Question

. Equilibrium, Taxes, and Surplus (30 pts)

The market for cake donuts is given by the following supply and demand functions:

qS = −10 + 2p

qD = 30 − 2p

(c) Calculate the consumer surplus, producer surplus, and total welfare levels.

(d) Now, let’s assume a per unit tax of $2 is charged to the buyer. What is the new

(e) Calculate the tax revenue and deadweight loss from this tax.

(a) Graph the supply and demand curves. Make sure to label correctly.

Answer 1

Initial equilibrium

30-2P = -10+2P

30+10 = 2P+2P

40 = 4P

P = 40/4 = 10

Q = 30-2*10 = 10

A)

C) CS = 0.5*10*(15-10) = 25

PS = 0.5*10*(10-5) = 25

TS = CS+PS = 50

D) With the tax, the demand equation becomes 30-2(P-2) = 30-2P-4

30-2P-4 = -10+2P

30+10-4 = 2P+2P

P = 36/4 = 9

Q = -10+2*9 = 8

CS = 0.5*8*(15-11) = 16

PS = 0.5*8*(9-5) = 16

E) TR = 2*8 = 16

DWL = 0.5*(10-8)*2 = 2