# If wage is equal to P x MPL then where is the profit of the firm?

Excuse me if the question is too simple...

Wage = Price x MPL (Marginal Productivity of Labor)

I wonder how we can come to this conclusion as there is nothing left for Profit. I mean let's suppose that in a company A there is 1 worker who produces 5 products monthly. Price of product is 6\$. In this case lets calculate the revenue (let's assume that all products are sold): 6x5=30\$

Now lets calculate wage of the employee which is again 6x5=30\$So now Revenue - Expense (here employee wage/salary) is 30-30=0 I am wondering where we are getting this assumption. Today in Economy class the whole Specific Factors Model based on this assumption. I asked ChatGPT and it says that in the real world it is not like that as wage is less than revenue. Please enlighten me. Thanks in advance for your time. • This sounds like the question of why economists say there is zero economic profit in the long run when we observe that firms seem to make a profit. This is because typically firms don't rent their capital, rather they own it so all those factor payments go to them directly. – EconJohn Nov 1, 2023 at 4:37 ## 2 Answers It depends. If production has decreasing returns to scale, then there will normally be profits. Decreasing returns to scale means that marginal product of labour decreases with labor. Let $$x$$ be the amount of labour and let $$f(x)$$ be the output. Decreasing marginal product of labour implies that $$f'(x)$$ decreases if $$x$$ increases. At the optimal level $$p f'(x^\ast) = w$$ ($$w$$ is wage) but for the levels below $$x$$, $$p f'(x)$$ will be higher than $$f'(x^\ast)$$. As such, we get that: $$f(x^\ast) = \int_0^{x^\ast} f'(x) dx \ge \int_0^{x^\ast} f'(x^\ast) dx = f'(x^\ast) x^\ast.$$ Then, $$p f(x^\ast) - w x^\ast \ge p f'(x^\ast) x^\ast - w x^\ast = 0.$$ As an example let $$f(x) = \sqrt{x}$$. Then the first order conditions give: $$\frac{p}{2 \sqrt{x^\ast}} = w \to x^\ast = \left(\frac{p}{2w}\right)^2$$ As such, profits are: $$p \sqrt{x^\ast} - w x^\ast = \frac{p^2}{2w} - \frac{p^2}{4w} = \frac{p^2}{2w} > 0$$ A less mathy version of tdm's answer: Marginal means marginal, i.e. based on the last (in this case labor unit's) measurement. Assume a price of 10\$.

If there are a 100 workers, with the first one having an MPL of 100, the second one of 99, etc. until the last one having 1, and you hire the first 50 of them at a wage of 500\\$, your profit will not be zero. Your profit from the first worker will be

$$100\cdot 10-50\cdot 10 = 500.$$

You will similarly profit from all but the last worker. To have a 'theoretical underpinning' in this case you can assume the production function $$f(L) = (100 - L/2) \cdot L$$.