<p>The tangent lines are drawn because they are trying to get you to think about the magnitude of the slope at each point on the production function. The marginal product of labour is the derivative of the production function, and will look like a decreasing function when drawn graphically, starting off with high values for low levels of labour, then decreasing to low values for high levels of labour. This corresponds to how the slope of the production function starts off steep and then gets flatter. Because the gradient decreases, this is called 'diminishing' returns.</p>

<p>We assume capital is constant when looking at this graph. </p>

CC BY-SA 4.0
2018-05-05T20:17:36.013Z
2018-05-05T20:17:36.013Z
ahorn
<p><a href="https://i.sstatic.net/DUh6D.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/DUh6D.png" alt="enter image description here"></a></p>

<p>Hi everyone, I am learning about the partial production function. I don't understand why a tangent it drawn next to the curve; I get that it shows the MPL. Does this mean diminishing marginal product of labour will be reached eventually? Also, it is always assumed that K0 is constant in partial production function? </p>

<p>Thank you</p>

CC BY-SA 3.0
2018-04-20T07:33:12.600Z
Do you know any calculus? If so, then the MPL is just the partial derivative of the production function with respect to L. (If you only know single-variable calculus, then you should know what a derivative is. It should be easy to learn what a partial derivative is from there.)
Theoretical Economist
CC BY-SA 3.0
2018-04-20T10:41:19.760Z
I understand how to perform the partial derivative, but I don't understand what it shows in the economics context. I read somewhere that if FOC is >0 and SOC<0, then this is showing diminishing marginal returns? I am not sure why however. thanks
D.I.N
CC BY-SA 3.0
2018-04-20T10:58:59.930Z
The partial derivative has the same interpretation here as it does in many other contexts. In general, ignoring the context, how do you interpret what the partial derivative of a function is? Also, I'm not sure what you mean by FOC and SOC. Normally I would interpret those as "first-order condition" and "second-order condition" respectively, but those interpretation make no sense here since they pertain to optimisation problems. There is no optimisation problem here. (There can be, but as stated, there isn't.)
Theoretical Economist
CC BY-SA 3.0
2018-04-20T11:30:06.880Z
My maths knowledge is very limited but from what I understand, partial derivative tells you the effect of one variable on the other. For example if you perform the partial derivative for production function with respect to labour to find MPL, this is showing how the change in labour affects the final output?  Thanks
D.I.N
CC BY-SA 3.0
2018-04-20T11:47:16.810Z
Yes, that interpretation is correct. Do you have a geometric interpretation of the derivative?
Theoretical Economist
CC BY-SA 3.0
2018-04-21T16:42:38.540Z
I don't get what it means by geometric interpretation of the derivative, could you elaborate on this part and how does that show diminishing returns ? Thanks
D.I.N
<macroeconomics><production-function>
Partial production function question
D.I.N
# Partial production function question

(Asked by: username_0 on 2018-04-19)

[![enter image description here](https://i.sstatic.net/DUh6D.png)](https://i.sstatic.net/DUh6D.png)

Hi everyone, I am learning about the partial production function. I don't understand why a tangent it drawn next to the curve; I get that it shows the MPL. Does this mean diminishing marginal product of labour will be reached eventually? Also, it is always assumed that K0 is constant in partial production function?

Thank you

**Tags:** macroeconomics, production-function

> **Comments:**
> **username_1**: Do you know any calculus? If so, then the MPL is just the partial derivative of the production function with respect to L. (If you only know single-variable calculus, then you should know what a derivative is. It should be easy to learn what a partial derivative is from there.)  
> **username_0**: I understand how to perform the partial derivative, but I don't understand what it shows in the economics context. I read somewhere that if FOC is >0 and SOC<0, then this is showing diminishing marginal returns? I am not sure why however. thanks  
> **username_1**: The partial derivative has the same interpretation here as it does in many other contexts. In general, ignoring the context, how do you interpret what the partial derivative of a function is? Also, I'm not sure what you mean by FOC and SOC. Normally I would interpret those as "first-order condition" and "second-order condition" respectively, but those interpretation make no sense here since they pertain to optimisation problems. There is no optimisation problem here. (There can be, but as stated, there isn't.)  
> **username_0**: My maths knowledge is very limited but from what I understand, partial derivative tells you the effect of one variable on the other. For example if you perform the partial derivative for production function with respect to labour to find MPL, this is showing how the change in labour affects the final output?  Thanks  
> **username_1**: Yes, that interpretation is correct. Do you have a geometric interpretation of the derivative?  
> **username_0**: I don't get what it means by geometric interpretation of the derivative, could you elaborate on this part and how does that show diminishing returns ? Thanks  

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## 1 answers

### Answer by username_2 on 2018-05-05. Score: 0 | Accepted answer

The tangent lines are drawn because they are trying to get you to think about the magnitude of the slope at each point on the production function. The marginal product of labour is the derivative of the production function, and will look like a decreasing function when drawn graphically, starting off with high values for low levels of labour, then decreasing to low values for high levels of labour. This corresponds to how the slope of the production function starts off steep and then gets flatter. Because the gradient decreases, this is called 'diminishing' returns.

We assume capital is constant when looking at this graph.


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