<p>$u=cx_1^adx_2^b$ is equivalent to $u=(cd)x_1^ax_2^b$
the values of $c$ and $d$ do not impact the optimal bundles. I'll provide complete working on your other question (<a href="https://economics.stackexchange.com/questions/4997/marshallian-demand-for-cobb-douglas">Marshallian Demand for Cobb-Douglas</a>).</p>

CC BY-SA 3.0
2015-04-09T01:45:29.973Z
2015-04-09T01:45:29.973Z
2017-04-13T12:51:38.253Z
Jamzy
<p>No impact because the constant will be eliminated after you do FOC's/first order conditions when you divide FOC of X1 by FOC of X2 to simplify for x1 and x2 </p>

CC BY-SA 4.0
2019-01-12T20:52:44.550Z
2019-01-12T20:52:44.550Z
Amanuel
<p>Suppose a utility function $u=x_1^ax_2^b$ with $a+b=1$. The following formula finds the values for $x$:</p>

<p>$x_1 = \frac{am}{p_1}\\
x_2 = \frac{bm}{p_2}$  </p>

<p>But what if the utility function looks like $u=cx_1^adx_2^b$ so has additional factors bevore $x_i$? Can the formula above be edited accordingly?</p>

CC BY-SA 3.0
2015-04-08T19:02:04.393Z
Certainly, and it is trivial. Just perform the same steps through which you arrived at the two optimal  equations.
Alecos Papadopoulos
CC BY-SA 3.0
2015-04-08T21:01:21.790Z
@AlecosPapadopoulos: Actually, I just found the equations on Wikipedia, without further explanations.
user1170330
CC BY-SA 3.0
2015-04-08T21:47:39.020Z
@BKay: I didn't mean I found the answer to my question on Wikipedia, but the equations in their final form. There was no further explanations about how to arrive at those equations.
user1170330
<microeconomics><consumer-theory><optimization><cobb-douglas>
Editing formula for finding Marshallian Demand with Cobb-Douglas utility function
user1170330
# Editing formula for finding Marshallian Demand with Cobb-Douglas utility function

(Asked by: username_0 on 2015-04-08)

Suppose a utility function $u=x\_1^ax\_2^b$ with $a+b=1$. The following formula finds the values for $x$:

$x\_1 = \frac{am}{p\_1}\\
x\_2 = \frac{bm}{p\_2}$

But what if the utility function looks like $u=cx\_1^adx\_2^b$ so has additional factors bevore $x\_i$? Can the formula above be edited accordingly?

**Tags:** microeconomics, consumer-theory, optimization, cobb-douglas

> **Comments:**
> **username_1**: Certainly, and it is trivial. Just perform the same steps through which you arrived at the two optimal  equations.  
> **username_0**: @username_1: Actually, I just found the equations on Wikipedia, without further explanations.  
> **username_0**: @BKay: I didn't mean I found the answer to my question on Wikipedia, but the equations in their final form. There was no further explanations about how to arrive at those equations.  

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## 2 answers

### Answer by username_2 on 2015-04-09. Score: 1 | Accepted answer

$u=cx\_1^adx\_2^b$ is equivalent to $u=(cd)x\_1^ax\_2^b$
the values of $c$ and $d$ do not impact the optimal bundles. I'll provide complete working on your other question ([Marshallian Demand for Cobb-Douglas](https://economics.stackexchange.com/questions/4997/marshallian-demand-for-cobb-douglas)).


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### Answer by username_3 on 2019-01-12. Score: 0

No impact because the constant will be eliminated after you do FOC's/first order conditions when you divide FOC of X1 by FOC of X2 to simplify for x1 and x2


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