Question

2. If the demand function for X is Q = 100 - P, and the supply function for X is Q = 40 + 2P, determine the effects on: (a) equilibrium price, (b) quantity traded and (c) government revenue (or cost) if:

1. A tax of $ 6 per unit produced is established. (Is it different from the case of establish a tax of $ 6 per unit consumed?)

Answer 1

Demand function is as follows -

Q = 100 - P

Supply function is as follows -

Q = 40 + 2P

At equilibrium,

Demand = Supply

100 - P = 40 + 2P

100 - 40 = 2P + P

3P = 60

P = 20

Q = 100 - P = 100 - 20 = 80

Thus, before tax,

The equilibrium price is $20 per unit.

The equilibrium quantity is 80 units.

Now, a tax of $6 per unit is imposed.

Supply function after tax is as follows -

Q = 40 + 2(P -6)

Q = 40 + 2P - 12

Q = 28 + 2P

Equilibrium, after tax,

Demand = Supply

100 - P = 28 + 2P

100 - 28 = 2P + P

72 = 3P

P = 72/3 = 24

Q = 100 - P = 100 - 24 = 76

The equilibrium price after tax is $24 per unit.

The equilibrium quantity after tax is 76 units.

Thus,

After tax,

(a) The equilibrium price has increased by $4 per unit (from $20 per unit to $24 per unit).

(b) The quantity traded has decreased by 4 units (from 80 units to 76 units).

(c)

Calculate the tax revenue -

Tax revenue = tax per unit * equilibrium quantity after tax

Tax revenue = $6 * 76 = $456

Thus,

The government revenue is $456.