<p>Since demand equals supply holds for every price $p$, this simply means that every $p$ is an equilibrium price. However, the equilibrium allocation that $p$ supports varies with $p$. To be precise, price $p$ supports the allocation in which 1 consumes $\left(\frac{1+3p}{1+p}, \frac{1+3p}{1+p}\right)$ and 2 consumes $\left(\frac{3+p}{1+p}, \frac{3+p}{1+p}\right)$.</p>

CC BY-SA 3.0
2017-01-24T08:16:06.590Z
2017-01-24T08:16:06.590Z
Amit
<p>There are two goods $1,2$ and two agents $ 1,2 $. Both have the utility function $ u_{i}=\min({x_{1i},x_{2i}}) $ for agent $i$ .The endowments are $(1,3)$ and $(3,1)$ for agent $1$ and $2$ respectively. I have to solve for the Walrasian equilibrium.</p>

<p>I found out the demand for $x_{1}$ for both agents and at this point I tried to clear the market for $x_{1}$:
(setting $p_{1}=1$ and $p_{2}=p$, I get)
$\frac{1+3p}{1+p}+\frac{3+p}{1+p} = 4$ 
 At this point I generally try to solve for the equilibrium price $p$. 
But In this case, Its a trivial equation. What does this mean ? What is the equilibrium price?</p>

<p>Sorry if I am not seeing the obvious. I am new to this and dont know much.</p>

<microeconomics><utility><general-equilibrium><walrasian><perfect-complements>
Doubt regarding Walrasian equilibrium with complements for both agents
earthboy
# Doubt regarding Walrasian equilibrium with complements for both agents

(Asked by: username_0 on 2016-05-01)

There are two goods $1,2$ and two agents $ 1,2 $. Both have the utility function $ u\_{i}=\min({x\_{1i},x\_{2i}}) $ for agent $i$ .The endowments are $(1,3)$ and $(3,1)$ for agent $1$ and $2$ respectively. I have to solve for the Walrasian equilibrium.

I found out the demand for $x\_{1}$ for both agents and at this point I tried to clear the market for $x\_{1}$:
(setting $p\_{1}=1$ and $p\_{2}=p$, I get)
$\frac{1+3p}{1+p}+\frac{3+p}{1+p} = 4$
At this point I generally try to solve for the equilibrium price $p$.
But In this case, Its a trivial equation. What does this mean ? What is the equilibrium price?

Sorry if I am not seeing the obvious. I am new to this and dont know much.

**Tags:** microeconomics, utility, general-equilibrium, walrasian, perfect-complements

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## 1 answers

### Answer by username_1 on 2017-01-24. Score: 3

Since demand equals supply holds for every price $p$, this simply means that every $p$ is an equilibrium price. However, the equilibrium allocation that $p$ supports varies with $p$. To be precise, price $p$ supports the allocation in which 1 consumes $\left(\frac{1+3p}{1+p}, \frac{1+3p}{1+p}\right)$ and 2 consumes $\left(\frac{3+p}{1+p}, \frac{3+p}{1+p}\right)$.


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