<blockquote>
<p>Is it the case that the demand curve for sugar shifts to the left only if the price increase is due to supply of coffee falling?</p>
</blockquote>
<p>You seem to be confusing to concepts here: when the demand curve shifts, the demand changes at all price levels. This change is not a result of changing prices. When price changes, the quantity demanded (at the given price, given the demand curve) changes.</p>
<hr />
<p>It is not easy to give a definitive answer to these demand shift questions when the reason for the demand shift is not given. If we assume that the underlying relationship between sugar and coffee is unchanged, they are still perfect complements and at the same ratio, then sugar's demand will have to shift like coffee's demand did:
<span class="math-container">$$
s(p_c,p_s,I) = r_{\text{complement_ratio}} \cdot c(p_c,p_s,I) 
$$</span>
If, however, coffee's demand shift is, for example, because in addition to drinking sugary coffee people also started to chew coffee beans without sugar, then sugar's demand curve could be unaffected.</p>

CC BY-SA 4.0
2022-10-05T20:56:22.700Z
Thank you for your reply.  Normally people say that when price of a complement (e.g., coffee) rises, the demand for the other complement good (e.g., sugar) falls.  The reason for the price rise is never specified.  But what if the reason for the price rise is an increase in demand?  If the demand for coffee rises due to news that coffee increases longevity, coffee price will rise, and we would say that the demand for sugar falls. But is that what would happen, in theory, in this case? Please help me understand this.
BillB
CC BY-SA 4.0
2022-10-05T21:43:34.567Z
@BillB If coffee drank together **with** sugar were to increase longevity than the complement ratio would be unchanged and both demand curves would shift upward. If the prices would remain constant, both quantities demanded would increase by a certain amount. However, assuming a usual supply function, the price of coffee will rise. This will decrease sugar consumption somewhat. Also, if sugar's supply function is also usual, sugar's equilibrium price will increase as well, further mitigating the growth of consumption.
Giskard
CC BY-SA 4.0
2022-10-05T21:44:34.360Z
Sugar consumption will still be larger than before the demand shift, but not as large as it would be if the goods were available at unlimited quantities at the previous prices.
Giskard
CC BY-SA 4.0
2022-10-06T00:28:44.113Z
Thank you!  In your example when demand for coffee shifted right, the demand for sugar increased too, even as the price of its complement good/coffee increased. The clarification above (for the case when coffee [with or without sugar] increases longevity) seems to imply that the economics rule "Demand curve shifts left when the price of a complement rises" is, in general, not true.  Right?  When the price rises as a result of the demand curve shifting right, the demand for the complement will tend to shift right too.
BillB
CC BY-SA 4.0
2022-10-06T00:29:00.370Z
The price can rise as a result of either demand curve shifting right or supply curve shifting left. When the price rises as a result of the supply curve shifting left, Then the demand for the complement is likely to shift left.
BillB
CC BY-SA 4.0
2022-10-06T06:16:55.337Z
Most microeconomics statements are *ceteris paribus* statements, not general rules. "Demand curve shifts left when the price of a complement rises" is true if that price change is the only change.
Giskard
CC BY-SA 4.0
2022-10-06T19:22:15.170Z
Are we saying that "demand curve shifts left when the price of a complement rises" is true only when the quantity of the complement doesn't change as the price rises?  In other words, is the statement quoted above true only when the complement's supply curve is vertical?
BillB
CC BY-SA 4.0
2022-10-07T06:53:55.093Z
In my previous comment I gave the general meaning of this statement.
Giskard
CC BY-SA 4.0
2022-10-05T08:43:18.770Z
2022-10-05T08:43:18.770Z
Giskard
<p>If the demand curve for Coffee shifts to the right, both Price of Coffee and Quantity of Coffee that gets sold go up.</p>
<p>What happens to the Price of Sugar?</p>
<p>Coffee and Sugar are complements, so one would think that as price of coffee goes up, people consume less of both complement goods, so demand for sugar should fall (demand curve for sugar shifts to the left).</p>
<p>However, since the reason for the price going up is the demand for coffee increasing, Quantity of Coffee is higher, meaning that people purchase MORE Coffee AND More Sugar. Is the demand curve for sugar shifting to the right, after all?!</p>
<p>Is it the case that the demand curve for sugar shifts to the left only if the price increase is due to supply of coffee falling?</p>
<p>Thank you for the clarification!</p>

<supply-and-demand>
If demand for complement good 1 goes up, BOTH its P and Q go up, so why does the demand for the complement good 2 fall?
BillB
# If demand for complement good 1 goes up, BOTH its P and Q go up, so why does the demand for the complement good 2 fall?

(Asked by: username_0 on 2022-10-05)

If the demand curve for Coffee shifts to the right, both Price of Coffee and Quantity of Coffee that gets sold go up.

What happens to the Price of Sugar?

Coffee and Sugar are complements, so one would think that as price of coffee goes up, people consume less of both complement goods, so demand for sugar should fall (demand curve for sugar shifts to the left).

However, since the reason for the price going up is the demand for coffee increasing, Quantity of Coffee is higher, meaning that people purchase MORE Coffee AND More Sugar. Is the demand curve for sugar shifting to the right, after all?!

Is it the case that the demand curve for sugar shifts to the left only if the price increase is due to supply of coffee falling?

Thank you for the clarification!

**Tags:** supply-and-demand

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## 1 answers

### Answer by username_1 on 2022-10-05. Score: 1

> Is it the case that the demand curve for sugar shifts to the left only if the price increase is due to supply of coffee falling?

You seem to be confusing to concepts here: when the demand curve shifts, the demand changes at all price levels. This change is not a result of changing prices. When price changes, the quantity demanded (at the given price, given the demand curve) changes.

---

It is not easy to give a definitive answer to these demand shift questions when the reason for the demand shift is not given. If we assume that the underlying relationship between sugar and coffee is unchanged, they are still perfect complements and at the same ratio, then sugar's demand will have to shift like coffee's demand did:
$$
s(p\_c,p\_s,I) = r\_{\text{complement\_ratio}} \cdot c(p\_c,p\_s,I)
$$
If, however, coffee's demand shift is, for example, because in addition to drinking sugary coffee people also started to chew coffee beans without sugar, then sugar's demand curve could be unaffected.

> **Comments:**
> **username_0**: Thank you for your reply.  Normally people say that when price of a complement (e.g., coffee) rises, the demand for the other complement good (e.g., sugar) falls.  The reason for the price rise is never specified.  But what if the reason for the price rise is an increase in demand?  If the demand for coffee rises due to news that coffee increases longevity, coffee price will rise, and we would say that the demand for sugar falls. But is that what would happen, in theory, in this case? Please help me understand this.  
> **username_1**: @BillB If coffee drank together **with** sugar were to increase longevity than the complement ratio would be unchanged and both demand curves would shift upward. If the prices would remain constant, both quantities demanded would increase by a certain amount. However, assuming a usual supply function, the price of coffee will rise. This will decrease sugar consumption somewhat. Also, if sugar's supply function is also usual, sugar's equilibrium price will increase as well, further mitigating the growth of consumption.  
> **username_1**: Sugar consumption will still be larger than before the demand shift, but not as large as it would be if the goods were available at unlimited quantities at the previous prices.  
> **username_0**: Thank you!  In your example when demand for coffee shifted right, the demand for sugar increased too, even as the price of its complement good/coffee increased. The clarification above (for the case when coffee [with or without sugar] increases longevity) seems to imply that the economics rule "Demand curve shifts left when the price of a complement rises" is, in general, not true.  Right?  When the price rises as a result of the demand curve shifting right, the demand for the complement will tend to shift right too.  
> **username_0**: The price can rise as a result of either demand curve shifting right or supply curve shifting left. When the price rises as a result of the supply curve shifting left, Then the demand for the complement is likely to shift left.  
> **username_1**: Most microeconomics statements are *ceteris paribus* statements, not general rules. "Demand curve shifts left when the price of a complement rises" is true if that price change is the only change.  
> **username_0**: Are we saying that "demand curve shifts left when the price of a complement rises" is true only when the quantity of the complement doesn't change as the price rises?  In other words, is the statement quoted above true only when the complement's supply curve is vertical?  
> **username_1**: In my previous comment I gave the general meaning of this statement.  

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