22. Starting with QD 300 2.5P and QS 60 5P and supposing that the government imp

Question

22. Starting with QD 300 2.5P and QS 60 5P and supposing that the government imposes an excise tax of $3 per unit collected from producers, find (a) the new equilibrium price and quantity and (b) how much of the tax is actually paid by consumers and how much falls on producers To work problem 22, you must do the following. Find the pre-tax equilibrium. The amount of the tax paid by consumers is the amount by which the price of the product goes up. You the pre-tax equilibrium to compare to the post-tax equilibrium Find the reverse supply function. A normal supply equation tells you what the quantity supplied is for any given price. You, however, need to add the excise tax, measured in dollars, to the cost, measured in dollars. So, you need to rewrite the supply equation algebraically so that is shows dollars (i.e., price) at each possible quantity supplied. This is called a reverse supply function Add the excise tax to the constant to get the reverse supply function with the tax included. Algebraically convert the reverse to the standard supply function (i.e., reverse the reverse supply function) Find the new equilibrium. The change in the price is the amount paid by the consumers. Any remaining amount of the tax is paid by the producer a. b. c. d. e.

Explanation / Answer

QD = 300 - 2.5P

QS = 60 + 5P

(a) In pre-tax equilibrium, QD = QS

300 - 2.5P = 60 + 5P

7.5P = 240

P = $32

Q = 60 + (5 x 32) = 60 + 160 = 220

(b) QS = 60 + 5P

5P = QS - 60

P = 0.2QS - 12

(c) After tax of $3, new level of P is:

P - 3 = 0.2QS - 12

P = 0.2QS - 9

(d) 0.2QS = P + 9

QS = 5P + 45

(e) Equating QD with after-tax QS,

300 - 2.5P = 5P + 45

7.5P = 255

P = $34 (Price paid by consumers)

Q = 300 - (2.5 x 34) = 300 - 85 = 215

Tax paid by consumers = $34 - $32 = $2

Tax paid by producers = $3 - $2 = $1

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