Suppose that a market is described by the following supply and demand equations:
QS = 2P
QD = 400 - 3P
Solve for the equilibrium price and the equilibrium quantity.
Suppose that a tax of T is placed on buyers, so the new demand equation is
QD = 400 – 3(P+T)
Solve for the new equilibrium. What happens to the price received by sellers, the price paid by buyers, and the quantity sold?
Tax revenue is T x Q. Use your answer from part (b) to solve for tax revenue as a function of T. Graph this relationship for T between 0 and 400.
Qs = 2P
Qd = 400 - 3P
In equilibrium Qd = Qs
400 - 3P = 2P
5P = 400
P = 80
Q = 160
Now a tax of T is imposed,
Qd = 400 - 3(P+T)
Qs = 2P
Qd = Qs
400 - 3(P+T) = 2P
400 - 3P - 3T = 2P
5P = 400 - 3T
P = (400-3T)/5
Q = 2(400-3T)/5
Earlier the sellers were receiving price = 80, now they are receiving P = 80 - 0.6T
Earlier the consumer paid price = 80, Now they are paying P = P + T = 80 + 0.4T
Earlier quantity sold = 160, Now Q = 2(400-3T)/5 = 160 - 1.2T
Tax revenue TR = T*Q = T*(160 - 1.2T)
TR = 160T - 1.2T2
TR is zero when T = 0 and T = 133.33. When T = 400, TR = -128000
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