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

Equilibrium, Taxes, and Surplus

qS = −10 + 2p

qD = 30 − 2p

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

Now, let’s assume a per unit tax of $2 is charged to the buyer. What is the new equilibrium quantity, new price paid by the buyer, and new price received by the seller? )

Calculate the tax revenue and deadweight loss from this tax.

Solutions

Expert Solution

Initial equilibrium is where QD=QS

30-2P = -10+2P

30+10 = 2P+2P

40 = 4P

P = 40/4 = 10

Q = 30-2*10 = 10

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

Price consumers pay = 11

Price producers receive = 11-2 = 9

New equilibrium quantity = 8

TR = Tax* quantity = 2*8 = 16

DWL = loss in surplus due to change in consumption = 0.5*(10-8)*2 = 2

Rahul Sunny answered 1 year ago

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