3.3 Consider the market of bottled oolte in City it. The demand fer cotte is given by Gd : sue RIDF. where the quantity D is in terms of million bottles and P is in terms of dollars {$1. The supply of coke is given by t], = 1Ei + 2UP. (Note: 1. The demand and supply equations are valid only when both P and [I are nonnegative. 2. Use continuous method for this question.) [a] What are the equilibrium price and equilibrium quantity for coke in City X? Calculate also the consumer surplus and producer surplus in this case. Now. consider that the government imposes a per-unit tax of $5 per bottle of coke to sellers. ibj With the per-unit tax imposed to the seller. what are the valid demand and supply equations? Explain. Also draw the demandsupply diagram representing the situation. lc} With the perunit tax imposed, what is the price a buyer needs to pay for a bottle of coite in the new equilibrium? What is the price a seller can receive for each bottle of coke after paying the tax? What is the new equilibn'um quantity? How do these numbers change from the case without the per-unit tax? id} After the perunit tax is imposed and we neglect here any issues related to externalities {to be introduced in Topic 5}, hoil.I large are the values ofconsumer surplus, producer surplus. tax revenue and deadweight loss? How are they compared to the values in part {a} without the tax? Show your steps of calculations and show the corresponding areas in a diagram