<p>Let us quickly define a competitive market. A competitive market satisfies the following:</p>

<p>1) All firms sell an identical product</p>

<p>2) All firms and buyers are price takers (have no control over price)</p>

<p>3) Buyers and firms have complete information about the market</p>

<p>4) The market is characterized by free entry (no barriers to entry)</p>

<p>If this is the market structure, we can have the existence of pareto optimality, so I am assuming this is the competitive market to which you are referring in your question. What happens when we try to relax assumption 4?</p>

<p>We can show this using your example of startup capital: </p>

<p>Suppose we have a competitive market and the amount of startup capital needed to enter this market is $A$. When deciding to enter this market the firm would subtract $A$ from the long term profit possibility $\Pi$ (because it would be another cost). By definition $A\geq 0$. Because the situation where $A=0$ is trivial (because that means there is no startup capital needed), we know that $A&gt;0$. Suppose at a point in time there is opportunity for profit in this market. As long as $\Pi\geq 0$ firms will decide to enter the market, but if $\Pi &lt;0$, a firm would decide not to enter the market. However, note that firms who are already in the market are earning positive profit. This is a contradiction because if positive profits persist, we do not have a competitive market. </p>

<p>As you noted in your question, a competitive market is a necessary condition for the existence of pareto optimality. If the nonexistence of barriers to entry is a necessary condition for a competitive market, nonexistence of barriers to entry is also a necessary condition for pareto optimality.</p>

CC BY-SA 3.0
2016-03-30T18:35:42.570Z
Could you please give your definition of 'competitive market'. Does it have anything to do with so called price-taking behavior?
Giskard
CC BY-SA 3.0
2016-03-30T20:51:35.853Z
@denesp yes, we are using the standard definition of a perfectly competitive market. I have revised my answer to reflect that.
DornerA
CC BY-SA 3.0
2016-03-30T21:18:01.960Z
But this seems like circular reasoning to me. The startup capital and profit possibility are not independent variables. If your lifetime expected return for entering a venture is less than the startup capital needed, then your profit possibility would be less than 0, even before considering opportunity costs. In which case, tendency toward pareto optimality is preserved.
B T
CC BY-SA 3.0
2016-03-30T21:24:31.560Z
@BT this seems to be a problem of my word selection. Would revenue opportunity be more appropriate?
DornerA
CC BY-SA 3.0
2016-03-30T21:33:42.310Z
@BT or should I specify that $\Pi$ is the profit possibility if $A=0$?
DornerA
CC BY-SA 3.0
2016-03-30T22:26:55.333Z
But Pareto optimality and the first welfare theorem isn't supposed to be talking about some kind of costless market - such a thing wouldn't make any sense at all. I don't see why startup costs would be treated fundamentally different from marginal costs in this context. To my knowledge, pareto optimality, and economics in general, isn't ever about maximizing revenue.
B T
CC BY-SA 3.0
2016-03-30T23:44:27.323Z
@BT I have adjusted the answer to address your problem
DornerA
CC BY-SA 3.0
2016-03-30T23:57:15.200Z
Thanks! I see where you're going with the contradiction. If we frame this in the context of defining barriers to entry as costs new firms have to pay that existing firms didn't and won't have to pay, I think we can get closer to the real answer. Certainly some cases are clear market failures, like if new firms have to pay for a license but existing firms are "grandfathered" in. But what about a more natural case? (cont)
B T
CC BY-SA 3.0
2016-03-31T00:00:19.890Z
What if a building was crucial and existing firms built the necessary building in an era of good weather, but the weather has changed to being stormy literally 100% of the time, so building that necessary building costs more. This clearly fits the definition of barriers to entry I'm using, but does this lead to a failure to tend toward pareto optimality? I don't think so, in fact, the fact that firms took advantage of the era of good weather is more totally optimal than if all firms had to pay the cost of bad weather. In that context, it doesn't seem that the barrier reduced efficiency.
B T
CC BY-SA 3.0
2016-03-31T00:33:29.440Z
@BT this would still cause some firms who are considering entering not to enter and the existing firms would still make positive profits because of this
DornerA
CC BY-SA 3.0
2016-03-31T00:49:22.293Z
Sure, theoretically a situation could exist like this where only existing firms would be able to survive. I would think that for this situation to be not tend toward Pareto-optimal, there would have to be an achievable alternative that's more optimal. Would there be one in this case? Perhaps if it was possible to rent out that necessary building, that could be a more optimal alternative.. But if the relevant market *was* providing buildings for rent, it doesn't seem like there would be a more efficient achievable alternative.
B T
CC BY-SA 3.0
2016-03-30T16:47:27.410Z
2016-03-30T23:43:47.600Z
2016-03-30T23:43:47.600Z
DornerA
<p>I understand that a competitive market is necessary for a market to equilibriate to a pareto optimal state, and that things like economies of scale, network effects, government restrictions, and government imposed costs can prevent reaching pareto optimality. But do other barriers like startup capital also prevent reaching pareto optimality? I would think the answer is no, since something like sunk costs can be amortized over all products sold by a market actor. Is this correct, or am I missing something?</p>

CC BY-SA 3.0
2016-03-27T08:32:58.853Z
I think my confusion stems from the many conflicting definitions of "barriers to entry" out there, as is exhaustively articulated by this paper: http://authors.library.caltech.edu/11284/1/MCAaer04.pdf
B T
CC BY-SA 3.0
2016-03-30T17:23:02.943Z
I suggested an edit to the name because this is really asking about whether a lack of barriers to entry is a necessary condition for pareto optimality (rather than the first welfare theorem).
DornerA
CC BY-SA 3.0
2016-03-30T21:13:19.307Z
@DornerA Thanks, I modified your edit a bit
B T
<pareto-efficiency><barriers-to-entry>
Is a lack of any barriers to entry a necessary condition for ensuring pareto optimality is reached?
B T
# Is a lack of any barriers to entry a necessary condition for ensuring pareto optimality is reached?

(Asked by: username_0 on 2016-03-27)

I understand that a competitive market is necessary for a market to equilibriate to a pareto optimal state, and that things like economies of scale, network effects, government restrictions, and government imposed costs can prevent reaching pareto optimality. But do other barriers like startup capital also prevent reaching pareto optimality? I would think the answer is no, since something like sunk costs can be amortized over all products sold by a market actor. Is this correct, or am I missing something?

**Tags:** pareto-efficiency, barriers-to-entry
> **Comments:**
> **username_0**: I think my confusion stems from the many conflicting definitions of "barriers to entry" out there, as is exhaustively articulated by this paper: http://authors.library.caltech.edu/11284/1/MCAaer04.pdf  
> **username_1**: I suggested an edit to the name because this is really asking about whether a lack of barriers to entry is a necessary condition for pareto optimality (rather than the first welfare theorem).  
> **username_0**: @DornerA Thanks, I modified your edit a bit  

---

## 1 answers

### Answer by username_1 on 2016-03-30. Score: 1

Let us quickly define a competitive market. A competitive market satisfies the following:

1) All firms sell an identical product

2) All firms and buyers are price takers (have no control over price)

3) Buyers and firms have complete information about the market

4) The market is characterized by free entry (no barriers to entry)

If this is the market structure, we can have the existence of pareto optimality, so I am assuming this is the competitive market to which you are referring in your question. What happens when we try to relax assumption 4?

We can show this using your example of startup capital:

Suppose we have a competitive market and the amount of startup capital needed to enter this market is $A$. When deciding to enter this market the firm would subtract $A$ from the long term profit possibility $\Pi$ (because it would be another cost). By definition $A\geq 0$. Because the situation where $A=0$ is trivial (because that means there is no startup capital needed), we know that $A>0$. Suppose at a point in time there is opportunity for profit in this market. As long as $\Pi\geq 0$ firms will decide to enter the market, but if $\Pi <0$, a firm would decide not to enter the market. However, note that firms who are already in the market are earning positive profit. This is a contradiction because if positive profits persist, we do not have a competitive market.

As you noted in your question, a competitive market is a necessary condition for the existence of pareto optimality. If the nonexistence of barriers to entry is a necessary condition for a competitive market, nonexistence of barriers to entry is also a necessary condition for pareto optimality.

> **Comments:**
> **username_2**: Could you please give your definition of 'competitive market'. Does it have anything to do with so called price-taking behavior?  
> **username_1**: @denesp yes, we are using the standard definition of a perfectly competitive market. I have revised my answer to reflect that.  
> **username_0**: But this seems like circular reasoning to me. The startup capital and profit possibility are not independent variables. If your lifetime expected return for entering a venture is less than the startup capital needed, then your profit possibility would be less than 0, even before considering opportunity costs. In which case, tendency toward pareto optimality is preserved.  
> **username_1**: @BT this seems to be a problem of my word selection. Would revenue opportunity be more appropriate?  
> **username_1**: @BT or should I specify that $\Pi$ is the profit possibility if $A=0$?  
> **username_0**: But Pareto optimality and the first welfare theorem isn't supposed to be talking about some kind of costless market - such a thing wouldn't make any sense at all. I don't see why startup costs would be treated fundamentally different from marginal costs in this context. To my knowledge, pareto optimality, and economics in general, isn't ever about maximizing revenue.  
> **username_1**: @BT I have adjusted the answer to address your problem  
> **username_0**: Thanks! I see where you're going with the contradiction. If we frame this in the context of defining barriers to entry as costs new firms have to pay that existing firms didn't and won't have to pay, I think we can get closer to the real answer. Certainly some cases are clear market failures, like if new firms have to pay for a license but existing firms are "grandfathered" in. But what about a more natural case? (cont)  
> **username_0**: What if a building was crucial and existing firms built the necessary building in an era of good weather, but the weather has changed to being stormy literally 100% of the time, so building that necessary building costs more. This clearly fits the definition of barriers to entry I'm using, but does this lead to a failure to tend toward pareto optimality? I don't think so, in fact, the fact that firms took advantage of the era of good weather is more totally optimal than if all firms had to pay the cost of bad weather. In that context, it doesn't seem that the barrier reduced efficiency.  
> **username_1**: @BT this would still cause some firms who are considering entering not to enter and the existing firms would still make positive profits because of this  
> **username_0**: Sure, theoretically a situation could exist like this where only existing firms would be able to survive. I would think that for this situation to be not tend toward Pareto-optimal, there would have to be an achievable alternative that's more optimal. Would there be one in this case? Perhaps if it was possible to rent out that necessary building, that could be a more optimal alternative.. But if the relevant market *was* providing buildings for rent, it doesn't seem like there would be a more efficient achievable alternative.  

---

