Question

. The (inverse) equations for the supply and demand for French Champagne are given below. Supply: P = 40 + ¼Q Demand: P = 100 – ½Q [Half point for each question]

a) compute the equilibrium price and quantity of Champagne.

b) Suppose and excise tax (i.e. a tax paid by producers) of $18 per bottle is imposed. What are the equations for the new supply and demand curves? What is the new EQ price and quantity? Specify what the prices paid by consumers and received by producers are?

c) Do the same as (b) for a sales tax (i.e. a tax paid by consumers) of $18 per bottle and explain whether the burden has shifted from producers to consumers along with the incidence of the tax from excise to sales.

d) Calculate the Consumer Surplus and Producer Surplus before and after the tax is put into place. How much revenue is raised? Calculate any deadweight loss from the tax.

Answer 1

(a) In equilibrium, demand price equals supply price.

40 + 0.25Q = 100 - 0.5Q

0.75Q = 60

Q = 80

P = 100 - (0.5 x 80) = 100 - 40 = $60

(b) A tax on producers will lower the effective price received by producers, shifting supply curve left. New supply function is:

P - 18 = 40 + 0.25Q

P = 58 + 0.25Q

Demand function remains unchanged. Equating it with supply function,

100 - 0.5Q = 58 + 0.25Q

0.75Q = 42

Q = 56

P = 100 - (0.5 x 56) = 100 - 28 = $72 (Price paid by buyers)

Price received by sellers = $(72 - 18) = $54

Tax burden of buyers = $(72 - 60) = $12

Tax burden of sellers = $(60 - 54) = $6

(c) A tax on buyers will raise the price paid by buyers, shifting demand curve to left. New demand function becomes

P + 18 = 100 - 0.5Q

P = 82 - 0.5Q

Supply function remains unchanged. Equating it with demand function,

82 - 0.5Q = 40 + 0.25Q

0.75Q = 42

Q = 56

P = 82 - (0.5 x 56) = 82 - 28 = $54 (Price received by sellers)

Price paid by buyers = $(54 + 18) = $72

Tax burden of buyers = $(72 - 60) = $12

Tax burden of sellers = $(60 - 54) = $6

Therefore, tax burden remains unchanged.

(d)

Before tax,

From demand function, when Q = 0, P = $100 (Reservation price)

Consumer surplus (CS) = Area between demand curve & price = (1/2) x $(100 - 60) x 80 = 40 x $40 = $1,600

From supply function, when Q = 0, P = $40 (Minimum price)

Producer surplus (PS) = Area between supply curve & price = (1/2) x $(60 - 40) x 80 = 40 x $20 = $800

After tax (imposed on producers):

CS = (1/2) x $(100 - 72) x 56 = 28 x $28 = $784

PS = (1/2) x $(54 - 40) x 56 = 28 x $14 = $392

Tax revenue = $18 x 56 = $1,008

Deadweight loss = (1/2) x Unit tax x Change in quantity = (1/2) x $18 x (80 - 56) = $9 x 24 = $216