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Supply and Demand Functions with Tax

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0

$begingroup$

I've been given the below supply and demand functions:

$q^s(p)=50p~~~~~~q^d(p)=100(frac12p-1)$

I've answered the first few questions, which include finding the equilibrium etc, and inverting the above:

$p^s(q)=fracq50~~~~~~p^d(q)=frac1200q+100-1$

Now it says the price is 1/unit and the government introduces a tax on the production of t per unit. It also says "after these changes, the demand function
remains the same, but the new inverse supply function is $p^s(q)= 1+t$

The part I'm stuck on is where it asks for a function of the total tax collected $T$, in terms of $t$. I assume that $~T=q^d*t$, so do I just sub $p=1+t$ into my original demand equation for $q^d$ then multiply that by $t$ for the answer?

$q^d(1+t)=100(frac121+t-1)=frac100(11-t)1+t$

$T=q^d*t=frac100t(11-t)1+t$

parametric economics

share|cite|improve this question

asked Mar 21 at 23:25

tom982tom982

2416

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  $p^d(q)$ should be $frac1200q+100$
  $endgroup$
  – Akash Patel
  Mar 22 at 0:04
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks, not sure how that made its way in there
  $endgroup$
  – tom982
  Mar 25 at 19:37
  

  
  
  
  

add a comment | 

0

$begingroup$

I've been given the below supply and demand functions:

$q^s(p)=50p~~~~~~q^d(p)=100(frac12p-1)$

I've answered the first few questions, which include finding the equilibrium etc, and inverting the above:

$p^s(q)=fracq50~~~~~~p^d(q)=frac1200q+100-1$

Now it says the price is 1/unit and the government introduces a tax on the production of t per unit. It also says "after these changes, the demand function
remains the same, but the new inverse supply function is $p^s(q)= 1+t$

The part I'm stuck on is where it asks for a function of the total tax collected $T$, in terms of $t$. I assume that $~T=q^d*t$, so do I just sub $p=1+t$ into my original demand equation for $q^d$ then multiply that by $t$ for the answer?

$q^d(1+t)=100(frac121+t-1)=frac100(11-t)1+t$

$T=q^d*t=frac100t(11-t)1+t$

parametric economics

share|cite|improve this question

asked Mar 21 at 23:25

tom982tom982

2416

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  $p^d(q)$ should be $frac1200q+100$
  $endgroup$
  – Akash Patel
  Mar 22 at 0:04
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thanks, not sure how that made its way in there
  $endgroup$
  – tom982
  Mar 25 at 19:37
  

  
  
  
  

add a comment | 

$begingroup$

I've been given the below supply and demand functions:

$q^s(p)=50p~~~~~~q^d(p)=100(frac12p-1)$

I've answered the first few questions, which include finding the equilibrium etc, and inverting the above:

$p^s(q)=fracq50~~~~~~p^d(q)=frac1200q+100-1$

Now it says the price is 1/unit and the government introduces a tax on the production of t per unit. It also says "after these changes, the demand function
remains the same, but the new inverse supply function is $p^s(q)= 1+t$

The part I'm stuck on is where it asks for a function of the total tax collected $T$, in terms of $t$. I assume that $~T=q^d*t$, so do I just sub $p=1+t$ into my original demand equation for $q^d$ then multiply that by $t$ for the answer?

$q^d(1+t)=100(frac121+t-1)=frac100(11-t)1+t$

$T=q^d*t=frac100t(11-t)1+t$

parametric economics

share|cite|improve this question

asked Mar 21 at 23:25

tom982tom982

2416

$endgroup$

share|cite|improve this question

asked Mar 21 at 23:25

tom982tom982

2416

share|cite|improve this question

asked Mar 21 at 23:25

tom982tom982

2416

asked Mar 21 at 23:25

tom982tom982

2416

asked Mar 21 at 23:25

tom982tom982

2416