<p>Here is the Edgeworth box of your exercise:</p>
<p><a href="https://i.sstatic.net/O01my.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/O01my.png" alt="Graph of Edgeworth box of exercise" /></a></p>
<p>The green dot with the curves running through it is your equilibrium allocation. The red and blue lines are indifference curves of <span class="math-container">$A$</span> and <span class="math-container">$B$</span>, while the orange line is the budget line.</p>
<p>The other green dot in the lower right corner is the initial endowment. You want to move this to the budget line (orange line) by not trading the second good, so by moving only along the horizontal axis. Seems doable if you move this dot left by 7.5 units as your solution guide suggested.</p>

CC BY-SA 4.0
2024-04-09T15:11:11.150Z
That makes perfect sense! Thank you so much for your help!
badeconomist101
CC BY-SA 4.0
2024-04-09T15:13:12.510Z
Like and subscribe...er I mean check the green tick to the left of my answer to accept it.
Giskard
CC BY-SA 4.0
2024-04-09T15:07:40.257Z
2024-04-09T15:07:40.257Z
Giskard
<p>If we have 2 consumers (a and b) and 2 goods (x and y) -- so we are in an exchange economy setup.</p>
<p>From what I understand, due to 2FWT, we can choose any Pareto efficient outcome (x*), calculate the corresponding relative prices, redistribute endowments to anywhere along the budget line, and then the consumers will trade to reach x*.</p>
<p>However, how are we able to implement this if one of the goods cannot be traded?</p>
<p>E.g. Imagine consumer a has an endowment 20 of x and 0 of y. Consumer b has an endowment of 0 of x and 12 of y.</p>
<p>Consumer a has utility function: u = 2lnxa + 3lnya.
Consumer b has utility function: u = 2lnxb + lnxb.</p>
<p>We want to implement the Pareto efficient allocation (xa, ya) = (5, 6); (xb, yb) = (15, 6) using lump sum transfers but we are unable to trade good 2.</p>
<p>How can we implement the Pareto efficient equilibrium using only transfers of good 1?</p>

CC BY-SA 4.0
2024-04-09T14:44:55.683Z
What is "2FWT"? Second fundamental welfare theorem?
Giskard
CC BY-SA 4.0
2024-04-09T14:46:16.410Z
"*how are we able to implement this if one of the goods cannot be traded?*" Do you have reason to believe that this can be implemented with such a restriction, did you read such a claim somewhere?
Giskard
CC BY-SA 4.0
2024-04-09T14:57:20.070Z
Yes, 2FWT = second fundamental welfare theorem - sorry for not being clear! And my solution sheet seems to suggest that it can be implemented as follows: 
To trade from the bundle (ω1a,0) to the bundle (5,6), consumer a must be willing to exchange ω1a−5 units of good 1 for 6 units of good 2. With a relative price of 4/5, he will trade when 4(ω1a − 5) = 5 × 6, so ω1a = 12.5. The Social Planner should transfer 7.5 units of good 1 from a’s endowment of 20 to b.

The problem is that I don't really understand what they mean by this solution!
badeconomist101
<microeconomics><utility><pareto-efficiency>
Lump sum transfers to implement any Pareto efficient equilibrium as the market outcome
badeconomist101
# Lump sum transfers to implement any Pareto efficient equilibrium as the market outcome

(Asked by: username_0 on 2024-04-09)

If we have 2 consumers (a and b) and 2 goods (x and y) -- so we are in an exchange economy setup.

From what I understand, due to 2FWT, we can choose any Pareto efficient outcome (x\*), calculate the corresponding relative prices, redistribute endowments to anywhere along the budget line, and then the consumers will trade to reach x\*.

However, how are we able to implement this if one of the goods cannot be traded?

E.g. Imagine consumer a has an endowment 20 of x and 0 of y. Consumer b has an endowment of 0 of x and 12 of y.

Consumer a has utility function: u = 2lnxa + 3lnya.
Consumer b has utility function: u = 2lnxb + lnxb.

We want to implement the Pareto efficient allocation (xa, ya) = (5, 6); (xb, yb) = (15, 6) using lump sum transfers but we are unable to trade good 2.

How can we implement the Pareto efficient equilibrium using only transfers of good 1?

**Tags:** microeconomics, utility, pareto-efficiency
> **Comments:**
> **username_1**: What is "2FWT"? Second fundamental welfare theorem?  
> **username_1**: "*how are we able to implement this if one of the goods cannot be traded?*" Do you have reason to believe that this can be implemented with such a restriction, did you read such a claim somewhere?  
> **username_0**: Yes, 2FWT = second fundamental welfare theorem - sorry for not being clear! And my solution sheet seems to suggest that it can be implemented as follows:  To trade from the bundle (ω1a,0) to the bundle (5,6), consumer a must be willing to exchange ω1a−5 units of good 1 for 6 units of good 2. With a relative price of 4/5, he will trade when 4(ω1a − 5) = 5 × 6, so ω1a = 12.5. The Social Planner should transfer 7.5 units of good 1 from a’s endowment of 20 to b.  The problem is that I don't really understand what they mean by this solution!  

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## 1 answers

### Answer by username_1 on 2024-04-09. Score: 2 | Accepted answer

Here is the Edgeworth box of your exercise:

[![Graph of Edgeworth box of exercise](https://i.sstatic.net/O01my.png)](https://i.sstatic.net/O01my.png)

The green dot with the curves running through it is your equilibrium allocation. The red and blue lines are indifference curves of $A$ and $B$, while the orange line is the budget line.

The other green dot in the lower right corner is the initial endowment. You want to move this to the budget line (orange line) by not trading the second good, so by moving only along the horizontal axis. Seems doable if you move this dot left by 7.5 units as your solution guide suggested.

> **Comments:**
> **username_0**: That makes perfect sense! Thank you so much for your help!  
> **username_1**: Like and subscribe...er I mean check the green tick to the left of my answer to accept it.  

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