# Calculating Percentage of Tax Revenue

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 $$T = \2$$

• % tax revenue with respect to what? – alexjo Nov 3 '18 at 19:59

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 $$\frac{\Delta R}{R_1}=75\%$$.