<p>This is probably a silly question, but I am misunderstanding something about the definition of a price equilibrium with transfers. Consider an Edgeworth Box (2 goods, 2 agents) consumer economy with both agents having utility function <span class="math-container">$U_a = U_b = x^2 + y^2$</span>, and both having initial endowments <span class="math-container">$\omega_a = \omega_b = (2,2)$</span>.</p>
<p><strong>What is wrong with the following reasoning?</strong></p>
<p>Consider the state <span class="math-container">$(x_a, y_a) = (4,3)$</span> and <span class="math-container">$(x_b, y_b) = (0,1)$</span>. I argue that this is an equilibrium supported by prices <span class="math-container">$p = (1,1)$</span> and transfers <span class="math-container">$T_a = 3, T_b = -3$</span>. First, agent <span class="math-container">$a$</span> wants to optimize <span class="math-container">$x^2 + y^2$</span> over the budget set <span class="math-container">$\{(x,y) \in [0,4]^2 : x + y \le 7\}$</span>. This is achieved by the state <span class="math-container">$(4,3)$</span>. Likewise <span class="math-container">$b$</span> wants to optimize <span class="math-container">$x^2 + y^2$</span> over their wealth of 1, and <span class="math-container">$(0,1)$</span> is one of the optimal states. Markets clear because this is an allocation.</p>

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2022-12-09T10:55:56.483Z
Who says that this isn't an equilibrium?
VARulle
<microeconomics><mathematical-economics><nonexpert>
Why isn't this state a price equilibrium with transfer?
user43029
# Why isn't this state a price equilibrium with transfer?

(Asked by: username_0 on 2022-12-08)

This is probably a silly question, but I am misunderstanding something about the definition of a price equilibrium with transfers. Consider an Edgeworth Box (2 goods, 2 agents) consumer economy with both agents having utility function $U\_a = U\_b = x^2 + y^2$, and both having initial endowments $\omega\_a = \omega\_b = (2,2)$.

**What is wrong with the following reasoning?**

Consider the state $(x\_a, y\_a) = (4,3)$ and $(x\_b, y\_b) = (0,1)$. I argue that this is an equilibrium supported by prices $p = (1,1)$ and transfers $T\_a = 3, T\_b = -3$. First, agent $a$ wants to optimize $x^2 + y^2$ over the budget set $\{(x,y) \in [0,4]^2 : x + y \le 7\}$. This is achieved by the state $(4,3)$. Likewise $b$ wants to optimize $x^2 + y^2$ over their wealth of 1, and $(0,1)$ is one of the optimal states. Markets clear because this is an allocation.

**Tags:** microeconomics, mathematical-economics, nonexpert
> **Comments:**
> **username_1**: Who says that this isn't an equilibrium?  

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## 0 answers

