Answer to Question #201651 in Microeconomics for Tristin

Question

In South Africa, cigarettes are forbidden, so people trade cigarettes in a black market. The cigarette demand is 𝑄𝐷 = 12 − 𝑝, and cigarette supply is 𝑄𝑆 = 2𝑝. (5) Find the equilibrium price and quantity in the black market. Interpret your results The government becomes aware of the black market and reinforces the polices that half of the cigarette supply would be seized and destroyed. Under this circumstance, what are the demand and supply functions? What is the new equilibrium price and quantity? Show the change by using a supply and demand diagram. (6) How does the consumer surplus change between (a) and (b)? Calculate total surplus. (4)

Answer 1

5.

equilibrium price and quantity

$Qd=65$

$12-P=2P\\12=3P\\P=4\\Q=2\times4\\Q=4$

Demand and supply functions

$Qd=12-P\\Qs=P$

Now equilibrium price and quantity

$Qd=Qs\\12-P=P\\12=2P\\P=6\\Qs=P\\Qd=12-6=6\\\\\therefore Q=6$

6.

Consumer surplus

a). Pd is calculated when Qd=0

For A

$Qd=12-P\\0=12-P\\P=12$

Consumer surplus $=\frac{1}{2}\times base\times height$

$=\frac{1}{2}\times8\times(12-4)\\=32$

For B

$Qd=\frac{1}{2}\times 6\times (12-6)\\=18$

Consumer surplus decrease by 14

$32-18=14$

b.

Total surplus=producer surplus + consumer surplus

For A

$Qs=2P\\0=2P\\P=0\\\frac{1}{2}\times 8\times (4-0)\\=16$

Total surplus for A

$=32+16\\=48$

$Qs=P\\0=P\\\frac{1}{2}\times8\times(6-0)\\=24$

Total surplus for B

$=18+24\\=42$