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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:

$OC_1=(\frac{P_1a}{P1+P_2},\frac{P_1a}{P1+P_2})$

$OC_2=(\frac{2P_2b}{2P1+P_2},\frac{P_2b}{2P1+P_2})$ (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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The picture below presents the competitive equilibrium in different situations:

enter image description here

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  • $\begingroup$ This is literally a set of formulas and image shared without source or attribution, close to zero knowledge is imparted... $\endgroup$
    – Giskard
    Commented May 27 at 13:29
  • $\begingroup$ Any job that requires you to solve problems according to formulas can (and will) be performed by a program. Are you preparing people for these jobs? Or are you a firm believer in the unfairness of the testing system, and think that all students should get a passing grade? $\endgroup$
    – Giskard
    Commented May 27 at 13:31
  • $\begingroup$ I created this picture. Do I also need to mention that when I create the picture? Carefully going through the picture explains why three cases are needed. This is an old question with no useful answer. I posted it because I believe that this is a useful answer. $\endgroup$
    – Amit
    Commented May 27 at 13:37
  • $\begingroup$ It's nice that you created the picture; my point was that if it came from a textbook or something one could at least go the source to read the surrounding text and get the theory, not just the formula. Missing a theoretical explanation I find the statement "Carefully going through the picture explains why three cases are needed." astonishing. $\endgroup$
    – Giskard
    Commented May 28 at 2:59
  • $\begingroup$ You are welcome to write a complete theoretical answer of your own in a new answer. In my opinion, my answer has sufficient graphical explanation - "A picture is worth a thousand words" Thanks for your inputs/comments/suggestions. $\endgroup$
    – Amit
    Commented May 28 at 3:29

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