Question

suppose the supply curve and demand curve for the market of shoes is as follows:

Qd=30-2p  

Qs=15+p

Find equilibrium P and Q

suppose a $2 / unit tax is imposed on the seller. Find the new equilibrium Q, Pb and Ps.

Now rework the problem with at $2 / unit subsidy (a subsidy is the opposite of tax)

Answer 1

At equilibrium, Qd = Qs

Or, 30 - 2P = 15 + P

Or, 3P = 15

Or, P = 5

At P = 5, from any of the demand or supply equation we get, Q = 20.

Therefore, equilibrium price is $5 and equilibrium quantity is 20 units.

Now, a $2 per unit tax is imposed on the seller. This will shift the supply curve leftward by the tax amount.

Let P = after tax equilibrium price. That is, consumers pay P dollars but sellers receive (P - 2) dollars.

Therefore, after tax demand equation remains unchanged: Qd = 30 - 2P

Supply equation changes (replace P with (P - 2)):

Qs = 15 + (P - 2) = 13 + P

At after tax equilibrium, 30 - 2P = 13 + P

Or, 3P = 17

Or, P = (17/3)

Therefore, buyers pay (Pb) = $(17/3) and sellers receive (Ps) = $(17/3) - 2 = $(11/3)

At P = (17/3), from any of the after tax demand or supply equation we get, Q = (56/3).

Therefore, after tax equilibrium quantity is (56/3) units.

Now a subsidy of $2 per unit is given. Let P = after subsidy equilibrium price. That is, consumers pay P dollars but sellers receive (P + 2) dollars.

After subsidy demand equation: Qd = 30 - 2P

Supply equation (replace P with (P + 2)):

Qs = 15 +(P + 2) = 17 + P

At after subsidy equilibrium, 30 - 2P = 17 + P

Or, 3P = 13

Or, P = (13/3)

Therefore, after subsidy buyers pay (Pb) = $(13/3), sellers receive (Ps) = $(13/3) + 2 = $(19/3).

At P = (13/3), from any of the after subsidy demand or supply equation we get, Q = (64/3).

Therefore, after subsidy equilibrium quantity is (64/3) units.