<p>I have the utility function $U^A=\alpha ln(x^A)+\beta ln(y^A)$ for consumer $A$ and $U^B=\gamma ln(x^B)+\phi ln(y^B)$ for consumer $B$. They are endowed with $\omega^h_x$ and $\omega^h_y$ of $x$ and $y$, where $h=A,B$. $p_y = 1$.</p>

<p>They are allowed to trade and I have solved for the Walrasian equilibrium price $p^*_x$ and found that this is </p>

<p>$$ p^*_x=\frac{\alpha \omega^A_y+\gamma \omega^B_y}{\beta \omega^A_x+\phi \omega^B_x}
$$ </p>

<p>I believe that I'm missing out on some basic intuition here. What is the significance of $\alpha$ being swapped from good $x$ (in the utility function) to $y$ (in the price), for instance? There also seems to be a link here to the MRS? It seems like the first term in the nominator divided by the first term in the denominator yields the MRS for $A$ and the same for the second terms for $B$?</p>

CC BY-SA 3.0
2018-03-07T10:20:43.290Z
How did you solve for Walrasian equilibrium? Given that you could solve the equations your MRS related questions are very unclear to me.
Giskard
CC BY-SA 3.0
2018-03-07T23:29:51.560Z
Perhaps showing your derivation steps **explicitly** will help both you and the people who try to help better understand where your confusion lies.
Herr K.
<microeconomics><cobb-douglas><walrasian>
MRS in Walrasian equilibrium price expression?
GreenHumbollt
# MRS in Walrasian equilibrium price expression?

(Asked by: username_0 on 2018-03-07)

I have the utility function $U^A=\alpha ln(x^A)+\beta ln(y^A)$ for consumer $A$ and $U^B=\gamma ln(x^B)+\phi ln(y^B)$ for consumer $B$. They are endowed with $\omega^h\_x$ and $\omega^h\_y$ of $x$ and $y$, where $h=A,B$. $p\_y = 1$.

They are allowed to trade and I have solved for the Walrasian equilibrium price $p^\*\_x$ and found that this is

$$ p^\*\_x=\frac{\alpha \omega^A\_y+\gamma \omega^B\_y}{\beta \omega^A\_x+\phi \omega^B\_x}
$$

I believe that I'm missing out on some basic intuition here. What is the significance of $\alpha$ being swapped from good $x$ (in the utility function) to $y$ (in the price), for instance? There also seems to be a link here to the MRS? It seems like the first term in the nominator divided by the first term in the denominator yields the MRS for $A$ and the same for the second terms for $B$?

**Tags:** microeconomics, cobb-douglas, walrasian
> **Comments:**
> **username_1**: How did you solve for Walrasian equilibrium? Given that you could solve the equations your MRS related questions are very unclear to me.  
> **username_2**: Perhaps showing your derivation steps **explicitly** will help both you and the people who try to help better understand where your confusion lies.  

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## 0 answers

