Suppose the demand and supply of clothing is given by the following two function

Question

Suppose the demand and supply of clothing is given by the following two functions (where Q is measured in millions of units): QD = 165-2p and QS = 3p. a) Solve for the equilibrium price and quantity of clothes consumed in the economy if there are no taxes collected on clothes. b) Suppose a 25% sales tax is imposed on clothing with the statutory liability falling on consumers. (That is, if p is the market price for clothes charged by producers, the after-tax price to consumers is 1.25p.) Solve for the new equilibrium quantity and the new market price for clothing? What is the after-tax price that consumers now face? c) Calculate the tax revenues generated. Does the burden of the tax fall more heavily on consumers or producers? Explain. d) Suppose, instead of the 25% sales tax, a 20% tax is imposed on producer revenues from the sale of clothing. (That is, if p is the market price for clothing paid by consumers, producers receive an after-tax price of 0.8p, with 0.2p going to the government.) How does this affect the economic incidence of the tax?

Explanation / Answer

a). For equilibirium-->

QD= QS

5p= 165

p= 33 Units

therefore,

QD at market equilibirium is QD= 99

QS at market eqilibirium is QS= 99

b)

P(s)= QS/3

P(D)= (165-QD)/2

After tax, P(S1)=1.25P(s) = 1.25QS/3 = P(D) = (165-QD)/2

1.25Q/3= (165-Q)/2

Q= 90

P(s1)=1.25* 37.5= 46.875

P(d)= 37.5

c) Tax revenue-->

Q*(P(s1)-P(d))= (46.875-37.5)*90= 9.375*90= 843.75 million units

the burden falls on the consumer, because they have to pay 9.375 units more for the same quantity of good.

d) Now, 0.8P will be given to the producers, and 0.2P will go to the gov.

Therefore, P(D1) =P(D)/0.8

P(s)= QS/3

P(D)= (165-QD)/2

P(D1) = (165-QD)/1.6= P(s)= QS/3

(165-Q)/1.6= Q/3

Q= 107.6

P(S)=35.86

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