Consider the following Edgeworth economy. There are two consumers $i \in {1,2}$ and two goods x and y. Consumer $i$ consumes $(x_i,y_i)$, where $x_i ≥0$ and $y_i ≥0$. Endowments are $ω_1 =(a,0)$ and $ω_2 =(0,b)$,where a>0 and b > 0. That is, consumer 1 is endowed with good x and consumer 2 is endowed with good y. We are given $u_1=\min\{x,y\}$ and $u_2=\min\{x,2y\}$. I need to find the competitive equilibrium and draw the offer curves. What I got so far based on MGW ch.15,pg:515-525 is find the offer curves for both consumers and my results are:


$OC_2=(\frac{2P_2b}{2P1+P_2},\frac{P_2b}{2P1+P_2})$ (if I haven't made any mistakes in calculations).

From that we determine the walrasian eq. prices by equaling $\frac{P_1a}{P1+P_2}+\frac{2P_2b}{2P1+P_2}=a(=\omega_{11}+(\omega_{12})$ and get that $\frac{P_1^*}{P_2^*}=\frac{a-2b}{2(b-a)}$ again if I haven't done any miscalculations.

Is this the correct way of getting the competitive equilibrium?



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