<p>Equilibrium conditions will require, among other things,: </p>

<p>1.) $MRS_{a,b}^i=MRS_{a,b}^j \forall [i,j] \in N$ , $N$ the set of agents</p>

<p>2.) $MRTS_{x,y}^i=MRTS_{x,y}^j \forall [i,j] \in J$ , $J$ the set of firms</p>

<p>3.) $MRT=MRS$ (Assuming that 1,2 hold) </p>

<p>And I note that 1,2 are efficiency conditions. 3 is efficiency in the output market. </p>

<p>Why? Suppose 1,2 hold at:</p>

<ul>
<li><p>$MRS^i_{y,x}=3$ </p></li>
<li><p>$MRT_{y,x}=2$ </p></li>
</ul>

<p>Obviously, condition 3 does not hold. </p>

<p>Can you see why this cannot be an equilibrium outcome? Think about what should happen in the economy and the forces that will drive this economy toward a state s.t. condition 3 holds. </p>

<hr>

<p>So:</p>

<p>$MRT_{x,y}=\frac{MC_x}{MC_y} \equiv \frac{P_x}{P_y} = MRS$</p>

<p>where I assume 1 holds so MRS is same for all agents. </p>

CC BY-SA 3.0
2016-05-13T19:42:48.227Z
2016-05-13T19:48:52.193Z
2016-05-13T19:48:52.193Z
123
<p>I am doing an Intermediate Microeconomics class... in a 2*2*2*2 economy, I know that MRS (marginal rate of substitution) is supposed to be equal to MRTS (marginal rate of technical substitution) in order for it to be a competitive equilibrium. Why is this? I understand that supply is supposed to be equal to demand... 
Thank you! </p>

CC BY-SA 3.0
2016-05-12T22:46:03.693Z
I don't think that MRS = MRTS is a condition for a competitive equilibrium. Are you sure you are not confusing with an equilibrium of pure exchange (cf. Edgeworth's box) where TMS1 (marginal rate of substitution of person 1) = TMS2 (marginal rate of substitution of person 2) ?
Alexis L.
CC BY-SA 3.0
2016-05-13T07:09:46.297Z
This is for a 2x2x2x2 economy where there is both production and consumption. So, it is correct. Just wanted to get a clearer understanding of why.
TheEconomist
CC BY-SA 3.0
2016-05-13T19:46:21.850Z
I think you're a little off the mark.
123
<pareto-efficiency><competitive-equilibrium>
Productive Allocative Efficiency (Competitive Equilibrium)
TheEconomist
# Productive Allocative Efficiency (Competitive Equilibrium)

(Asked by: username_0 on 2016-05-12)

I am doing an Intermediate Microeconomics class... in a 2\*2\*2\*2 economy, I know that MRS (marginal rate of substitution) is supposed to be equal to MRTS (marginal rate of technical substitution) in order for it to be a competitive equilibrium. Why is this? I understand that supply is supposed to be equal to demand...
Thank you!

**Tags:** pareto-efficiency, competitive-equilibrium
> **Comments:**
> **username_1**: I don't think that MRS = MRTS is a condition for a competitive equilibrium. Are you sure you are not confusing with an equilibrium of pure exchange (cf. Edgeworth's box) where TMS1 (marginal rate of substitution of person 1) = TMS2 (marginal rate of substitution of person 2) ?  
> **username_0**: This is for a 2x2x2x2 economy where there is both production and consumption. So, it is correct. Just wanted to get a clearer understanding of why.  
> **username_2**: I think you're a little off the mark.  

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## 1 answers

### Answer by username_2 on 2016-05-13. Score: 1

Equilibrium conditions will require, among other things,:

1.) $MRS\_{a,b}^i=MRS\_{a,b}^j \forall [i,j] \in N$ , $N$ the set of agents

2.) $MRTS\_{x,y}^i=MRTS\_{x,y}^j \forall [i,j] \in J$ , $J$ the set of firms

3.) $MRT=MRS$ (Assuming that 1,2 hold)

And I note that 1,2 are efficiency conditions. 3 is efficiency in the output market.

Why? Suppose 1,2 hold at:

* $MRS^i\_{y,x}=3$
* $MRT\_{y,x}=2$

Obviously, condition 3 does not hold.

Can you see why this cannot be an equilibrium outcome? Think about what should happen in the economy and the forces that will drive this economy toward a state s.t. condition 3 holds.

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So:

$MRT\_{x,y}=\frac{MC\_x}{MC\_y} \equiv \frac{P\_x}{P\_y} = MRS$

where I assume 1 holds so MRS is same for all agents.


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