In Rampur, Alcohol are forbidden, so people trade Alcohol bottles in a black market. The Alcohol demand is QD = 12 − P , and the supply is Qs = 2P (a) Find the equilibrium price and quantity in the black market.  (b) The government becomes aware of the black market and reinforces the police so that half of the alcohol supply would be seized and destroyed. Under this circumstance, what are the demand and supply functions? What is the new equilibrium price and quantity?  (c) How does the consumer surplus change between (a) and (b)?

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Most of the world’s governments have struggled to handle the issue of
allowing consumption of forbidden goods, such as alcohol, cigarette,
tobacco etc. to its population. Various methods of control have been
exercised world over, such as, complete ban on these goods, a restricted
consumption regime with quota on consumption or quota on selling, price
floors
keeping the price of these goods high up in order to reduce demand
and imposing high taxes to generate same effect. None of thee seem to have
worked to control the availability and consumption of such goods by the
society. These are called social bads, as they not only are harmful for the
person consuming them, there are external effects on others, such as family
and friends and the larger society.
In Rampur, Alcohol are forbidden, so people trade Alcohol bottles in a black
market. The Alcohol demand is QD = 12 − P , and the supply is Qs = 2P
(a) Find the equilibrium price and quantity in the black market. 
(b) The government becomes aware of the black market and reinforces the
police so that half of the alcohol supply would be seized and destroyed.
Under this circumstance, what are the demand and supply functions? What
is the new equilibrium price and quantity? 
(c) How does the consumer surplus change between (a) and (b)?
(d) Suppose that the government changes the policy and legalizes alcohol
trade. Now alcohol bottles are traded in an open market. However, for every
bottle of alcohol purchased, the buyer has to pay tax T to the government. T
is equal to the pre-tax price P (from question a). What are the demand and
supply functions under this circumstance? What are the equilibrium (pre-
tax) price and quantity? What is the after-tax price paid by buyers?
(e) Compare (b) and (d). Which policy do consumers prefer? Which policy
does the government prefer? Why? 

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