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Finding the supply function from a production function

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$begingroup$

Given the production function $f(z_1,z_2)=sqrtaz_1+bz_2$ where $z_1$ and $z_2$ are inputs, $a$ and $b$ are scalars; find the supply function: $y(p)$ output as a function of prices, and the profit function: $pi(p)$ profit as a function of prices. I tried setting it up as a profit maximizing problem but everything cancels out and you can't find an optimal bundle of $z_1$ and $z_2$.

economics

share|cite|improve this question

edited Mar 22 at 13:19

user103828

1,3161232

asked Dec 13 '16 at 0:05

Mitch HughesMitch Hughes

878

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You need to explain what the various symbols represent.
  $endgroup$
  – rogerl
  Dec 13 '16 at 0:44
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @rogerl is that better?
  $endgroup$
  – Mitch Hughes
  Dec 13 '16 at 0:55
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Depends on how economists use the terms above. I am only speculating, but perhaps supply is defined as the rate of production? Also, the variables aren't defined at all. What are the $z$'s -- are they units, of what, the ingredients?
  $endgroup$
  – Allawonder
  Mar 22 at 13:28
  

  
  
  
  

add a comment | 

0

$begingroup$

Given the production function $f(z_1,z_2)=sqrtaz_1+bz_2$ where $z_1$ and $z_2$ are inputs, $a$ and $b$ are scalars; find the supply function: $y(p)$ output as a function of prices, and the profit function: $pi(p)$ profit as a function of prices. I tried setting it up as a profit maximizing problem but everything cancels out and you can't find an optimal bundle of $z_1$ and $z_2$.

economics

share|cite|improve this question

edited Mar 22 at 13:19

user103828

1,3161232

asked Dec 13 '16 at 0:05

Mitch HughesMitch Hughes

878

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You need to explain what the various symbols represent.
  $endgroup$
  – rogerl
  Dec 13 '16 at 0:44
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @rogerl is that better?
  $endgroup$
  – Mitch Hughes
  Dec 13 '16 at 0:55
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Depends on how economists use the terms above. I am only speculating, but perhaps supply is defined as the rate of production? Also, the variables aren't defined at all. What are the $z$'s -- are they units, of what, the ingredients?
  $endgroup$
  – Allawonder
  Mar 22 at 13:28
  

  
  
  
  

add a comment | 

$begingroup$

Given the production function $f(z_1,z_2)=sqrtaz_1+bz_2$ where $z_1$ and $z_2$ are inputs, $a$ and $b$ are scalars; find the supply function: $y(p)$ output as a function of prices, and the profit function: $pi(p)$ profit as a function of prices. I tried setting it up as a profit maximizing problem but everything cancels out and you can't find an optimal bundle of $z_1$ and $z_2$.

economics

share|cite|improve this question

edited Mar 22 at 13:19

user103828

1,3161232

asked Dec 13 '16 at 0:05

Mitch HughesMitch Hughes

878

$endgroup$

share|cite|improve this question

edited Mar 22 at 13:19

user103828

1,3161232

asked Dec 13 '16 at 0:05

Mitch HughesMitch Hughes

878

share|cite|improve this question

edited Mar 22 at 13:19

user103828

1,3161232

asked Dec 13 '16 at 0:05

Mitch HughesMitch Hughes

878

edited Mar 22 at 13:19

user103828

1,3161232

edited Mar 22 at 13:19

user103828

1,3161232

asked Dec 13 '16 at 0:05

Mitch HughesMitch Hughes

878

asked Dec 13 '16 at 0:05

Mitch HughesMitch Hughes

878