Question

1.     The market demand and supply functions for toothpaste are: Qd = 12 - .04P and Qs = 3.8P + 4

a.     Calculate the equilibrium quantity and price and point elasticity of demand in equilibrium.

b.     Next, calculate consumer surplus.

Suppose the toothpaste market is taxed $0.25 per unit.

c.      Calculate the revenues generated by the tax.

d.     Calculate the loss in consumer surplus.

What percentage of the burden of the tax is paid for by consumers?

Answer 1

(a)

In equilibrium, Qd = Qs.

12 - 0.04P = 3.8P + 4

3.84P = 8

P = 2.08

Q = 12 - (0.04 x 2.08) = 12 - 0.08 = 11.92

Elasticity of demand = (dQd/dP) x (P/Qd) = -0.04 x (2.08/11.92) = -0.007

(b)

From demand function, when Qd = 0, P = 12/0.04 = 300

Consumer surplus (CS) = Area between demand curve and price = (1/2) x (300 - 2.08) x 11.92 = 5.96 x 297.92 = 1775.60

(c)

Assuming tax is imposed on producers, supply curve will shift left by $0.25 at every output level. New supply function is:

Qs = 3.8(P - 0.25) + 4 = 3.8P - 0.95 + 4 = 3.8P + 3.05

Equating with Qd,

12 - 0.04P = 3.8P + 3.05

3.84P = 8.95

P = 2.33 (Price paid by consumers)

Price received by producers = 2.33 - 0.25 = 2.08

Q = 12 - (0.04 x 2.33) = 12 - 0.09 = 11.91

Tax revenue = Tax per unit x Quantity after tax = 0.25 x 11.91 = 2.98

(d)

After-tax CS = Area between demand curve and price paid by consumers = (1/2) x (300 - 2.33) x 11.91 = 5.955 x 297.67

= 1772.62

Loss in CS = 1775.6 - 1772.62 = 2.98

Tax burden of consumers = After-tax price paid by consumers - Pre-tax equilibrium price = 2.33 - 2.05 = 0.25

% of tax borne by consumers = (0.25/0.25) x 100% = 100%