Question

Q=-20+2p P=100-q

: Suppose, Congress passed a resolution to curb drinking among Americans (a weaker version of Prohibition). And the Senate and House have different ideas regarding how to impose the tax. 1. The House, controlled by the Democrats, wants to tax the producers of Whiskey and plans to impose a $5 tax on the whisky producers (the rich).

a) Solve for the equilibrium with the House proposed tax (there should be two prices, the price consumers pay, and the price producers get).

b) Calculate the total tax revenue. How much of the tax incidence is borne by the consumer and how much by the producers?

c) Calculate the CS, PS, and TS with the tax.

d) What is the DWL?

2. The Senate, controlled by the Republicans, want to impose the tax on consumers of the Whiskey.

a) Solve for the equilibrium with the House proposed tax (there should be two prices, the price consumers pay, and the price producers get).

b) Calculate the total tax revenue. How much of the tax incidence is borne by the consumer and how much by the producers?

c) Calculate the CS, PS, and TS with the tax.

d) What is the DWL?

Answer 1

1) a) supply function:Q=2p-20

Inverse supply function:p=10+Q

Supply function after tax:P=10+q+5=15+Q

Equilibrium:

15+Q=100-Q

Q=85/2=42.5

P=100-42.5=57.5 ( price consumer pay or market price)

P=57.5-5=52.5( price seller get)

B) Total tax revenue= 5*42.5=212.5

Without tax equilibrium;,

10+q=100-q

Q=90/2=45

P=100100-45=55

Tax burden Borne by consumer=New equilibrium price- old equilibrium price=57.5-55=2.5

Tax burden by seller=Old equilibrium price- new price seller get=55-52.5=2.5

C)Consumer surplus ( CS)=1/2*42.5*(100-57.5)=0.5*42.5*42.5=903.125

Producer surplus( PS)=1/2*42.5*(57.5-15)=0.5*42.5*42.5=903.125

Total surplus=(TS)=CS+ PS=903.125+903.125=1806.25

D) deadweight loss refers to loss of surplus .

Deadweight loss( DWL)=1/2* tax*Decrease in equilibrium quantity

DWL=1/2*5*(45-42.5)=0.5*5*2.5=6.25