<blockquote>
<p>I'm studying the Richardian model now - it says that, if labour is the only input into production, there are no profits, so workers receive the full value of their output - i can't wrap my head around what this means. Why will there be no profit in this case?</p>
</blockquote>
<p>In this case when workers are paid their marginal product <span class="math-container">$w= dF/dL$</span> (where <span class="math-container">$w$</span> is wage <span class="math-container">$F$</span> production function and <span class="math-container">$L$</span> labor input) then once firm pays wages to the worker there is nothing left.</p>
<p>Consider simple (non-Ricardian) model, if we have price taking firm that has profit given by:</p>
<p><span class="math-container">$$\Pi = pq - wq$$</span></p>
<p>where <span class="math-container">$\Pi$</span> is a profit, <span class="math-container">$p$</span> price, <span class="math-container">$w$</span> wage and <span class="math-container">$q=F(L)=L$</span> quantity produced, in optimum we will have:</p>
<p><span class="math-container">$$p=w$$</span></p>
<p>As a consequence</p>
<p><span class="math-container">$$\Pi = pq - wq = 0 $$</span></p>
<p>The model above is not Ricardian, but you can show the same in Ricardian model, I just wanted to give you a more clearer example since you said you can't wrap your head around it. Also note <span class="math-container">$w= dF/dL$</span> is not something that generally holds in any model, but it holds in both perfectly competitive model and in Ricardian model you are asking questions about</p>
<blockquote>
<p>If we also take capital as an input then how does the situation change such that workers do not (?) receive the full value of their output?</p>
</blockquote>
<p>Workers will still receive full value of their output. All output value does not come from labor some comes from capital.</p>
<p>If we add capital to the production function so that <span class="math-container">$F(K,L)$</span> then workers will still get paid full value of their output <span class="math-container">$dF/dL=w$</span> but now portion of the value was created by the person who provided capital and that person will get <span class="math-container">$dF/dK=r$</span> (at least in Ricardian model again there are some models where factors are not paid according to the marginal product).  If that person who provided capital was the firm owner the <span class="math-container">$r$</span> will be recorded as a profit (even though technically its payment for the supply of factor).</p>

CC BY-SA 4.0
2022-11-01T17:24:55.250Z
Thank you so much for the answer , I have two questions again, sorry  1. In your simple model, why do we first take p=w and then get profit = 0? Is it just an assumption? 2. Why will the person who provided capital get dF/dL and not dF/dK? Thank you so much for claryfing that workers still get full value of their output. So does the conclusion change depending on whether we have constant, increasing ir decreasing returns to scale?
viktor nikiforov
CC BY-SA 4.0
2022-11-01T17:44:17.850Z
@viktornikiforov 1. No that is not an assumption, that is because profit maximizing firm will produce such that p=w. To maximize profit take $d\Pi/dq$ you get $p-w=0\implies p=w$. Simply perfect competition is so cutthroat that best a firm can ever dream to do is to have 0 economic profit and no loss, nothing better is possible due to maximum levels of competition. 2.  that was a typo they do get $dF/dK$ sorry I made the typo
1muflon1
CC BY-SA 4.0
2022-11-01T17:45:43.977Z
@viktornikiforov 3. The conclusion can change in various models depending on returns to scale, but if I remember correctly not in basic Ricardian model, although do not quote me on that I am not 100% sure, I would have to check it and I do not have time for that right now
1muflon1
CC BY-SA 4.0
2022-11-01T21:23:19.867Z
I am baffled that you don't mention all this is only true with constant returns to scale. E.g.: it would not work with $F(L) = \sqrt{L}$.
Giskard
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2022-11-01T21:35:58.097Z
@Giskard but OP is talking about simple ricardian model where there isnt even an explicit firm
1muflon1
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2022-11-01T21:41:04.863Z
...so? Also, in your answer you state that your example is not Ricardian, yet make the generalist claim "*when workers are paid their marginal product [...] once firm pays wages to the worker there is nothing left.*"
Giskard
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2022-11-01T21:44:50.203Z
@Giskard you are just linking back to economics.se I dont know what that is even supposed to mean
1muflon1
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2022-11-01T21:45:50.830Z
That is a way to post a comment of less than 15 characters (: But I have edited it with actual content since then.
Giskard
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2022-11-01T21:51:42.750Z
@Giskard please instead of jumping into conclusion read my answer carefully. I have written "Why will there be no profit in **this** case? when workers are paid their marginal product [...] once firm pays wages to the worker there is nothing left." I was clearly referring to the preceding paragraph...
1muflon1
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2022-11-01T21:53:54.123Z
Wow, you actually edited that in after posting the comment. Weird.
Giskard
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2022-11-01T21:53:56.517Z
@Giskard I now edited the sentence to make it clear, but sometimes it feels you are just nitpicking
1muflon1
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2022-11-01T21:54:16.280Z
@Giskard huh? I did not edited anything in before posting comment
1muflon1
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2022-11-01T21:55:27.623Z
@Giskard go and look into edit history. The paragraph was originally there, afterwards I edited it to make it more clear but in my comment I copied the original pre-edited text where it was already refering to this case
1muflon1
CC BY-SA 4.0
2022-11-01T21:57:36.480Z
Yes, I now see you meant you quoted that part from the OPs question, not that you wrote "this case". I think the OP means labor is the only input, it is never made clear they know CRS is an explicit condition of the Ricardian model. Zero profit is a clear result of CRS, not labor being the only input. Perhaps it feels like knitpicking, but I think you are not making a crucial assumption clear. (Usual in economics.)
Giskard
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2022-11-01T21:58:41.333Z
@Giskard but with in house supplied capital there wont be zero profit regardless of cost function, thats the whole point
1muflon1
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2022-11-01T21:59:16.177Z
Aren't you the guy who regularly writes "economic profit is not the same as accounting profit"?
Giskard
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2022-11-01T21:59:42.090Z
@Giskard I am talking about economic profit
1muflon1
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2022-11-01T22:00:14.073Z
@Giskard like isnt it clear? If you supply inhouse capital then you get r, in that case economic profit up to value r is possible, although its just compensation for r.
1muflon1
CC BY-SA 4.0
2022-11-01T22:02:30.360Z
You get that as rent for the capital, not profit from the production...? It is not clear to me what you mean, though I see several (imho unreasonable) arguments against the zero profit condition. Rather than argue endlessly I am just goint to ask the OP, though I fear they were a one time visitor.
Giskard
CC BY-SA 4.0
2022-11-01T22:03:35.137Z
@Giskard what I meant is that this return to capital would show up in economic model as $\Pi>0$, but the economic model does not work with accounting profit either, you are right that ultimately its return to capital but in the model it would show up as profit in the profit equation
1muflon1
CC BY-SA 4.0
2022-11-01T22:05:22.780Z
So if you are paid a positive price for your resources, than you are paid more than 0 in total? Should we publish this finding in Economic Letters? What do you think? Perhaps we should make the result more difficult by throwing in some partials just to be safe.
Giskard
CC BY-SA 4.0
2022-11-01T22:07:59.950Z
@Giskard  I'm open to possibility that I written something that was wrong and should be corrected, its already quite late after all, but you are not really making clear what exactly your issue is and the excessive sarcasm and hostile tone does not help
1muflon1
CC BY-SA 4.0
2022-11-01T22:09:12.643Z
Not sure how much clearer I can make that the result depends on CRS and CRS only; anything else is window dressing.
Giskard
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2022-11-01T22:10:25.530Z
Sorry about the sarcasm. I get frustrated sometimes.
Giskard
CC BY-SA 4.0
2022-11-01T22:50:06.773Z
@Giskard but consider the following we have CRS=F(K,L)= K^0.5 L^0.5 then firm supplies its own capital, suppose firm can supply up to $K \leq 100$, and the capital is free of charge from the firm perspective labor gets paid w hence profit will be given by pi=pF - wL. focs 1/2pL^-0.5K^0.5=w; 1/2pL^0.5K^-0.5 - \lambda =0 and K=100, here we will have corner solution for K^*=100 and L^*=(5w/p) consequently profit is: Pi= (p(5p/w)^2)^0.5*100^0.5 -w (5p/w)^2 = 10*5*p^2/w - 25p^2/w= 25p^2/w > 0. So firm is A) price taker B) earns \Pi>0 C) we have CRS so CRS in itself is not sufficient
1muflon1
CC BY-SA 4.0
2022-11-02T05:58:03.927Z
Also, if a meteor hits the Earth after they pay for labor but before they can sell their product, they will earn negative profits!
Giskard
CC BY-SA 4.0
2022-11-08T06:59:11.597Z
https://economics.stackexchange.com/questions/53346/no-profits-if-labour-is-the-only-input-into-production?noredirect=1#comment87412_53346
Giskard
CC BY-SA 4.0
2022-11-01T17:15:01.400Z
2022-11-01T21:53:18.587Z
2022-11-01T21:53:18.587Z
1muflon1
<p>I'm studying the Richardian model now - it says that, if labour is the only input into production, there are no profits, so workers receive the full value of their output - i can't wrap my head around what this means. Why will there be no profit in this case? If we also take capital as an input then how does the situation change such that workers do not (?) receive the full value of their output? Thank you !</p>

CC BY-SA 4.0
2022-11-01T22:03:37.423Z
Hi @viktornikoforv! Was it clear to you from the answer below that this only work for production functions like $F(L) = L/a$? The statement is not generally true if, e.g., $F(L) = \sqrt{L}$.
Giskard
CC BY-SA 4.0
2022-11-07T15:57:18.787Z
@Giskard I admit it was not. But now i know, thank you!!
viktor nikiforov
<international-trade><profits><input-output>
No profits if labour is the only input into production?
viktor nikiforov
# No profits if labour is the only input into production?

(Asked by: username_0 on 2022-11-01)

I'm studying the Richardian model now - it says that, if labour is the only input into production, there are no profits, so workers receive the full value of their output - i can't wrap my head around what this means. Why will there be no profit in this case? If we also take capital as an input then how does the situation change such that workers do not (?) receive the full value of their output? Thank you !

**Tags:** international-trade, profits, input-output
> **Comments:**
> **username_1**: Hi @viktornikoforv! Was it clear to you from the answer below that this only work for production functions like $F(L) = L/a$? The statement is not generally true if, e.g., $F(L) = \sqrt{L}$.  
> **username_0**: @Giskard I admit it was not. But now i know, thank you!!  

---

## 1 answers

### Answer by username_2 on 2022-11-01. Score: 1 | Accepted answer

> I'm studying the Richardian model now - it says that, if labour is the only input into production, there are no profits, so workers receive the full value of their output - i can't wrap my head around what this means. Why will there be no profit in this case?

In this case when workers are paid their marginal product $w= dF/dL$ (where $w$ is wage $F$ production function and $L$ labor input) then once firm pays wages to the worker there is nothing left.

Consider simple (non-Ricardian) model, if we have price taking firm that has profit given by:

$$\Pi = pq - wq$$

where $\Pi$ is a profit, $p$ price, $w$ wage and $q=F(L)=L$ quantity produced, in optimum we will have:

$$p=w$$

As a consequence

$$\Pi = pq - wq = 0 $$

The model above is not Ricardian, but you can show the same in Ricardian model, I just wanted to give you a more clearer example since you said you can't wrap your head around it. Also note $w= dF/dL$ is not something that generally holds in any model, but it holds in both perfectly competitive model and in Ricardian model you are asking questions about

> If we also take capital as an input then how does the situation change such that workers do not (?) receive the full value of their output?

Workers will still receive full value of their output. All output value does not come from labor some comes from capital.

If we add capital to the production function so that $F(K,L)$ then workers will still get paid full value of their output $dF/dL=w$ but now portion of the value was created by the person who provided capital and that person will get $dF/dK=r$ (at least in Ricardian model again there are some models where factors are not paid according to the marginal product). If that person who provided capital was the firm owner the $r$ will be recorded as a profit (even though technically its payment for the supply of factor).

> **Comments:**
> **username_0**: Thank you so much for the answer , I have two questions again, sorry  1. In your simple model, why do we first take p=w and then get profit = 0? Is it just an assumption? 2. Why will the person who provided capital get dF/dL and not dF/dK? Thank you so much for claryfing that workers still get full value of their output. So does the conclusion change depending on whether we have constant, increasing ir decreasing returns to scale?  
> **username_2**: @viktornikiforov 1. No that is not an assumption, that is because profit maximizing firm will produce such that p=w. To maximize profit take $d\Pi/dq$ you get $p-w=0\implies p=w$. Simply perfect competition is so cutthroat that best a firm can ever dream to do is to have 0 economic profit and no loss, nothing better is possible due to maximum levels of competition. 2.  that was a typo they do get $dF/dK$ sorry I made the typo  
> **username_2**: @viktornikiforov 3. The conclusion can change in various models depending on returns to scale, but if I remember correctly not in basic Ricardian model, although do not quote me on that I am not 100% sure, I would have to check it and I do not have time for that right now  
> **username_1**: I am baffled that you don't mention all this is only true with constant returns to scale. E.g.: it would not work with $F(L) = \sqrt{L}$.  
> **username_2**: @Giskard but OP is talking about simple ricardian model where there isnt even an explicit firm  
> **username_1**: ...so? Also, in your answer you state that your example is not Ricardian, yet make the generalist claim "*when workers are paid their marginal product [...] once firm pays wages to the worker there is nothing left.*"  
> **username_2**: @Giskard you are just linking back to economics.se I dont know what that is even supposed to mean  
> **username_1**: That is a way to post a comment of less than 15 characters (: But I have edited it with actual content since then.  
> **username_2**: @Giskard please instead of jumping into conclusion read my answer carefully. I have written "Why will there be no profit in **this** case? when workers are paid their marginal product [...] once firm pays wages to the worker there is nothing left." I was clearly referring to the preceding paragraph...  
> **username_1**: Wow, you actually edited that in after posting the comment. Weird.  
> **username_2**: @Giskard I now edited the sentence to make it clear, but sometimes it feels you are just nitpicking  
> **username_2**: @Giskard huh? I did not edited anything in before posting comment  
> **username_2**: @Giskard go and look into edit history. The paragraph was originally there, afterwards I edited it to make it more clear but in my comment I copied the original pre-edited text where it was already refering to this case  
> **username_1**: Yes, I now see you meant you quoted that part from the OPs question, not that you wrote "this case". I think the OP means labor is the only input, it is never made clear they know CRS is an explicit condition of the Ricardian model. Zero profit is a clear result of CRS, not labor being the only input. Perhaps it feels like knitpicking, but I think you are not making a crucial assumption clear. (Usual in economics.)  
> **username_2**: @Giskard but with in house supplied capital there wont be zero profit regardless of cost function, thats the whole point  
> **username_1**: Aren't you the guy who regularly writes "economic profit is not the same as accounting profit"?  
> **username_2**: @Giskard I am talking about economic profit  
> **username_2**: @Giskard like isnt it clear? If you supply inhouse capital then you get r, in that case economic profit up to value r is possible, although its just compensation for r.  
> **username_1**: You get that as rent for the capital, not profit from the production...? It is not clear to me what you mean, though I see several (imho unreasonable) arguments against the zero profit condition. Rather than argue endlessly I am just goint to ask the OP, though I fear they were a one time visitor.  
> **username_2**: @Giskard what I meant is that this return to capital would show up in economic model as $\Pi>0$, but the economic model does not work with accounting profit either, you are right that ultimately its return to capital but in the model it would show up as profit in the profit equation  
> **username_1**: So if you are paid a positive price for your resources, than you are paid more than 0 in total? Should we publish this finding in Economic Letters? What do you think? Perhaps we should make the result more difficult by throwing in some partials just to be safe.  
> **username_2**: @Giskard  I'm open to possibility that I written something that was wrong and should be corrected, its already quite late after all, but you are not really making clear what exactly your issue is and the excessive sarcasm and hostile tone does not help  
> **username_1**: Not sure how much clearer I can make that the result depends on CRS and CRS only; anything else is window dressing.  
> **username_1**: Sorry about the sarcasm. I get frustrated sometimes.  
> **username_2**: @Giskard but consider the following we have CRS=F(K,L)= K^0.5 L^0.5 then firm supplies its own capital, suppose firm can supply up to $K \leq 100$, and the capital is free of charge from the firm perspective labor gets paid w hence profit will be given by pi=pF - wL. focs 1/2pL^-0.5K^0.5=w; 1/2pL^0.5K^-0.5 - \lambda =0 and K=100, here we will have corner solution for K^*=100 and L^*=(5w/p) consequently profit is: Pi= (p(5p/w)^2)^0.5*100^0.5 -w (5p/w)^2 = 10*5*p^2/w - 25p^2/w= 25p^2/w > 0. So firm is A) price taker B) earns \Pi>0 C) we have CRS so CRS in itself is not sufficient  
> **username_1**: Also, if a meteor hits the Earth after they pay for labor but before they can sell their product, they will earn negative profits!  
> **username_1**: https://economics.stackexchange.com/questions/53346/no-profits-if-labour-is-the-only-input-into-production?noredirect=1#comment87412_53346  

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