So the question asks me to find the % tax revenue but I can't seem to get the right answer, can anyone help?
The demand and supply functions for pens with a tax imposed on the buyers is given by:
$Q^D = 92 – 4 (Ps + T)$
$Q^S = -168 +12 (Ps)$
$Q = Q^D = Q^S$
The price to the buyer was initially \$16 and \$1 tax. However, the government decided to raise the tax to \$2.00 for this amount. This caused a drop in the quantity sold from the initial $Q=24.$
Assume $T = \$2$
Demand function $$ P^D(Q,T)=23-\frac{Q}{4}-T=P^D(Q,0)-T $$ Supply function $$ P^S(Q)=14+\frac{Q}{12} $$ For $T=T_0=0$, the equilibrium is at $(Q_0,P_0)=(27,65/4)$.
For $T=T_1=1$, we have the equilibrium quantity $Q_1=24$ and the tax revenue $$ R_1=\big[P^D(Q_1,T_0)-P^D(Q_1,T_1)\big]\times Q_1=T_1\times Q_1=24 $$ For $T=T_2=2$, we have the equilibrium quantity $Q_2=21$ and the tax revenue $$ R_2=\big[P^D(Q_2,T_0)-P^D(Q_2,T_2)\big]\times Q_2=T_2\times Q_2=42 $$ with an increase of $\Delta R=R_2-R_1=18$, that is an increase of $\frac{\Delta R}{R_1}=75\%$.
