# Is it true that for Cobb-Douglas preferences, the demand function is always iso-elastic?

As we know that $$Q*P=const.$$ for Cobb-Douglas preferences, we can thus conclude that $$\frac{dQ/Q}{dP/P}$$ is always $$-1$$:

$$QP=const. \implies 0=d(PQ)=Q\ dP+P\ dQ \implies \frac{dQ}{Q}=-\frac{dP}{P}$$

This will be a weird answer:

As we know that $$Q*P=const.$$ for Cobb-Douglas preferences.

$$QP=const. \implies 0=d(PQ)=Q\ dP+P\ dQ \implies \frac{dQ}{Q}=-\frac{dP}{P}$$ thus we can conclude that $$\frac{dQ/Q}{dP/P}$$ is always $$-1$$.

• @j3141592653589793238 I still don't know what you were asking, I copied the answer from the body of your question. May 12 '21 at 10:35
• I'm asking whether the assumption about Cobb-Douglas preferences always leading to iso-elastic demand curves is correct. Should I avoid such yes/no questions? Sorry. I just wasn't quite sure. @Giskard May 12 '21 at 10:35
• Allright. If you feel my copying the body of your question into an answer helped, you are welcome. May 12 '21 at 10:40
• Sure, just needed some confirmation from a professional! :) @Giskard May 12 '21 at 10:41
• I added an answer for extra confirmation ;-) May 12 '21 at 13:37

Yes.

I have to include at least 30 characters in an answer, so let me repeat: Yes.

• Cheers. I feel very much confirmed now indeed. May 12 '21 at 16:58