Question

Suppose you work for the state government of California. Due to the heavy traffic jam on I-880, the state has decided to decide to construct a new highway. To fund a part of construction, the state needs to generate tax revenue. You, as a tax analyzer in the government, need to propose the amount of the tax. After careful examination, you have decided that collecting tax from the consumption of notebook PC. A consumer pays $t per unit of notebook PC consumed. The demand and the supply curves in free market (without tax) are represented by the following equations:

D: Q_D = 80,000 - 20P

S: Q_S = 30P - 20,000

(i) What are the market equilibrium price (P*) and quantity (Q*) in the notebook PC market in California when no tax is imposed.

(ii)  What is the price elasticity of demand at the market equilibrium when no tax is imposed?

Now assume that a per unit tax, t = $10 is imposed to the consumers.

(iii) What is the new market equilibrium price under the tax policy? What is the price that buyers pay (P_B)? Price that sellers receive (P_S)?

(iv) You have been asked to find the amount of per unit tax t that would maximizes the tax revenue from this market. Let's denote the tax revenue maximizing t by t_MAX. Find out t_MAX.