<p>You don't actually need the supply functions at all.  You can determine whether two goods are complements or substitutes based on their demand functions alone.  All you need to do is look at the coefficient (number in front of) on $P_1$ and $P_2$ in each of the demand functions.  In the first demand function $QD_1$, the coefficient on $P_2$ is -2.  What this means is that, holding $P_1$ constant, a one-dollar increase in $P_2$ causes the quantity demanded of good 1 $QD_1$ to decrease by 2 units.   The important thing here to keep in mind is that this is a <strong>negative</strong> coefficient.  Otherwise, $QD_1$ would increase rather than decrease.  </p>

<p>As for $QD_2$, you have a similar situation.  Because the coefficient on $P_1$ is -2, if you hold $P_2$ constant, a one-dollar increase in $P_1$ causes the quantity demanded of good 2 to decrease by 2 units.</p>

<p>Now, just use the definitions of substitutes and complements to determine which one this situation describes.</p>

CC BY-SA 3.0
2016-08-05T03:37:43.057Z
2016-08-05T03:37:43.057Z
ExpelledFromParadise
<p>QD1 = 190 - 2P1 - 2P2 </p>

<p>QS1 = - 10 + 2P1 </p>

<p>QD2 = 240 - 2P1 - 4P2 </p>

<p>QS2 = - 40 + P2</p>

<p>Are these goods substitutes or complements?</p>

CC BY-SA 3.0
2016-08-04T10:21:15.067Z
Please read your book or google the definition and then think a bit.
Giskard
<consumer-theory>
How do you know if a good is a complement or a substitute from given demand and supply functions?
Footy
# How do you know if a good is a complement or a substitute from given demand and supply functions?

(Asked by: username_0 on 2016-08-04)

QD1 = 190 - 2P1 - 2P2

QS1 = - 10 + 2P1

QD2 = 240 - 2P1 - 4P2

QS2 = - 40 + P2

Are these goods substitutes or complements?

**Tags:** consumer-theory
> **Comments:**
> **username_1**: Please read your book or google the definition and then think a bit.  

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## 1 answers

### Answer by username_2 on 2016-08-05. Score: 1

You don't actually need the supply functions at all. You can determine whether two goods are complements or substitutes based on their demand functions alone. All you need to do is look at the coefficient (number in front of) on $P\_1$ and $P\_2$ in each of the demand functions. In the first demand function $QD\_1$, the coefficient on $P\_2$ is -2. What this means is that, holding $P\_1$ constant, a one-dollar increase in $P\_2$ causes the quantity demanded of good 1 $QD\_1$ to decrease by 2 units. The important thing here to keep in mind is that this is a **negative** coefficient. Otherwise, $QD\_1$ would increase rather than decrease.

As for $QD\_2$, you have a similar situation. Because the coefficient on $P\_1$ is -2, if you hold $P\_2$ constant, a one-dollar increase in $P\_1$ causes the quantity demanded of good 2 to decrease by 2 units.

Now, just use the definitions of substitutes and complements to determine which one this situation describes.


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