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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?

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  • $\begingroup$ Certainly, and it is trivial. Just perform the same steps through which you arrived at the two optimal equations. $\endgroup$
    – Alecos Papadopoulos
    Commented Apr 8, 2015 at 19:02
  • $\begingroup$ @AlecosPapadopoulos: Actually, I just found the equations on Wikipedia, without further explanations. $\endgroup$
    – user1170330
    Commented Apr 8, 2015 at 21:01
  • $\begingroup$ @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. $\endgroup$
    – user1170330
    Commented Apr 8, 2015 at 21:47

2 Answers 2

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$u=cx_1^adx_2^b$ 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).

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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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