<p>There is an indirect relationship. PPF size and shape is determined by production functions. Set of production functions <span class="math-container">$F_i= AK{^0.5}L^{0.5}$</span> will produce different PPF then set of production functions <span class="math-container">$F_i= A(K+L)^{0.5}$</span>.</p>
<p>Only some production functions exhibit increasing, decreasing and constant returns to scale. So there is some relationship. However, you can generate so many varied PPF with various production function that it is difficult to exhaustively describe it.</p>
<p>You can see how PPF is calculated in microeconomics textbooks. Frank Microeconomics and Behavior has some examples of PPF for different production functions.</p>

CC BY-SA 4.0
2023-10-30T14:41:46.897Z
@Giskard yes production functions do produce PPF. PPF is derived from production functions for goods. If good A has production function $A=10L$ and good B production function $B=L$ then PPF for A and B if country has L=100 is $100 = A/10 + B$. If you change production function for B to $B=10L$ you get new PPF $100=A/10 + B/10$. How else can you get PPF if not by using production functions for goods?
WilliamT
CC BY-SA 4.0
2023-10-30T17:15:49.237Z
Note the **emphasis**. Production function**s** can determine a PPF, but **A** production function, what you write about in your answer, cannot.
Giskard
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2023-11-03T14:38:02.597Z
@Giskard you could just said so
WilliamT
CC BY-SA 4.0
2023-11-03T14:48:19.657Z
I did, and when you asked for clarification, I clarified.
Giskard
CC BY-SA 4.0
2023-10-19T20:49:49.163Z
2023-11-03T14:37:41.400Z
2023-11-03T14:37:41.400Z
WilliamT
<p>Guys any material that discusses the above in detail for a two commodity case?</p>

CC BY-SA 4.0
2023-10-19T19:54:44.753Z
PPF is for Production Possibility Frontier (for all non english economists)
vanya
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2023-10-19T19:55:16.923Z
In what context are you interested in it? You mean in the sense of: „if I consume more of A, A will become cheaper“?
vanya
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2023-10-20T02:51:54.100Z
This might help: https://qr.ae/pGLAbN
Amit
CC BY-SA 4.0
2023-10-20T04:55:34.653Z
@vanya I wanted to understand the geometry of the PPF for a two commodity case like conditions for it to be concave/convex/linear depending on the returns to scale each commodity exhibits.
user205152
<microeconomics><international-trade>
the relationship between Returns to Scale and shape of Production Possibility Frontier (PPF)?
user205152
# the relationship between Returns to Scale and shape of Production Possibility Frontier (PPF)?

(Asked by: username_0 on 2023-10-19)

Guys any material that discusses the above in detail for a two commodity case?

**Tags:** microeconomics, international-trade
> **Comments:**
> **username_1**: PPF is for Production Possibility Frontier (for all non english economists)  
> **username_1**: In what context are you interested in it? You mean in the sense of: „if I consume more of A, A will become cheaper“?  
> **username_2**: This might help: https://qr.ae/pGLAbN  
> **username_0**: @vanya I wanted to understand the geometry of the PPF for a two commodity case like conditions for it to be concave/convex/linear depending on the returns to scale each commodity exhibits.  

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## 1 answers

### Answer by username_3 on 2023-10-19. Score: 1

There is an indirect relationship. PPF size and shape is determined by production functions. Set of production functions $F\_i= AK{^0.5}L^{0.5}$ will produce different PPF then set of production functions $F\_i= A(K+L)^{0.5}$.

Only some production functions exhibit increasing, decreasing and constant returns to scale. So there is some relationship. However, you can generate so many varied PPF with various production function that it is difficult to exhaustively describe it.

You can see how PPF is calculated in microeconomics textbooks. Frank Microeconomics and Behavior has some examples of PPF for different production functions.

> **Comments:**
> **username_3**: @Giskard yes production functions do produce PPF. PPF is derived from production functions for goods. If good A has production function $A=10L$ and good B production function $B=L$ then PPF for A and B if country has L=100 is $100 = A/10 + B$. If you change production function for B to $B=10L$ you get new PPF $100=A/10 + B/10$. How else can you get PPF if not by using production functions for goods?  
> **username_4**: Note the **emphasis**. Production function**s** can determine a PPF, but **A** production function, what you write about in your answer, cannot.  
> **username_3**: @Giskard you could just said so  
> **username_4**: I did, and when you asked for clarification, I clarified.  

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