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

$q^s(p)=50p~~~~~~q^d(p)=100(\frac{12}{p}-1)$

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

$p^s(q)=\frac{q}{50}~~~~~~p^d(q)=\frac{1200}{q+100}-1$

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?

$q^d(1+t)=100(\frac{12}{1+t}-1)=\frac{100(11-t)}{1+t}$

$T=q^d*t=\frac{100t(11-t)}{1+t}$

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  • $\begingroup$ $p^d(q)$ should be $\frac{1200}{q+100}$ $\endgroup$
    – Akash Patel
    Mar 22, 2019 at 0:04
  • $\begingroup$ Thanks, not sure how that made its way in there $\endgroup$
    – tom982
    Mar 25, 2019 at 19:37

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