Suppose that a market is described by the following supply and demand equations: QS = 2P...

Suppose that a market is described by the following supply and demand equations:

Q^S = 2P

Q^D = 400 - 2P

Suppose that a tax of $40 is placed on buyers, so the new demand equation is:

Q^D = 400 – 2(P + 40)

a) Solve for the new equilibrium. What happens to the price received by sellers, the price paid by buyers, and the quantity sold? Calculate the new consumer surplus, producer surplus and total surplus.

b) Calculate the Tax revenue and the deadweight loss generated by the tax.

Expert Solution

a) Qd=Qs
400-2(P+40) = 2P
400-2P+80=2P
480=4P
P=120
Price of $120, includes $40 as tax and hence the net price = $80
Qd = 400-2(80+40) = 400-2*120=160

Price received by sellers = $80

Price paid by buyers = $120

Quantity sold = 160

New consumer surplus = area of triangle = 0.5*160*(160-80) = $6400

New Producer surplus = 0.5*160*(80) = $6400

b) Tax revenue = Q*tax = 160*40 = $6400
DWL = area of triangle = 0.5*(200-160)*(120-80) =$800

Rahul Sunny answered 2 years ago

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