
<hr />
<p>Shocker, A. D., Bayus, B. L., &amp; Kim, N. (2004). Product Complements and Substitutes in the Real World: The Relevance of “Other Products.” Journal of Marketing, 68(1), 28–40. doi:10.1509/jmkg.68.1.28.24032 </p>

CC BY-SA 4.0
2024-03-05T11:53:42.597Z
Could you please edit your question so that it includes Shocker's definition of these terms? Or are they not defined in his paper? If they are not, most academic economists will respond by saying "we need the definitions". There are many claims that rely on hazy alternative definitions, e.g. I once sat through a presentation where the researcher claimed to have found a counterexample to Arrow's impossiblity theorem. Very embarassing IMO.
Giskard
<consumer-theory><elasticity-of-substitution>
Simultaneously a substitute and a complement (validity of a claim)
Athaeneus
# Simultaneously a substitute and a complement (validity of a claim)

(Asked by: username_0 on 2024-03-04)

I have read the following claim:

> Sometimes the relationship between products can be
> both substitute and complement; that is, two products may
> be complements for one purpose but substitutes for another. (Shocker et al. 2004)

**How would an economist respond?**

To me, this makes sense and simultaneously does not. I agree, two goods can be either substitutes or complements depending on a specific context (i.e., when preferences change). But, on the other hand, I would argue that they cannot be both at the same time. Contexts may change in time, so of course in one setup I could perceive goods as substitutes and in another time, I could perceive them as complements.

What if I buy 2 pieces of the same good but with two different reasons in mind (i want to buy mango and ananas together for tomorrow's poké, but also I buy one mango instead of ananas for pure eating today)? Would we say that it averages out? Are two goods in this context both substitutes and complements?

The classic CES function does not allow for this to happen, and as that seems to me to be the best definition of substitutes and complements (since it is derived from tastes, not prices), I am inclined to stick with this definition.

---

Shocker, A. D., Bayus, B. L., & Kim, N. (2004). Product Complements and Substitutes in the Real World: The Relevance of “Other Products.” Journal of Marketing, 68(1), 28–40. doi:10.1509/jmkg.68.1.28.24032

**Tags:** consumer-theory, elasticity-of-substitution

> **Comments:**
> **username_1**: Could you please edit your question so that it includes Shocker's definition of these terms? Or are they not defined in his paper? If they are not, most academic economists will respond by saying "we need the definitions". There are many claims that rely on hazy alternative definitions, e.g. I once sat through a presentation where the researcher claimed to have found a counterexample to Arrow's impossiblity theorem. Very embarassing IMO.  

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## 1 answers

### Answer by username_2 on 2024-03-06. Score: 1 | Accepted answer

First, you need a clear definition of what is a substitute and what is a complement (as there are various definitions out there).

I do not know how most economists would answer, but I would model your example in the following way.

Utility depends on three things: eating mango $m\_e$, eating pineapple $a\_e$ (ananas as us europeans like to say) and eating poké $p$. Poke is made out of mango $m\_p$ and pineaple $a\_p$, using say a production function $p = f(m\_p, a\_p)$.

Then utility would look like $u(m\_e, a\_e, f(m\_p, a\_p))$.

In such case, $m\_e$ and $a\_e$ could be substitutes but $m\_p$ and $a\_p$ could be complements (in the production of $p$).

The ``reduced form" utility function then looks like
$$
U(m,a) = \max\_{m\_e, a\_e, m\_p, a\_p} u(m\_e, a\_e, f(m\_p, a\_p)) \text{ s.t. } m = m\_e + m\_p \text{ and } a = a\_e + a\_p.
$$
Whether $m$ and $a$ are substitutes or complements in $U$ will then depend on how they are (optimally) allocated over their different uses.

> **Comments:**
> **username_0**: Yeah, this is a very good answer, but I would then argue that $m_e$ and $m_p$ are, in fact, two different goods from the perspective of the consumer, that are just indistingushable to an outsider's perspective.  

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