Given that demand for a good X is equal to $q_D=393-2p$ and market supply is $q_S=p/4-12$. Find equilibrium price and quantity, consumer and producer surplus and draw a diagram illustrating the situation. Given that:
a) $T=2q$, every single item sold is taxed.
b) $T=20\% TR$ total revenue is taxed
Obviously i have calculated the equilibrium price and quantity before taxation that is $p=180,q=33$.But i have no idea how to caculate those two values after taxation.
Suppose after the tax, $p$ is the price charged by the supplier. In the first case, the price paid by the consumer is $p+2$. To find the new equilibrium price (charged by the supplier), solve:
$$393-2(p+2) = \frac{p}{4} -12$$
The new price charged by the supplier is $178.22$ the consumer pays $\$180.22$. New quantity is $393-2(180.22)=32.56$. Notice that the tax collected is exactly $2q$.
In the second case, if the supplier charges $p$, they receive only $80\%$ of that price for each item sold. Thus, it is as if they receive $0.8p$ when they charge $p$. We solve:
$$393-2(p) = \frac{0.8p}{4} -12$$
The new price charged by the supplier is $\$184.091$ quantity sold is $393-2(184.091)=24.818$.