Question

1) Recently, McDonald's re-introduced its Szechuan dipping sauce as an option at its restaurants located across the United States. Suppose that the U.S. government considers the Szechuan sauce market as a potential source of government revenue and that the government decides to levy an excise tax on Szechuan dipping sauce of $.80 per unit of sauce. The market clearing price before the excise tax is levied is $1.20 and the equilibrium quantity is 1500 units of Szechuan dipping sauce. After the excise tax is levied the consumer will pay $1.80 and the equilibrium quantity in the market will drop to 1200 units of Szechuan dipping sauce.

a. Given the above information, derive the equations for the supply curve and the demand curve in Szechuan source market.

b. Consider this market prior to the implementation of the excise tax. Calculate the values of Consumer Surplus (CS), Producer Surplus (PS) and Total Surplus (TS) when this market is initially at equilibrium.

c. Now, consider this market after the implementation of the excise tax. Calculate the value of Consumer Surplus with the excise tax (CSt), Producer Surplus with the excise tax (PSt), the tax revenue the government receives from implementing the tax (Tax Revenue), Total Surplus in this market after the excise tax is implemented (TSt) and the Deadweight Loss (DWL) due to the implementation of this excise tax. 2

d. Consider this market after the implementation of the excise tax. Calculate the Consumer Tax Incidence(CTI) and Producer Tax Incidence(PTI) of this excise tax. Which one is larger? If the demand curve became more elastic (eg: if the new demand curve was “flatter” but went through the initial equilibrium point before the excise tax was levied), would consumers pay a higher or lower share of the total taxes collected? What conclusion can you make about the relationship between elasticity and tax incidence?

Answer 1

(a)

Demand function: Q = a - bP

When P = $1.2, Q = 1500

1500 = a - 1.2b.......(1)

When P = $1.8, Q = 1200

1200 = a - 1.8b.......(2)

(1) - (2) yields:

0.6b = 300

b = 500

a = 1500 + 1.2b [From (1)] = 1500 + (1.2 x 500) = 1500 + 600 = 2100

Demand function: Q = 2100 - 500P

Supply function: Q = c + dP

When P = $1.2, Q = 1500

1500 = c + 1.2b.......(3)

When P = $1.8 - $0.8 = $1 (Since tax of $0.8 will lower the price received by sellers by $0.8), Q = 1200

1200 = c + d............(4)

(3) - (4) yields:

0.2d = 300

d = 1500

c = 1200 - d [From (4)] = 1200 - 1500 = - 300

Supply function: Q = - 300 + 1500P

(b) Before tax,

From demand function, When Q = 0, P = 2100/500 = $4.2 (Reservation price)

CS = Area between demand curve & price = (1/2) x $(4.2 - 1.2) x 1500 = 750 x $3 = $2250

From supply function, When Q = 0, P = 300/1500 = $0.2 (Reservation price)

PS = Area between supply curve & price = (1/2) x $(1.2 - 0.2) x 1500 = 750 x $1 = $750

TS ($) = CS + PS = 2250 + 750 = 3000

(c) After tax,

CSt = (1/2) x $(4.2 - 1.8) x 1200 = 600 x $2.4 = $1440

PSt = (1/2) x $(1 - 0.2) x 1200 = 600 x $0.8 = $480

TSt ($) = CSt +PSt = 1440 + 480 = 1920

Tax revenue = $0.8 x 1200 = $960

DWL = Unit tax x Difference in quantity = $0.8 x (1500 - 1200) = $0.8 x 300 = $240

(d)

CTI = Tax paid by buyers before tax - Tax paid by buyers after tax = $1.8 - $1.2 = $0.6

PTI = Unit tax - Tax paid by buyers = $0.8 - $0.6 = $0.2

Tax incidence for buyers is larger.

If demand became more elastic, consumers would pay lower tax burden and producers would pay higher tax burden.

Therefore, if Elasticity of demand is higher (lower) than elasticity of supply, then consumers pay lower (higher) tax burden and producers pay higher (lower) tax burden.