The equation>> for an Inverse demand curve and an inverse supply curve of cigare

Question

The equation>> for an Inverse demand curve and an inverse supply curve of cigarettes are at follows: p^a(q) - 27-q (p) = (q) = 3 + 1/2q Find the equ· Ubrium quantity q^* and price p^* Calculate the sellers' rent at q* Suppose that there's ? Si unit tax on demond side ond $2 unit tax on supply side (therefore, in totol, there's a S3 unit to* on the transactions of cigarettes): Find the quantity under the tax. q^t d. The price paid by consumers, p' and the price received by sellers, p Draw a curve that represents the relationship between ta* rate on a good and the dead weight loss caused by the tax. The horizontal axis represents tax rate, in do/lars per unit of the good; the vertical axis represents the scale of the dead-weight loss (DWl), in dollars. Draw another graph to briefly justify the shape of the curve you draw

Explanation / Answer

4a

For equilibrium, Pd=ps

27-q=3+q/2

54-2q=6+q

q=16

p=27-q=27-16=11

4b

Seller rent=Producer surplus

At q=0,ps=3+0/3=3

Producer surplus=1/2*(equilibrium price-3)*equilibrium quantity

Producer surplus=(1/2)*(11-3)*16=64

Seller rent=64

4c

At tax of $1 the quantity demanded=27-(p+1)=27-(11+1)=15

At tax of $2 , the quantity supplied =2*((p-2)-3)=2*((11-2)-3)=12

4d

The Price paid by consumer =p+1=11+1=12

Price received by supplier=p-2=11-2=9

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