# price and quantity after taxation

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) $T=20\% \pi$, total profit is taxed

b) $T=200$ tax does not depend on volume and value of goods sold

will it be simply $$393-2p=p/4-12-200$$ ? Obviously i need to find $p$.

Obviously i have calculated the equilibrium price and quantity before taxation that is $p=180,q=33$. How to find situation after taxation in those two cases?

• Assuming a competitive market, the supply price for a given quantity should be equal to the marginal cost, and the marginal profit should be zero. This does not change with either a lump-sum tax or a percentage profit tax, with the same price and quantity giving a zero marginal profit. What will change is the producer surplus. – Henry Jan 12 '16 at 14:36
• Could you be more specific? i do not think i get it – mkropkowski Jan 12 '16 at 14:42

$$393 − 2p = \frac p 4 − 12 − 200 - 0.2 \cdot \text{profit} .$$